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CHAPTER 6 4T H E T H E O R Y A N D D E S I G N O F B U B B L E B R E A K W A T E R S

b yP . S . B u l s o n , P h . D . , B . S c . ( E n g ) . , M . I . S t r u c t . E . , M . I . M e c h . E .

MilitaryEngineering ExperimentalEstablishmentan dSouthamptonUniversity,GreatBritain

A B S T R A C TThispapersetsdownbasicinformationonthe behaviour of

bubblebreakwaters,drawnfromanalyticalan dexperimentalstudiescarriedoutbytheauthoran dothersinrecentyears.Designformulaear egivenforsurfacevelocityan dthicknessof th ehorizontalcurrentproducedby abubblecurtain,andforthequantityoffreeairrequiredtosuppresswavesofknownlengthan dheight.heeffectofanintermittentai rsupplyisexamined. Itisconcludedthatthequantityofairrequiredisastronomicaland thepracticaldifficulties

9 9 5

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996OASTAL ENGINEERINGINTRODUCTION

Ifasurfacecurrentofsufficientstrengthispropagatedinoppositiontooncomingwaves,theirlengthisreducedandtheirheightincreaseduntilinstabilityoccurs,andtheybreakoverth ecurrentinthe mannerofwavesbreakingona beach.hiswellknownactionoccurs naturallywhenwindformedwavesmeetanopposingtidalcurrentinanestuary.nemethodofartifici-allyproducinganopposingsurfacecurrentisbymeansofabubblecurtain,whichcanbeobtainedbyreleasingairfromalineof]etsontheseabed.Asthebubblesrisewaterisentrainedintheformofaverticalcurrent,andthisspreadsintoopposinghorizontalcurrentsatthesurface.

InrecenthistorythisconceptwasfirstemployedbyBrasher^-ofNewYorktoprotectcivilengineeringworksin1907.epatentedhi sdesign,whichconsistedbasicallyofaperforatedpipeontheseabedfed byairfromshorebasedcompressors,anditwasusedby theStandardOilCompanyin1915atElSegundo,California.therprojectsseem tohavebeenundertaken,buttheresultswerenotpromisingandinterestdiminished.esearchcontinuedspasmodically,however,an din1936ProfessorThysseofDeftshowedthatth esurfacecurrentsproducedbythebubbleswerethemammechanismof thesystem,untilthentherehadbeenconsiderablespeculationaboutth eprecisewayabubblebreakwaterworked.

Duringthe1939-19^5 war,fundamentalresearchwascarriedoutbyProfessorWhite2andSirGeoffreyTaylor3inEngland,becausethemethodwasseentohavepotentialasatransportablebreamwaterformilitarypurposes.Asaresultoftheirworkitbecamepossibleforth efirsttimetopredictthequantityofai rrequiredtoproduceagivensurfacecurrent,and thespeedofcurrentrequiredtokillwavesofknownlength.aylorstheory,however,assumedwavesofinfmitessimal amplitudeandsinusoidalform anddid no ttakeaccountofwaveheightorth epossibilityofpartialwavedamping.hisfundamentalworkandtheexperimentsassociatedwithi tshowedthatfo rthesuppressionofstorm wavescharacteristicofN.W.Europe,th equantityofai rrequiredperfootrunofbreakwaterwouldbeastronomical.

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BUBBLEBREAKWATERS9 7Afterthewar,inventorsandscientistsfromanumberofcountries

searchedfor methodsofincreasingth eefficiencyofthebubblecurtain. Itisinappropriatetogiveacompletesurveyhere,andthereaderisdirectedtoasummarybytheauthor 1 *publisheda fewyearsago. Evans5carriedoutanumberofilluminatingexperiments,anditwascleartohimandothersthatlargescaletestsweredesirabletoascertainwhetherlargecurrenthorse-powerscouldbeeffectivelyproducedmdeepwater,and whetherameasureofwavedampingcouldbeobtainedinafullscaleinstallation.hesetestswerecarriedoutbyBulson6>7intheearly1960'sandlatertheeffectofanintermittentairsupplywasinvestigated8"

Fromalltheseexperimentalandanalyticