FlSH CAGESYSTEM EXPERIMENTALHYDRODYNAMICSTIJDYOFANOVELGLOBE-SHAPEDSUBMERSmLE

EXPERIMENTAL HYDRODYNAMICSTIJDY OF A NOVEL GLOBE-SHAPEDSUBME RSm LE FlSH CAGE SYSTE M

BY

~WE NJIB2BENG, B. ENG.

A THESIS SOBMITTED TO TBE SCHOOLOir GRADUATE

STUDIES IN PARTIAL FULFILMENT OF THE REQUIRP.KEN'rS FORTBED~(;nEEOF

MASTER OF ENGINEERING

FACULTY OF ENGINEERING AND APPLIED SCIENCE MEMORIALUNIVERSITYOF HEWFOtnmLAND

OCTOBER, 1991

ST. JOHN'S HEWFOUNDLAND CANADA

11+.

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ABSTRACT

In order to meet the inc r e a s ing requi rement of farmin g fish in more exposed offshore sites , a novel gl ebe-shaped submersible fish ca g e system with two tensi onmoo ri ng lines has been proposed . Inno r ma l sea conditionsthe cage remains on the surface ; during storms the cagee-m be subme rg e dsome dis ta nc e below the water surfaceto reduce the waveforce s and motionsof theca g e; andhence reducethe forcesinthemoo ring system and thestress on the fer-nedfish.Since the proposed system is a qu ite new design concept , few theoret ical and experiment al results can be found to guide the pro t otype design.

To have a better unde rst an d ing of the hyd rody na mi c performance of the proposedsystem,qualitativeanalyseswere co nduc t e d and a seriesof resistancetests and mooredte s ts were ca r ri e d out with two globe-shaped ca g e models, one sphericaland the other geodesic, to study the re s i s t anc e forces of the cages in currents and the motionand mooring forcere s pons e s ofth e cage system inwave s.In the resi stance tests , three orientations of the cage axle to the cur r ent directionwerete s t e d. In the moored tests, threesubme r ge d positionsandthr e e orientat ionsweretestedand the effects of pre tensionand axial stiffne s s ofthe mooring lines were

11

investigated in bothregularwaves and irregularwave s .

The study shows that the relationship bee v ee n the curre nt vel ocit y and the eee ciea ne resistance force ca n be interpolated very well witha qu a d r a tic equation regressed from the test results . Provided theRe ynol ds numbe r s of the cageelements are stillwithin the range of subcriti c alflow regime,the regressedequationcan alsobe used to extrapolate theres ista nce forceouts idetheReynoldsnumber range tested.

The st Ud y alsosho....s that theme t hodofSUbmerging th e ca g e below the water surface toreduce the mot i ons of thecage and thefo r c e sin the mooringsystemisvery effect i ve in deep water waves, but becomes le s s and less effective in intermediatewaterwaves.The pretensionof themoori nglines has little effect on the dynamic mooring force and motion respo ns es of thecage system as long as the mooring 1ine s do not go slack. The stiffness of the mooring line s has a significanteffect on the responses of mooring force, he a ve androl l ,buthaslit t l e effect on the responses of surge and swa y. When the cage is perpendicUlar to the wavefront, the vertical displaceme ntand mooringfor ce on one side of the ca g e maybe significant lylarger thanthose onthe ot herside becauseof the phase difference between the heave and roll motions of the cage.

iii

ACKNOWLEDGEMENTS

First of all, I would like to thankDr..J.H. A.ll e n for hi s excellent sup ervision an d guidance through out my who le study andthe supporthe pz-cvided all the time.

I"'a u l d also li k e to thank Dr.C.A.Sharpe,th e Assoc ia te Dean of theSc h o o l of GraduateStudies; Dr.G.R.Peters, the Dean of Faculty of Engineering and Or. T.R. Ch a r i , the Associate Deanof Faculty of Engineering for the financial aids of Gradua teFellowshipandTeaching Assistantships wh i c h ma d e this :;tudy possible .

Fur thermo re, I wish to say special thank you to Or. D.B. Mugge rid ge, the Di r e c t or of Ocean I::ng i ne e ri ng Research Centre for our long discussionswhich pr ovedto be ve ryhelpfu l; and toMr.L. Li tt leandMr.A. Kuczora of the Ocea n Enginee ri ng Re sea rch Centre fo r thei r patie nc e and inva luabl e ass i stanc e all the time dur i ng the experime nt.

Finally, I wish to thankmy parents fo r their rcve and enc o urage me nt.

Iv

CONTE!''TS

ABSTRACT... ... .•• •• • •..•••• •• ••. ••••••••.• ••••••••.. 1i

1<CQ01rL EDGEMENT8 •••• •••••• ••••••• •• • •• •••••••••• ••••• • iv LISTorTABL ES •• • • • • ••••• •• •• ••••• ••• •••• •••••••••••••vi i i LI S TorPIGURES ••••••• •••• •• •••••• •••••• • •••••• ••••••• ix DEPI NI TIONor SYMIIOL8DBED••••••••••••••••••• ••• • ••••• xvi 1 INTRODUCTION. ••• •• •••••••• •• • ••••• •• •••••••••••• •• 2 REVIElf OF LITER.1oTtJRE•••• • •••••.•••• ••• • • ••••• •• ••• • 10 3 THEORE TICAL BACKGROUND ••• •••••••••••• • •• • •.••• . • ••• 15 3.1 variat i on of WaveMotion....ith Otlpt hbelow Water Surf aceand its Effect on Sub mer sibleFishCage 15 ).2 Motionand Moor ing Force Re s po ns esofthe Moored Cage toWave Act i on . . ... ... .. ... ... .. 2]

3.2.1 Motionresponse . ... .... .... ... . . ... 23

3.2.2Moor ing force re s pon s e . .•. ... ... ... 32

3.3 Hyd rauli cModell ing... ...•.•. ...• .•• 34

3.3.1Resistancetests..•.. .••.•• ...•• ..•..•... 35

3.3 . 2 Mooredtest s . ... .. .. ... •.. . ... •. 40

3. 3.3Selection o! a propt!rmodel ne t •.. ...•.. . 41

.. EXPERIMENTALSTUDY...••••••• • •••••• ••••• ••••••• •••• 45 4.1Test Facil i ty andModel s .•... ••...••....•...••. 45

4.1.1Wave/towtank...•...•.•.•..• ...•.•.... 45

4. 1.2 spneric a l and geodesic models... -17 4.1.3Mod e l net.. .. •. .. .... . .. ... . ... .,. -19

4.1.4 Moo ringsystem 51

4.2 Resist a nce Test s . .. . . .. .. 52 4.2.1 Experime ntalar rang ement.. .. ... ... 5?

4.2 .2 Instrume nt ation andda taacquisition . .. .. 5-1 4.:2.3Experi mentalproc e d ure. ... .. . ... 56 4. 2.4 Method of data anal ysis .... ... 57

4.3xc oeedTests S9

4.3.1Exp erimentalar r a ng e me nt.. ... . .. S9 4.3. 2Ins tr u ment at i o n and dat a acq u i s itio n ... 60 4.3.3 Experime ntal procedure. ... . .. . . ... ... 6S

4.3. 4Method of data analys i s 68

5 E.lPERIMENTALRESCtTS AND DISCUSSIONS.. ••••••••.••• 72 5.1 ResistanceTests . ... .. .. . . ... 72 5.1.1Resistance forcesof themod e ls ... ... 72 :

.L1.2 Applicationof themodel te st resu lts to prototyp e ... . . . ..•.... . ... . ... . . . 81 5.2 MooredTe s t s .... .... .. . ... ... .. . ... 88

5.2. 1 Motion respon ses 91

5.2 .2Mooring fo r c e respo ns e s.. . ... .. ... . U8 5.2.3 Application of the mod e l test re su l t s to

prototype ... . . . .... . .•. .. .. . . .. ...•. ... 1)9

, CONCLUS ION S.. . .. . . ... ..•.•... . ... . . .... ...•• 142

vi

7 RE1UEHCES.. .... ... ... . ... .. .. .. 148

APPENDICES. . ... ... 150 A Resistance Force !'of the models ... .... 150 B Me a sure d Resul ts of the Re si s t a nc eTest s... . 163 C Mot i o n and Moo ri ng Force Res po nsesot:the

sphericalca g eHod e l ... ... ... .. .. . . . .... . .. . . 175 o Mo t i on and Moor i ngFor ce Respons es ofthe

Ge ode s i cCage Mod e l .. . . .... .... .. .... . . .. 192

vii

LISTOF TABLES

Table3.1-wave peri odrangescorrespondin gto deep, Lnt.e r me diate and shallow...ater ....aves n Tabl e 3.2-Scale fact-ors based on Reynoldslaw... .. 3&

Table J.3-Scale factorsbas ed on Froude rev 42 Tabl e4.1-Param e te rsof the sphericalC3<:1e model 50 Table 4.2 -Pa r amoi! t er s of the geodesiccage model ..., 50 Ta bl e4.3-Wave frequenciesus e dinregular wave tests

and correspond ing ave periodsformodeland

prototype 65

Table5.1 - Reynoldsnumber ranges of modelte s t ing _.,. . 79 Ta bl e 5.2-Compa r i s on of resistance forcesIn different

orientat ions.... ... ... . ... 81 Tabl e 5.J- Example of correction tee t ers Kcfor

resista nceforce calculat ionsof spherica l and geode s i c frames.. ... ... ... 86

viii

LISfOF FIGURES

figure 1.1 - Spherical cagein fullysu bme r .;e d posit ion . Figure 1.2 - Geodesic cage in fully sUbll',ergedposition • Figure 1.3 - Geodesic cagein operational posi tion.. . . . Figure3.1- Definitionsketch fora progressivewave .. 15 Figure 3.2- Var i ati on of particleorbitsand kinematics

with depthby linearthe o r y. . ... ... . ... 20 fiqure J.J- Ratio of kinetic energy atsId to kinetic

energyat sId "1.0 (water surface) 21 FigureJ.4- Percent kineticen e r g y cuncentratedabove

elevationsId... .. .. ... ... .. . .. .. . . 21 Figure 3.5- Six degrees of motion of the cage •• ... .••• 24 Figure J.6 - Co- Reinteraction.. •... ... ... . ... .. . . 38 Fi g ur e. 4.1- Elevationand plan vi ewof the wave/towtank46 Figure-4.2 - spher i cal model.... ... • ... 47 Figure 4.3 - Floatsof the models. .... ... . ... .... 48 Figure 4.4 - Experimenta l arrangem('nt ofthere s i sta nc e

t,ests 53

Figure 4.5- Instrume ntati o nand data recording system ofthere s i s t a nc e tests... . . . .... .... . . ... 55 Figure 4.6- Exper imen talarrangementof themooredtests 51 Figure 4.7 - Ins tr ume ntati onand datarecordi ngsy&tem

of themoored tests ..•.. . . . •... ....• . • •. .. 52 Figure4.8- Mode l subme r ge d posit ionsduri ngte st ing. . 65 Figure 4.9- orie nt a tio ns ofth e mode l duringtesting.. 57 Fi gure 4.10 - Ge odesic mod e l inmidd le pos i t ionand

parallelorien t a tion. ... .. ... .. .. 67

ix

Figure 5.1 • Resistance force of the sphe r icaL fr ame with ne t . . ... ... ... ... ... . 74 Figure5.2 - Resistancefo rce of thespherica l fr a me

without ne t .. . ... .... .. ... .. ... 74 Figu r e 5.3 - Re s i s t a nc e forceof the neton the spher icaL

fra me... 75

Figure5.4 - Resistanc e:forceof thege od e si c frame with net... ... .... . .... .. .. .. . . .... . . ... 75 Figure5.5 - Resistancefo r c e of the geodes ic frame

without net .... ... ... ... ... 76 Figure 5.6- aesree a nce ror ce ofthe net on the geodesic

frame. .. .. . .... .. ... .... 76 Figure 5.7 - Resistanceforce of the mod eL nee teste d on

the1.0 mx1.0mmodelhQldinl:lframe... Figure 5.8- Resistance forceof the fLoat . Figure5.9 - compar i s on betweenhea ve respons es of two

ori7n~at ions: spherical mode L,sur fa c e

pos.1.t.1.on . . 93

Figure5.10- comparison between heave ees ponsesoftwo orientations: spherica l wodek, mi dd le posit ion... .. .... . .. .. 93 Figure5. 11- cceperdacn between heave responsesof two

orientations: spherical model , bottom

position... .. .. 94

Figure 5.12 - comparisonbetwe e n surge ofpa r a lle l orientationand sway of perpendicular orientation: sphericalmodel,surface

position. .. . 94

Figure5.13 -Comparison between surge of parallel orientationand sway of pe r pe nd icu l a r orientation: sph.ericalmodel, midd le position.. . ... ... 95 Fig ur e 5.14- Comparisonbetween surge of parallel

orie ntationand sway of perpendicu lar orientation: spherical model,bottom

position. .. ....•.. . 95

Figu r e5. '.5- Compari s on be t wee nhe ave resp o nsesof two ori e ntat i ons : geod esicmodel,sucface pOlSit i on ....•.... ... . •... • ... 96 Figure5.16- Comparis o nbe tweenbeeve re s po nse s of two

orientati o ns: geodesicmodel ,middle po sition... . . ...• .. ... 96 Figu re 5. 1 7- compariso nbetween hea verespo ns esof two

or i e nt ations: geodesicmode l, bottom pos ition.... . ... . .. ... . . ... . 97 Fi g ur e 5.18- Compariso n betweensurg eof paralle l

orien ta ti o n andSWi:.Yat perpend ic ular orienta tio n: geodes i cmod el,surface

pos it i on... . .. .. 97

f'i g u_~c$.19- com p a~' isonbetweensur qe 01:parall el orientationand sway of'perpendicular orientat i on: geodesicmod e l,mi ddl e pos ition. .... .... .. . ...• 98 Figur e5.20- Comj,oari s onbe t wee n surge of pa r all e l

or ie nt ationand sway of perpe ndic ular ori entation:geodes i cmode l ,bottom po siti on... ...•....•... •... ... ..•.. .. 98 Figure 5.21- Surgeresponse s indif fere n t SUbme rged

pos itions:sphe r icalmodel, paralle l or ient a tion.•. ...••.••• ••.•... ... .. 103 Fig ure 5.22• Heavere s po nses in dit f ere nt SUbme rged

pos it i ons: spheri cal model, paralle l orientat ion...• .. ..•.•.. . . • .... ..•••••. 103 Figure 5. 23- Surqere spo nses indifferentsubillerge d

po sitio ns:geodesic mod el, para llel orientat i on... •.... ...•.• ...•... .. 104 Figu r e 5.24- aeaverespons e s indif fere nt sUbme r ge d

posit io ns:geo d esicmode l , parallel or ient a tio n•• .• .• ..• • •• ••••••••. ...•... 104 Fi gur e 5.25- Sur ge re ep c nses.in di fferent SUbme r ge d

pos i ti ons:geodesic model , para l lel orientation ,withst it fer moo ri ng lines •. 105 Fig ur e 5.26- Heave re sponses in dif feren t sub merged

po s i t i on s:geo d e s i c mode l, pa ral le l orie ntation,withstiffer moor i ng lines•. 105

xi

Figure 5.27- Sway re sponses in diff erent sUbmerge d po si tions: sph e rica l mod el, perp e nd i c u lar orie ntati on.•... . ... ... .... 106 Figure5.28- Heavere sponses in d1ffet' e nt subme r ge d

posit i o ns:sph erica l model, perpendi cu lar or ienta t i on.. .... .. . .. ...•... . 106 Figu r e 5.2 9- Rollres pons esin diff e r ent submerged

posit ions:spherica l model,perpendic ula r

orientati on 107

Figu r e 5. JO- Sway respons es in diffe re n t eubmer qed po~iti o n ~: spherical mode l, perpend icu lar or tencat.Lc n .. .. ..•... . . ... ... . .. 107 Fi g ure 5.J1 - Heave resp onees indif fe r e ntsubme rg e d

positi o ns:geo desic model, pe r p endicular orien t a t io n... ... ... ... •... .. ... 108 Fi gure 5.J2- Roll respon ses in dif f e re n t subme rged

pos it i ons : geodes icmode l, perpend i c ular

orien t ation 108

Figure 5.JJ•He ave and s....ay responses indifferent submer ge dpos i ti on s:geo d e sic mode l , perpendicu lar or i e ntat ion, with stiffer moor i ng lin e s ... . .. .. •... 109 Fig u r e5.J4- Rollresponses indiffer entsubmerged

positi ons : geo des i c model, perpend i c ula r orientation,withst i f f e r mcor-Lnq lines .. 109 Fi g u r e5.J5- Effect of mool"inglinepretensionon heave

response :middle po s i tio n , parallel

orientation 1Ll

Fi g u r e5.J6 - Effectof moo ring line pretensi on onsu rg e response: midd l eposit ion, paral l el orie nt a tio n... . .. ... . ... ... ... 112 Fig ure 5. J7- Effect of moo ri ng line pretension on heave

res po ns e : bottompos ition. parall e l orientation ... .... •" 11J Fig u r e 5.J8- Effect ofmoo ri ng li nepretens io nonsurge

response:bot t.om pos ition, parallel orientation ..•... .••...•... •... ... 11J

xii

Figure 5.39- Effect ofmooringline stiffness on surge response:middleposition, paral lel orienti!l.tion.... ...•• •. .. •.. ... . •11 4 Figure5.40- Effectof mooring line stiffness on heave

response: middle position, parallel orientation .•...•••.•... ••... • .•••11 4 Figure 5.41- Effectof mooring linestiffnessonsurge

re s pon s e : bottom position, parallel orientation.•... •• •.••.•. •••...•... 115 Fi g ur e5.42- Effect of mooring linest i f~i" esson heave

re sp on s e : bottomposition, pClralle l orientation...•... . .... ... ... 115 Figure 5.43- Effectof mooringl ine sti ffnessonhe ave

andsway responses: middleposition, perpendicula r orientation •• •... ... .... . 116 Figure 5.44- Effe c t of mooring line stiffness onroll

re sp on s e:middleposition, per pend ic ula r orien tation.••... . •••..••. . . .•... . . . ... 116 Figure 5.45- Ef f e c t of mooringlinestiffnes son heave

andsway responses: bottomposition, perpendicularorien ta tion .... ..•.. . .•.. • •117 Figure 5.46- Effect of mooring linestiffnes,;on roll

response: bottompos i ti on . perpendicular orienta tion.•. ....•..• ...• •.. .•. .•.. .••.. 117 Fi g ure 5.47- Comparison among forceresponses of both

mooring lines in pa rallel ori e nta t i on , sea si de and leesidemooringlinesin perpe nd i c ula r orientatio n :spher icalmodel, su rfac eposi tion..•. .. ..• .•... .... •.•• •.. 121 Figure 5.48- Comparison among force responses of both

mooring linesin par a lle l orien tation, sea side and lee sidemooring li ne s in pe rpend icularorientatio n: spherical mode l, middl e pos i t i on ... •.•.. ... .•. ....••• 121 Figure5.49- Compar ison among forcerespon sesofbo t h

moo r ing linesinpa ralle l orie ntati on, sea sideand le e side mooring li ne sin perpe nd icular orie ntatio n : sphe rica lmodel, bottom pos i t i on .••. .•••• ..•• •..•... ... 122

xiii

Figure5.50- Comparison among forcere s p ons e s of both mooring lines in parallel orientation , sea sideand lee sidemooring lines in perpendicularorientat ion : geodesi c mode l, surfac e posit i on... ... ... ... 122 Figure5.51 - Comparisonamong for c e responses of both

mo oring lines inpa r a lle l orie ntation , sea side and lee side mooring lines in perpendicu larorientation : geod e sic mode l,

midd le pos it ion 123

Fig ure5.52 ~comparison among force responses of both moori ng lines in parallel or ientat ion , sea side and lee side mooring li nes in perpendicular ori e nt a t io n : geod e s i c model, bottom pos iti on .. .. ...•... . .... 12 3 Fig ure 5.5 3 - Effectof phase difference betweenhe a ve

and roll on vertical displacementsat the ends of sea sideand lee side mooring

lines 124

Figure5.54- Force responsesof both mooring lines in differentSUbme r ge d posit ions: spherical

model, parallel orienta tion 13 1

Figure 5. 55- Force responsesof both mooring lines in different submerged posi tions: geodesic mod e l, parallel or i e nt a ti o n 131 Figure 5.56- Force responses of both mooring line s in

different SUbmergedposit ions :geodesic model, parallelorientation, with stiffer mooring lines ... . .. .. .... . . .. .•.,... 132 Figure5.5 7- Force responsesof seaside moori ngline

in differentSUbmerged positions :spheri cal model, perpendiCUlar orientation 132 Figure5.5 8- Force responsesof lee side mooring line

in differentsubmerged positi ons:spherical model , perpendicu larorientation 133 Figure 5.59- Forceresponses of seaside mooringline

in different submerged positions:geodesic model, perpendicu larorientation 133

xiv

Figure 5.60- Forc e responses of leesi de mooring li ne in differe n t submerged positions:geodesic model, perpe ndicu laroriencation 134 Figure 5.61 - Force respo n s es of se a si de and lee side

mooring linesin differentSUbmerged pos it i o ns: qe ades Lc model,perpendicular orientation, with stiffermooring lines .. 134 Figure 5.62 - Ef f ectof mooring line pretensionon force

res pon s es of both moor inglines:middle position, parallel cr IencecIon 135 Fi gur e 5.63 - Eff ect of mooring linepre t en s i on on force

responsesof both moori ng lines: bottom pos i t i o n,pa r a lle l orientation 135 Figure 5.64 - Effectof mooring line stiff nesson force

responses of bothmooring lines:middle position ,para llelorientat io n 136 Figur e 5.65 - Effect of mooring line stiffnes sonforce

resp onseof se a si demoor ing line:mi ddl e positi on, perpe nd i c ular orienta tion 136 Figure 5.66 - Effect of mooringline stiffnesson force

respo nse of lee sidemoo ri ng li nl!!:mi ddl e pos iti o n,perpend i cul ar orien t a tion 137 Figure5.67- Eff e c t of mooringline stiffnes son force

res pon s e s of bot hmoori ng lines:bot t om pos it ion ,paralle l orienta t i o,'l 137 Figure 5.68 - Eff ec t of mo o ri ng linestif f ne s s onforce

res pon s e s of seaside mooring line: bottom positio n ,per pen d icula r or i e ntat i on .. •... 138 Figure 5.69 - Effect of mooring line st i ffn e ss on force

respon s e of lee side mooring li ne:bo t t om pos iti o n,pe r pE'i nd i c ul ar or ienta tion 138

i i

,I

]

l

j

1

symbo l A B C C, C,o

f F F, F, Fr d

g H H{f) I I, k Kx,

K.

K.

1

m M RAO Re s 5, 5,!f) Sl"f{f) 5WL t T T, U v V

DEFlNfnON OF SnmOLS USED

Oe s erip tion

Amplitudeor se miax i s inx direction Semi axis inz di rect i on

Damping coef! icient Drag coe ffi cie nt of cylinde r Res i s tance force coe t ! icie n t Di a me t e r ofcyli nde r Wavefrequ ency(=lIT) Force

Dyna mic moor ingforce

Re s i s t a nc e forc e obtai ne dfro mmode l tes t Froude number

Wate rdepth or distanc e between the ce nt res of two floatation cha mba rs (a lso distance betwe e n two mooring line s)

Gr a vityac c eleration Wave height

Fre que n c y transferfurrc t.L cn Momentof iner tia Addedmomentof in e r tia

Wave numberor con s ta n t regr es sed from ser ies of res istancetests

Ax i al spri nq consta nt of mooring line Cor r e c t i on!a : tor

spr i ng con s t a ntof moo r ing syste m Hydrostatic restor i ngforcecoeff i cient Length of tens i onmooring line or length of wave tank

Lengthor wave le ng t h Mass of cage Addedmass of cage Response Amplitude Ope r a t o r Reynolds number

Elevation fromoc ean floor or cagemo t ion Sectionarea of floatationcha mbe r in waterline Spectraldensityof incidentwave

spectral de nsityof respcnse Still water level time

Waveperiodor pre t e ns ion inmoo ri ngline Natural oscillat i ngperiod of wavetank Horizontal water particleve l oc ity Ve r t i cal water parti clevelocity Currentvelocity

xv i

symbol Description Hori2:ontalcoordinate Transverse coordinate

Ve r t i ca l coordi nateor ins t antaneous heavemoti on of cage

~ Instantaneous rol laee Ien ofcage III Phase angle of wave force

III Phase anglebe t we e nmo tion response andwavefor ce ), Hodel scale t-prototype value /model val ue)

Angularwave frequency

r-

Ki ne maticviscosit y Densityofwater

Angle between cyli nderelementand cur rent direct i on Hor izontalwaterpartic l edLsplaceaent;

3.1415 9

SUbs c ri pt s prototype model

xvii

1 INTRODUcnON

With th e de cr e a s e of fish stocks inoceans becauseof ove r fi s h i ng in offshorewate r s , aqua c u l t ur e has oec cee mo re and more impor t ant and is one of the wor ld '5 rapid growth resource indu s t r i e s amongWes tern na t ions. The us e of cages is felt to be the mos t econom ically fea sible method of in te nsi v e ly re a r i ng fi s hsuch as salmoni ds , yellowtail and grou pe r in marine vaeece , and ca n be a comparatively pr o f ita b l e means of produci ng ot h e r species (Beveri d g e,1987 ).

Thereare fourbasi ctypes of fishca ge: fixed , floa ting, sub mer s i b l e and submerged (Beve r i dge, 1987). Floa ting cages ar e by far the most widelyused and resea r ch ha s be e ncarrie d out mainly on this type of cage. Wi th the incr e a sinq requirement of farming fi s h in more exposed offshore sites , mo r e and more at t ent i o n willbe focused onSUbmers i ble cages.

The advantageof thistypeof cageisthatit s pos i t i on in the wa t e r columncan be adjustedtotake advantage of prevailing environmental condit ions . In normal cond i tio ns the cage re ma in s on the sur:face; dur ing storms the ca g e ca n be SUb me r g e d below the water surface toreduce thewaveforces and motionsof the cage andhe nce the stre s s on the farmed fish. The ca g e can alsobe submerged to avoid super coo led surf acewater andsurface ice damage during wi nter periOdS,

and toavo i d exceptiona 1.toxic plankton blo oms inthesur f a ce water layer whichmay cause catastropllicloss of f ish. Upto now, few submersible cages havebeen bu il tandtes t edand few resear chpapers can be found .

The proposed qlobe·shaped submersible fishcage system and two kinds of cage frames whi chare studied in this thes i s are shownin Fiqures ~.1, 1.2and 1.3. Fi gur e 1.1 shows the spheri cal cage and Figure1.. 2showsthe geOdes i c cage ina fully subme r ged position.Figure 1.3sh o ws thegeod e sic cage in the normal operational pos ition. The diameters of the prototype cages would be about 12 a, The spherica l cage cons i s t s of 8 halfbows and t ....o bo.... reinforcements(notshown in theFig u r e) . The geodesic cage consistsof short barsand join t elements . Therefore, the geodesic is much. easier to manu f a ctu r e, transport and assemble, andhas a strongercage structure than the sphericalcage, but it mayalso have larger resistance forcesin currents.Both cageshav e an axleinthe middle of the cage ;,Ihlch can also be used as a foodfeeder.

For t:he proposed cage system. the cagecan be raised or submerged along the cables by adjusting the buoyancy of the floa t a t i o n chambe r s . The operational positionof the cage system is when the axle of the cage isabo u t 1/3 diameter belowthe water surface(thismay var y with tidal level ). The

FrLL YS U B\I ERGED

SlRFlC!FlOU

ClBt!

FlOlTllIOS ei.!iBER-

COUlfERIElGi1,

\

PEill\[~I .l~OR ~>""' __ -"-~/J I'

PiquU 1.1-Spheri cal ca g e in full y submerged posit ion

FGLLY S UBYERGED

"rustRf.ICE mmlf.lOlT

1l.0ATITIOl CBlIBEi\

roUllE11!1CHl

CEOOESICCICI

riqure 1. 2- Geodesiccage intUllysubme rge dpositio n

21:1 SUBYERGED

PERWm ANCHOi

1

Figure 1.3- Geodesiccage in operational::;Jositioll

cage can be loweredbelow the water surface duringstorm and winter conditions , and raised so that the axle isnea r the water surface for servicing.In the ser vicingposit i on, the fl oatationchambers can be used as work ing platforms, about half of the cage is exposed to the air and the cageca n be ro tated about its axle.Therefore,th e inspection, repai rand exchange of cage net can be carried out easily during continuousoperationwithoutremovingthe fish from the ca ge.

Also the problemof net-f ouling bymarine organisms can be greatly reducedand practic ally eliminatedby rotat ing the cage regUlarly andexposingto the airanymarinegrowth which hasocc u rre d . Havingdri e d , this gr owt h will talloff the net.

Compared to the conventional cage system, the globe- shaped fish cage also has the followingadvantages.The shape of the cage otters the largest volume tosurface ratio and very high structural strength . Becausethe net issupp o r t ed throughout the surface by the cage frame, netde f o rmat i C'nin current is sm&ll and the cage volume doe s not change with cur r e nt velocity.Also the same net "'ill provide protect i on against bird predati on . It has alsobeen foundthat a round cage would reduce stress on the farmed fish., a leading cause of di s e a s e and mortality in aquaculture . Certain fish in a group tend to be aggressive and cause stress byfo r cing groups into a herd.In a roundcage, aggressive fish could not easily

finda terri toryto dominate and the speciescouldqr ov with le s s stress (Norman, 1991 ).

A cage at sea wi l l experience the act i ons of winds , currentsand waves. For <1submersible ca g e, win d force s may not be so important,but currentfor c es and wa ve forc e s are ',-e ryimportant in designingdosa f e cage structureandmoo ring system. Under wave action the cage will have amotionof six degrees of freedom. The motion of the cage will affe ct the growth of the fi s h ins ide the cage and the dynamic forc e respons esin themooring system. The r e fo r e , an estimation of the static and dynamic responses of the cage system to environmental forces must be known to design a sa f e and eff i c ientcage systeM.

sinceth e proposed prototype ca g esys t e mis aquite new concept,few theoretical and exper ime nta lresultsor researc h papers canbe foundtoguidethe prototype desig n.The complex st ru c tur e and the multi-degree of freedomof the cage system means th at the interaction be t we e n the structure, ne t s and moor ings is not readily determined by ma t hema t i c a l calcula t i on. In orderto have a better unde rs t an d i ng of the hydrOdynamicperformance ofthe propc,sed pr ot o t ypecage system and providesome usef'llinfo rma t i on for the prototypedesign, a seri es of model tests were carried out on two kinds of

globe-shaped fish cages, spherical and geodesic cages. The purposes of the tests were to study the resistance forcesof the cages in currents when the cages were totallysubmerged below the water surface, to investigatethe mooring forceand motion responses of the cage system to waves in different SUbmerged positions and orientations, and to cbce rve the effects ofpretension and axial stiffness of themooring lines on the motion and mooring force responses.

Inadd i tionto being used as a guide to r the prototype design , the model t~st results can also be us e d in fur t h e r stages of research in the establishment, verification and calibrationof a numericalmodel. The numerica lmodel intur n may offer a general tool for a variety of purposes of the prototypedesign such as altering dimensions, mass, moment of inertia, net, stiffnessof mooring lines ,floatation chamber geometry, submerged depth of the cage and water depthof the si t e, as well as optimizing design parametersot th'"system.

In vi e w of the many assumptions and simplif icati on s made in co ns t r uc t ing a numerical model, feed back from model tests is ext r e me l y impo r t a nt in validating the result,,;. Therefore, model tests are necessary.

In this thesis, theoretica l background and qualitative analyses of the problem presented, experimental

met.hodo l ogy is de s cr i bed,and enemodel t.est resultsand their applica tion in t.he pro totype des ign are presented and analyze d. When theexper i me nt s were conducted, there was no detailed pro to t ype dea.iqn, so t.his Wa s only a pri mar y expe rime ntal researchaimingat havinga betterunderstand ing ofthe re sp on s e s of thepro pose dca ge and mooring systemto enviro nmental torces and providing inf orma tio n tor the pro t otype de sig n and the establish ment and verificationof nume ric al mode l s. All the parame t ers and tes t res utcs pr esented in thi s thesisarereferred to the model s .

2 REVIEW OF LITERATIJRE

Be causeoffshore cage aquacult ure isa ne wlyde velo p ed industry, not much published lit e r atu r eonhyd r odyna mic s of fishcage systems....as found.Mostof the research is focused on the conventional squa re shape sur face co llar floa ti ng se a - c a ge with conve ntio na l mooring sys tem ; few, or no, pubjIehad research papers ar e avail a b l e on globe- s hap e d subme rs ib l eca g e system at the present stage.

Beverid ge (198 7 ) pUblished a book on cage aquaculture which is asynt hes i s of available inf o r ma t i o n oncages and cage equecureuea,This book givesus a generalpicture of the developmentof cageculture,diversityof cage typesand their advantages and disadvantages, env ironmenta l forces onca ge s and the simple method to estimate these forces, cage construction , and the bio l ogical considerati ons in cage aquacUlture.Accordingto thisbook , there isev ide nc e that the coef fici e nt s of drag of the netting materials are independent of current velocity over the range typ ically encountered atfishfarm site s (0. 33 - 1.87m/s ).The author also describedsubmersiblecage designsas a strategy against stormy conditionsandprob l ems ....ith ice.

Rudi at al (19 8 8) gave a general description of a '0

preliminary study of the v Lnd fo rce, curre nt force , wave ind uc ed cage motions andmoo r inganalyses of a conve n t io nal floa t ingca gesyste m. Predicti o n ofcur ren t fo r ceis ba sedon norma l emp i r i c a l methods withthefo1101o'1ng fo rmula tion:

12.1)

wh.ere Fis th.e drag force ,pis th.edensityof water, Vis th.e currentvelocity , CDisthe totaldragcoeff ic i ent , A is the projected area, Co;, At is the loc a l drag coe f fi c ient and projectedarea of elementNo. i and n is the total number of elements of the structure. Quasi - s t a t i c method is us e d in mooring analysi s, taking no account of the iner tia or hydrodynam ic loadson themoo ring line. Mo tion amplitude is calculated by determiningfirst th e wave force act i ng on a fixe d cage and then the. forces acting on the cage when it is forced to oscillate in calmwater withthe sameperiod of oscillation as the wave and with uni t mot i o n amplitude . However, for a globe-shaped cage sys t em whi c h ha s a more complicatedshape,these methods canonly beuse d tointe r pr e t the ex peri me nt a lre sult s or prov idesomequali tativeresul ts, butitis difficu ltto use themtopr ov id esomequa ntita tive resu l t s.

Aarsnes et al (199 0) develope d ame t ho d for calculation of current forces on cagenet whichwasfo un d to reproduce the

11

currentfor c e sfrom the model tes t swl t nl n the range0.9- 1.3 ti mesthelIe a su r e d force s.The dr ag andlift coe f fi ci en t for thecurrentforces act i ng ona planarnet pane lweretreat ed as a fun c tionof thehea ding betweenthe current and the net plane and the solidity rat i o of the net. The dec r ea s e of current velocity at downs t r e a m ne t pa nel s cau s e d by the shieldingeffects of the upstream ne t panel s wa s taken int o account inthe calculations . Because this me t hodwa s deri ve d from the tests of planar net panel, it see mstha t it can not be used directly to ca lcul atethecu r r e nt. forces of the ne t

OTIa globe-shaped fish cage because theinteraction betwe e n ne t segments Would be different.

Model testing of a square-shape Wave master cage sys t e m wa s ca r rie d out byWhi ttaker et al (1990 ) to ee e eratne the movementsandmoor ingfor c e responsesofthecagesystem unde r waveacti on . In the tests, theFrou d e numbe r was ensured to bethe sama inbot h the model andtheprototype.Conside ra bl e carewa stak e n to select a netmateria l WhIch cou l d ac curate l y reproduce the motion s of the prototype. Drag tests were performed onacar i e s of the samplu of nots inilltowingta nk . Anet wi t h a drag force/velocitychar acte risticapproxImately 1.5 ti mes tha t at a clean prot o t ype net WillS chosen for the model in order torepre s e nt the prese nceat a heavily fouled net. This is a appropriate method to se l e c t a model ne t

12

material, but the comp a rison of the forc e / ve l oc i ty characterist icsof the prototype and mode l nets shou ld be in dif f e r en t velocit y rangesscaled accord ingto t'.)SFr ou delaw.

Ins tr umentatio n, data analys i s techn iqu e s and test resultsof ir re g ula r wavete s ts onse vera l model and prototype se a -ca ge s were prov i ded by Linf oo t and Hall (19 8 6). It va s fou nd that thepresenceof thenet signific a nt lyredu ced the he ave and pi tch mo ti o nre s ponses of thecages at resonance freq ue ncies.The r e f o re, the net us ed in thecage modeltests sho u l d beca r e f ull y selected.inorderthat the model te stsca n represent the pr ot ot ypepr o p e r ly.Linf ootandHa l l (1989)als o conducted modeltestingof si ngle-poi nt moori ngsystem s for se a-c a ge flotilla s at a scale of 1:16. Fibro us nylon netof 5 DUD knot-to-kn otwas us ed to si mul atea mod e r a t e lyfou led twine net. Obv i OUSly, thi sisnot amode l net sc aleddown fr om th e prototype net accord ingto th e mode l scal e, but howthe mod e l net waschosen was not pre s en tedin the i r pape r.

Most fish will suff e r when ke pt in waters with temperaturesnear 0⁰C. To avoid thelo w- tem pe r a t e problems and problems arising fr...dlenvironmental loa ds inthesur f ac e region ,an underwater offshor e sea cage has bee n devel ope dto a pre-e ng ineering level in No rva y (Dahle et a L, 1989) . calc ula t i o ns show the cage willexperiencelessenviro nmen t al

13

forces when it is submerged below the water surface, but no experiment has been conducted to confirm these calculations .

Olt e da l et a1 (1988) developed a computer prog ram for simulation of thfl: responses to environmentalloads of compl e x floatingfish farms.The program does not comprise an exact solution of the complicated hydrodynamic problem relatedto floating fish cages. It represents only an engineering approach based on appr o xi ma t e methods to impro ve the computational method available for fish farms. The program output has to be verifiedby comparisons with known results as obtainedfrom model testing.Therefore, model testingplays a very important rolein the numericalmodelestablishmentof a fis h cage system.

14

3 TIIEORETICALBACKGROUND

].1vari a t io n of .ave Kotion with Depthbelow Watersu rf ac e andit s Effect OD Subm.rsibleFisbeag.

Oneof the majorco n s i d e r a tions of submersib lefish ceqc design is th at th e cage wo u l d be submerged bel owthewat e r su rfaceduring storms to reduce the wave forces and mot.Le ns of the cage and hence redu cetheforc esin the moo ri ngsys t e m and stress on the fa r me d fish . In or d e r to stud y the effecti venessof thismethod, li nearwave theory ca n be used to determinethevariationof wave motionwith distance below the water surface andits effect on a submersible fish cage.

A two-dimensional wave prop a gating in the di r e ct i on is defined in FigureJ.1 in which the var iou s symbol s used to characteri ze the gi ven. From lin e a r

. -

1 /":sr. _,LS::::7 <== _I

L..-. i:t

Fi gure3.1 - nerLnLtIc n sketch fora progre s s ive wave th e or y it is known that the amplitUdes of wa t e r particle veloc i ti e s . accelerations anddi s p lac e men t s ind uc e d by ....ave ac tio ninxandzdirec tionsare functionsof pos i tional on g the ....ate r column .

15

Theho r i z o nt a l water particleveloc ityand acceleratio n ar e w-ritten as (Cha k r a ba r t i, 1987 ):

u•.!!!!coshkscos(kx-wel

Tsinhkd (3.11

(3.2)

and theve rtic a l waterpa r t i c l e ve locityand accelerati onar e written as:

(3. 4)

whereTis th e waveperiod, Histhe waveheig ht ,k ,.2rr/ Lis the wave number , Lis the wave length, d1~the waterdepth , S ,. z+d is the elevat ionfromthe oceanfloo r, and !oJ '" 2fll't is the angu larfre qu e nc yof the wave .

Th ehorizont al andve r t i c al waterpa r tic le disp lacements , and II, are giv.n by

and

~.

.s

". ~ :t~ ~~cos

(3.5)

(3.11 Squaring and adding yields the water particletrajectory as

,.

..E·~.1

(J. '.

A1 a¹

in wh i ch

A-!!cos h ks _{(3.8 )}

2srnnkd

B.J!sinhks _{(3.' )}

2si nhkd

arethe semiaxes in xandz:direct ion s re spect i vely andar c measuresof the horizont a l andve r ticaldisplaceme nt sof the waterpa r tic l es.

Certa i n simp lificatio n s of the above equ a t i on s ca n be mad ede p endi ng onthe rat i o of thewa ter dept hdtothewave leng t hL. For de e pwa te r wave s , d/L~0.5, the ex pre ss i ons may be simplif iedby the following app r o xima ti ons

coshks=s~nhks _~u si nhkd s.lnhkd and tor shal lowwaterwaves, d/L<0.0 5

coshks...!...

sinhkd kd sinh ks-1•.!.

sinhkd d

(3.101

(3.11)

(3.12)

Thevariationsot partic leorbitsand vel oc ityamplitude s with depth below water surfacetorshal low, int e rme d i ate and

17

deep water waves ar e shown in Figure 3.2. Fo r deep water waves, the waterparticl emovementsproducedby waves decay exponentiallywith the depth below the water surface. At a de pt hof about Lf9 , the movementsar e approximately ha l ve d , andat Lf2 the movementswill decrease to about4\ of those at the surface.For shallowwate r waves,horizonta l movements al mo st do not decay with depth and the vert ical movements decrease appro x i ma t e l y line arly, so the horizontal pa rticle displacementnea r thebo t t om canstill be large. Notethat the maximum amplitudeof ve rti cal displacement(a t water surface ) of a water particle is equa l to the wave amplitude,Hf2,while the maximum ampli tudeof horizonta l displacement is equal to the waveamplitude fordeepwaterwavesand islarge r than the waveamplitudefor intermediateand shallow waterwaves.

In orde r to obtain a clearer idea of the possible adva ntagesin submergingthecage at a particUlardepthbe l o w the water surface, consider the kinetic energy distribution withina wave. Derive d from line ar wavetheory, the ratio of the ki neticenergy at any elevation "s" to thatat the mean wate r surfacewhe re5 .. d is givenin dimensionless formby Dean and Harleman(19 6 6 ) as

KE(sl'" coshks

KE(dl coshkd (7 .13 )

Thisrelationisplottedin Figure3.3 fo rd/L -0.05(s ha ll ow

18

water limit), 0.1, 0.2 , 0.3 ,0. 5 (deeF....ener- limit) , 0.7, and 0.9.Thisfigureshowsthat fo r deep waterwaves (d/ L~ 0.5 ) the ener gyis concentrated ne a r the surface ,withthede cre a s e of d/L in intermediat e wa t e r waves (0 . 05 <d/L<O.S ) the ene r g ybe g i n s tobe distributedto lowe r....ater,and eventually for shal low waterwaves(d/L s0.05 )the energy concentration is near lyuniform with depth. One furtherrela ti onShip Which maybemore helpful isthe percentageof kineticenergyabove any elevation.Thisis obtainedas (De a n and Harleman , 1966)

,

JU{S)as

-;- --x lO O%" [1-:i:~~~l^{dOO% (3.1.'}

IU{S )ds

This equationis plottedinFigure 3.4. It showsthat a cage indeepwaterwaves occupying onlya small relative portion of the dept h (say 20%)in the surface will inte ract witha significant portionof the kineticwave energy (e q ua l to or la r ge r than 7lt), when the cage is submergedsome distance be low thewater sur facethe kineticenergyencountered by the cage will be gr e a tlyreduced. It can also be found from this figure that a cage in sha llow water waves will encounter almost the same portionof kineticenergyat differentdepths alo ng the wat er column. Th e value of d/Lis a functionof wave per iod and wa t e r de p th of the site. Table 3.1 gives some examples of the wave pe r i od ranges correspondi ng to deep,

rs

1

E'h~"O' '!~

, I •~B

I .!!o.'

: . I , .0 ¥ U

,..,.'.. " ". :,,:;;:, {~I.I~~U :':.~ , ~,~

(b)INTE RMEDIATEOE PTH

io <t <!

(clSI-lALLQW WAfE R

f > k

Fiqu re 3.2 - Va r i a t i on of particle orbitsand ki nema t ic s with de pth by line a r theory (Cha krabarti , 1987)

' 0

100

. .

Fiqure 3.3 Ratio of kineti c en ergy at sId to kinet icenergyat sId""1.0 (water sur face)

f _••

! i '"

l ..

.

./0

Figure 3.4 - Percent kine t ic energy co nc e nt r a t e d above elevationsId

21

intenedi a t e and shallowve eee ....ave s fo r dif f e re nt wa t e r depths .

Table 3.1- Wa veperiodrange s corres pondingto deep, intermediate and shallow wa t e r ....aves

WaterDepth Wate r Wave Type

(m) Dee p Int e rme d i a t e Shal l ow T S1., 1.6<T<9.2 T?:9.2 '0 T6 3.1 5. 1<T<29.0 T229 . 0 '0 T6 6.2

,.,

from thediscus s ions abo ve it can be pred i c ted thatthe eecbcd of SUbme rgingtheca g e some dist a nc e belowthe....ate r sur f a c e to reduce thewa'/e forc es andmo t i ons of thecag e and hence reducetheforces i ....the moori ng system.... ill be very effective indeepwat erwaves andpart of the intermed iat e wt,ter wave s.wit hthe decreaseof d/Lthi s method will become te as and les s efh ctive ininterm ed i a te wate r ....avesandno t effectivein sh al lowwate r waves. Ther efo re,theef fec tivene s s of this me thod depends onthe water depthandwaveperiodof the si t e. Neverthele s s, subme r gingthe cage below the ....ater surf a c e can sti l l reduc etheve r tica l....av eactiononthecage

"

to some degre e inallth e cases.

3.2 Motion and Moor ingFore. R••pOb•••ot tb. HoqredCageto

.av.

3.2.1Mo tio n response

The moored cage of the proposed cage system may exper ience six degrees of motionunde r wa ve action as shown in Figure 3.5. The definitions of surge, sway, heave, yaw, pitch, and roll used inthis the s i s ar ewithrespect to the cage.The motionaLo nq a horizontal line perpendicularto thp- axle at: the cag e is termed as surge, the mot i on along the di r ect i o n of the axleof the cage is sway , and the vertical motion is heave. The angularmotion abo ut avertica laxis is calledyalol, the angu la r motion abo ut the axle ofthe cage is pitch, and the angular motion about a ho rizontal axis perpendic ula r to the axle of the cage is roll.

Under th eassumptionsofline ar wave, linear i zeddamping and no current,themotionof th e mooredcage in regularwaves can be de s cribed by a set of coupleddifterentia l equations

,

~⁽(!1Ijk+Mjj:)!lk+Cjk~k+^{(KRjJ:+KHjJ:)Sk] ..}Fjsin (we -tj ) j =1,2 ,...,6 (3•.15)

2J

I'

-''

' , - - " , fa,

- =::-3t3t:'Jn :rai.lce,

I' 'I-

:, .:

, ---.,

'~':""-: . 10)

'c,

Figur e 3.5- Sixdegrees of mot ion of the cage. (al Frontview, (b) Side view, (c) Top vie w.

whereIT\kis the mass matrixcont a i n ing the mass and momentof ine r t i aof the cage,~kisthe added mass ormome n tofinertia of the cage in directionj due toac c ele r at i o n in direction k, s_ is the cage motion in direct ion k, C.. is the damping coefficient of thecagein directionj dueto thecag emot i o n indi re c t i o nk, K1>lii; is the spring cons t.ent of the moor ing systemin di r e c t ionj due to the cage motionin direction k, K~Jl: is the hyd r os t a t i c restoring fo r c e coeff icient in direction j due to thecage motion in directionk , and Fjand '. are the amp lit ud e of

24

forc e or mo me nt and the

correspondingphaseangle in direction j.Unf ortun a t e ly, it is difficult to obtain the exact mathematicalsolutionsot:the coupled equations of motion. In order to il l ustr ate qualitativelYhow the parameters of the systemwouldaff e c t the motion and mooring Coree responses, it is assumedthat the sixdeg r e e s of motion of the cage are uncoupled.

The uncoupledequat.Lcne of cage motioncan besimpl i fied

j =1,2,...,6 (J.16) where~is the mass of the cage fo r j ...1,2,J and moment of ine rtia of the cage in direction j for j - 4,S,6, ~ is the added mass of the cage for j - 1,2,J and added moment of inertia forj- 4,5,6in direction j,Sj isthe cage motion in dire ction j, Cj is thedamping coefficient of the cage in di r e c tion j, K_RJand KMj are the hydrostatic restor i ng force coefficient and spr i ng constant of the ecce ing system in direction j, Fj and ej 1 are the amplit u d e of wave force or moment actingon the cagein directionj and the corresponding phase ang le to inciden t wave .The added mass or moment of inertiaM;andth edampingcoefficient Cjof the cage dependon the geome t ryof thesubmergedpartsof th e cage and the net, the directionof motion, and the fre que ncy of the inci d ent wave. The hyd rostat i c re s t oring force coef ficien t J(~i and

25

spri nq constant K"'i of the moo ring system depen d on the submer ged posi tion ofth.e cage, the di rectio nof motion and the axial st i f f ne s s of th e moor i nglin es.Thewav e exciting force amplitud e Fj and phas e angle ejl ar e functions of sUbmer ge dposi tion , geometry of the cage and net, direction of motion,and frequencyof the incide n t wa ve.

The soluti ons ofthe equations consis t of a transient part and a ste a dy- sta t e par t. Beca use of the exi s t ence of dampi ng , the tra ns i ent pa rt would disappea r aft er a few in itia l os cillat io ns followin gthe startof the motio n. Th.e st e a dy- s tate solutions areof signif i canc eandcan be writ ten

(3.17) where th e amplitUde of the motio nres p o nse is

I

~ r.ln j r.ln j

(3.18) and the phase angle betw een the mot ion resp onse and the exciting for ceis

26

Th eterm

1J. 201

is the damping tact o r indirect i o nj, and

IJ.211

is the natural (anqu l a rlfreque ncy oftheece Lenindirec tion j. When the frequenc i e sof the incid e n t wa vesare near the natural frequencyin dire c t i on j, resonance wil l happen and t;h e ca g e will have the largest motion respons e in thi s di re ction.At thispointtheda mpinq ha s a pro found effect on themot ion amplitude. Increasi ng theda mpi ng ofthe caqewi ll re du ce th e mot ionre spons e siqn iticantl y.However, at lo....er or hi ghe r fr e q uenc i es away fromthe na t uraI frequency the response will decr ease and tbe dampi nqha v e a neglig i ble effect .

Fr oDEqu a tions (J .lS) to(3.2 11 it can befoun dtha t the ma s s or momen t ot inerti a, the dampinq coe ffici ent, the sUbmer g e d pos ition ot th e cage, and the stif fn es sof the mooring lines may affe ct themot i on re s ponses of the cage sys t em. Some ot the influences ot these puameters are analy :tedbelowtor themoti o ns ofsurg e ,s....ay. heaveandro l l.

The mot ions of pitc h and yav would be very smal lfor thll

27

proposed cilge system and are no t inc l uded here. Inall the ana l yses , the eUe c tsof the su r face floa ts are negl ected because the i r sizes are mu ch sMal l erco mpare d tothos e of the fl oata tionchambers or th e cage andthe cage struc ture.

2 1.1 surge ~

For the motio ns of s'.1r qe and sway. the hydr osta tic re s to ri ngtor c ecoe f fici ent K. is eee e.Whenthe horiz ontal deflect i o nis much small e r tha n the length ot themooring l ine,the rest ori ng for ce fro m thetwomoo r ingl ine s canbe ap p roximatedas

(3.2 2)

SOthe mo oring spri ngcon s tant to r surgeand sway is

(3.23J

whe re T isthe pr eten sion ineach mooring Hne, ax isthe de flectio n of 5Urq.orswayand1isthelength of the te nsion moori ng lines. Then the na t ural frequency ot'the surqe ors ....ay motioncanbe cal culatod as

w_Il

"

r2"Ti"l

Th e re f o r e,the natura l frequenci esandhenc ethe motionsof Bur g. and swa.y are not sign i fican t l y influ en c ed by the

ae

stif f ness ofthe mooring lin e sbut ,rath er , they areaffe c t ed main ly bytheprete ns ionand lengthof the.oori ng lines,and also the mass and added ma ss of th e cage. Because the fr eq uen ci e softheincidentwaves maybe much la r ger thanthe nat ur al fr equenciesof surg e and sway, theef f ect of damping may bene g ligi bl e.

3 2 1 2He a ye

Forthe mot ionof hea ve, the hydrostat i crestor ingforce coe f fici e n t K.is mainl yca u sed bythebuoyancychan g eof the two floatat ion chamber s of the cage. Whenthe fl oat at ion chamb e rs areonth e wa tersu rface . K.ca n beapp roximated as

lJ·2 5)

wher e p is the density of water , gis the accele ration of gravi tyandS, is the sectio narea ofth e flo a t atio nchamb e r inthewa te rlin e. Whe nthe floatati onchalllber s are sUb4lerg&d bel o w thewa t e rsurface.K.is abou t zer o .The spri ng constant ofmooring syst e min heavemotion is

K,,"ZK lJ·261

whe re Kis theaxial spri ngconstantoftheindi vi dual mooring line.The natur alfre q u e ncy ofthe heave moti o n will be

f.I ,,~^{2(pgS, +Xl}

" m+ M

"

1:1·271

whe n the float ation chamber s of the cage ar e on tl',e water surface. and willbe

to)

~ r2K

n~m+H (3.211

when the floa t atio n chamb e r s aresubmerged below the wat er surface . cons e quent l y, thena t ur al fr eque nc y of the heave moti onwi llbec cee smaller andmainlydepend onth e stiffness of the mooringlinesand the ml59 of th e cage whe n the flOl t at ionchambers ofthe cIge ar e su bmergedbelowthe water su rface .Thestiffne s s ofthelIIoori ngli neswillinfluencethe responseof th eheaveact.Le nsig nific a ntly .with theincrease of stif fness ofthe mooringlin es,th e natural fre quency of the hea ve motionwi l l teccraela r ger andthe amplitude of the motion wi n become smaller .Th e pr e t e nsionof the mo oring li neshaslitt l e ef fec t on the heave motio nas long as the prete nsionis 1lI.rge enough to pr event themooring line s from sl ac ken ingof f , while the nas s of thecage will affe c t the na tural frequency and he nce the response of themo tion.

Because the frequenc ie softhe seavevesKlaybecl ose tothe na t ura l frequ en cyofheav e ,th e damp ingof thecage maybe importa n t indet ermi ningtheIImplit ude oftheheavemot ion.

Be c ause the distancebetwee nthe centre ofbuoyanc yand 30

the cent r e of gravity of the cage wil l be small in the pro pos edsystem.when the float a ti on ch aabe r s ofth e cage ar e on the wa te r surtace the hydros tatic rest orinq force coeffici e n tX.ofro l l can beappro xi ma t ely calcu la tedas

(J.291

whe re d is th e dist ance between the cent res of the two flo a t atio nchambers (a ndis alsothedistancebe tw eenthetwo moori ng l in es inthe propos edsystem) ,andwhen thefl oata ti on cha mbers areSUbmerg ed belowthe water surface Kit. is about ze ro . The spring consta nt K,..from the mooring systemis

KH-i Kdl (3.30)

whe r edisthe distan cebet 'io/een thetwo moo ring li nes. When the floatati onchambersoftheca g ear eonth ewa t er sur f a c e , the naturalfreq uen c y of rol lwi ll be

~. ' ^13.31)

whe r eI is the mome nt ofine rti aand IAisth e adde dmomen tof inertiaofthe ro ll mo ti on. When thetloata tio n ch ambe rs ar e SUb me r ge d, the natural fr equ e ncy will bec ome

(3 . 32 )

There for e, conc lusionssimi l a r to thoseee th e he ave motion

31

can be obt ained, sUbst i t u ting momen t or iner t ia for mass.

Also, the distancebet ween the two moo ri ng lines wi llaffect the na t u ral frequencyand theamplitude ofthe ro l lmotion.

22Moori ngfor c e response

Su p pose thewa ve for c e s acti ngon the mooring lines are negligible , the dynami c force xesp c n e e a inthe two mooring li ne s ofthe cage canbe esti ma t e dby thequ a si~ sta t i cmethod afterthemot i o n respons e s of the cageare known. The mo tions of the conne c ti ng poi nts of the mooring lines areus ed to predi ct the dynamic mooring forc a re sp onse s (Oo r tme rs sen, 198 6).The dyna mi c force re sp onses inthe mooring line sdepend on the ins t an tane o u s chang es of the cable length whi c h are affectedbythehor izontaland vertic al motion softhecage, and can becalcul a tedas

(3.331

where F,.. isthe dyna mic forc e inthe moor ingline , Kisthe axi a lspri ng cons t a ntof the moo ring li ne andtrol is the change of cableleng t h causedby thecage motions.

Assumingthehorizontalexcu rsions of sur ge and swayare small comparedto the le ngt h of the mooring 1in&5in the equilibri ulllpos it ion , the extens i onsof moo r in g l ines caused bysur ge and swaywillbe ver y small andthecont r ibut i onof

32

surge and sway to the dynamic force responses in the mooring lines will be negligible.When the cage is oriented with its axle parallel to the wavefront, the dynamic forces in the mooring lines will be mainlycaused by the heave motion ofthe cage and can be estimated for both lines as

wnee-e or.is the instantaneous heave motion of the cage.When the cage is oriented with its axle perpendicularor obliqu e tothe wavefront, the dyna mi c forcesin the mooring li n e s wil l be mai nlycaused by the combined effect of heave and roll. the force in the sea side mooring line can be approximated as

(3.35)

whererpis the instantaneous roll motion of the cage, and the force in the lee side mooring line can be estimated as

(3.361

In such case, the phase angle betweenheave and roll wil l be important in determining the dynamic force ineach mooring line.

Because the mooring force rasponses are mainly determined by the heave and roll motions of the cage, the parameters which affect the heave and roll responses will also affect the mooring force responses.The responses will be different when

"

the cag e is in difterent submerqe d posi'tions. Theseitt ness ot 'the mooring lines wi l l influence the responses siqnif icant ly .Al s o the massan d Ilomentof In~rtiaofth e cage will atfe c t the mooring forc e responses. Pretension in the moor i n glines will have lit't l eeffect on the mooring for c e responsesaslongasit is la r geenoughto preven t the mooring lines fr om. being slack.

3,3Bydraul.ioKod e Ulb9'

Small scal e mode l tests are III co nve n i ent means of predi c tingfull-scaleperf or manc e .Theirus e canhelptoavoid disas trous mistakesin prot ot y pe design. In orde r to pr edic t theperf or ma nceofthe prototypecage systembymeansofmod el tests, cer tain laws of similarit y mus t be observed. These lIode l lawspr ovide relationshipsbetweenvariablespertaining totheIlodel and the prototype,thusenabli ngmeasurementsof the model te s tstobeus ed to predict pr ototypevalues.

Inadd i tion to geometric simila rity, the model andthe proto type must alsoac h i eve dyn amic similarity. For thefis h cage tests tobe conducted, this me ans 'the Reynol ds number (t he ra tio ofvi scous forces toinertial forc e s)

Re

"'.!f

34

(3.37)

and the Froude number (t he rati o ofgrav i ta tional forceto ine r t i a l forces)

Fr=~

r.r.

must be the same in both the mode l and pr o to typ e , in whi c h V is a particular velocit y, L is a typical len gth of the structure and " is the kinemati c vi s cosityof the fluid.The Reynoldsnumberensuresthe similarity of thevi s c ousfo r c es , ....hi l e the Froude numbe r ens ure s the simila ri ty of the gravitat iona l force s. Unfor tuna tel y , in pract i c e such requ i re ments canno tbe me t. There f ore , specia lconsiderations must be take n int o accountac cording to thechara cte ris tic s of the te s t s.

J J 1 Resistanc;;eTes ts

Because the res istance te sts of the cage are to be conductedwith themode l s SUbmerged belowthe watersurface, no significant surface waves wi ll be created and the fre e surface effects axe ne g lig ible. Th e floWaroun da submerged objectisa totallyviscousphenomenon .Thedra g force on suc h a object isca us e d byfri ct ionalres i sta n ce and bypressure differences acrosstheobjec t , neither of wh i ch are re l at e d to gravitat ionaleffects (Sha r p,1981).The effe c t of Froud e numberis thenun impo r t a nt. Therefore, Reyn olds numbe r mus t

35

havethe sameva lu e s inthe modeland prototypeandReynolds la w shou ld be used to ups c a l e the model test re s ults to pro to ty pe values. Table 3.2 gives the sca l e facto r s for len gth, velocity and force based on Reynolds law (Sharp , 1981).

orab l . ~L2-Sca le factors based on Rey nol d s law saee eeeer

Length Veloci t y Force nl-model

De fi niti on Scale Fa ctor L,/L.

V,/V.. (11,/1' .. )(l/}.,) F. /F.. (Pr/pm ) (1',/1' .. )1 p • prototyp e ).,- 1.,/r..,

Because the models ar e to be tes t ed in wat e r (1',/1'.:;1.0 , p,lp.. :;1.0 ),from Table3.2 itca n be found the model veloc i ty should be }.,times gr e a t e r tha nthe expected prototy p-:l ve l oc i t y and the force actingon themodel isabout the same as the force acting on the prototype. This is obviously impractical becauseof the limitat i on of the te s t facility .In mostca s e s , the Reyn o ldsnumbersinthe prot otype willbe much larger thanthe Rey nold s numbers which can be achieved in the model te s t s. Therefore, when the Reynolds number inthe prototypeis out of th e rangeof the Reyno l ds number tested, some approx imations ha ve tobe made tous ethe mode l test resultsto predict pr o to t yp eva l u e s.

36

The ca ge frameandnet can appr o x i mat ely be considered consisti ngof man y small cylindr i cal e reae nt.s which are norm a l or inclinedto the cu rren t direc tion .The drag forces on the incli nedcyl i nders can be decompos e dinto their normal and tangential co mpon e nts andthe tang e ntial components can usu allybene gl ected(Chakra ba r ti, 1987).Therefore , the drag force of the element i in the direction of cur r e nt can be ca l c ulate das

(3.39)

whereCo;is the dra gcoe ffic ientofthecylindrical element, u, is the diameter of the eleme nt, ds; is the leng t hof th e el eme nt and 9, is th e ang l e betwe en the element and the cur re ntdir ec tio n.Th eres ist anc e force of the frame and net F is thereforeequal to the integration of dF;

(3.40)

Thedr a gcoef f ici e nt CDiis depende nt on the Rey nolds number andsur f a ce roughnessof the cyli nd ri ca l ele ment .

Fi gure 3.6shows howthe dragcoeff ic i e ntCochangeswi th the Reynolds number. As theRey nolds numbe r is on the left side of the subcriticalflow regime, the dr ag coef f i c i e nt is la r g er than thatinthe sub crit i c alflow reg imeand decrea ses significantly with the Rey no ld s number. Whenthe Re ynolds

37

Fiqur_ 3.6 - CD - Reint e r a c t i o n(Gi s vo l d , 1980) number is within the range of subcritical flow regime, the drag coefficient is relatively constant and can be approximately considered to be independent of Reynolds number.

When the Reynolds number is within the range of criticaland supercritical flo.... regime, the drag coefficient varies significantly with the Reynolds number and becomes smaller than that in the subcriticalflow regime.consequently, if the model tests are carried out in the subcritical flow regime and the flow regime of the prototype is still within the subcriticalrange, it can be assumed that the resistance force coe f f icients of the cage frame and net obtained trom the model tests do not change because of the increase of Reynolds number in the prototype, and can still be used to estimate the resistance forces of the prototype frame and net. Whenthe flow regime of the prototypeiscritical or supercritical, the

38

resist a nc e forc ecoefficie nts obt a ined frollthe model tests are la r qe r than th e actual values inthe pr o t o type and the resis t a nce for c es of the pr ototype ....ould be overpeeeIet ed, Thus, a correction fa c t or sho uld be int rod uc ed accordinq to theReyno ld s number and surfa ce roughnessof the prototype it amo re ac c u rate estimation is....anted.

For the te sts tobe ca r r iedout, a mode l net wh i c h is scal e d down qe ometr i c a lly from the pr oto type net cannot reproduce the re s i stance for ce of the prototy pe net app r opria tely when the Reynoldsnumbers of the model and the prototype a.re not the same, spe cia l care has tobe taken to selecta propermodel ne t (se esection3.3.3 bel ow).

As for the res i s t a nce forces ofth e floatationchambers of the cage,becausethe sharpedqes of the chamberstend to caus e flo wsep ara tion regard l e s s of the Character of the bounda rylaye r,the fo r c e s are insensitiveto Reynoldsnumber (Whi t e, 1986). There f ore , it isrea s o na b l e to assumethatthe res i s t ancefor ce coefficie nt s obtained fromth emod eltests do not cha ng e sign i fi c antl y withthe increase of the Reyno lds number in prototype and arestUl validto be us e d toes tima t e the resistance force s of the prototype floa t a t ionchambe rs.

"

'3.3 2 Moored te sts

In order to achieve dynamicsimilarity bet....een the rnodeL and the prototype , both the Froude number and the Reyno lds numbe r should be as si milaras poss ible in themodel and the pr o t otype. unfortunate l y , as boththemod e land theproto ty pe ope r at e in water, it is impossible to co r r e c tlyscale the test results to prototype values in ....hi ch both the Froude and Reynold.s si mil ari t y criteria are satisfied simultaneously (Sharp, 1981). This means that all the forces cannot be correctlyscaled.

Since theeffects of gravitytend to dominate waves and wave inducedmotions of floatingob j e cts, Froude law should be used to upscalethe model test resultsto prototypevafues, Thismeansthe Rey noldsnumbers in the modelar e a factor of AJr.Ismallerthan those inthe prototype and thevi s c o u sfor c e s maynot be correctly scaled.Nevertheless ,fromthe discussion in section J.J. 1 it can be found that for the floatation chambers of the cage the effect of Reynoldsnumber onvis cous forces maybe negligible, and for the cage frame the effect of Reynoldsnumber onvi s c o u s forces may also be relatively un i mpor t ant as lo ngas the Reynolds numbers in the modelfr a me and in the prototype frame are both within the range ot subcritical flowre g i me. However , the viscous forces ac ti ng

'0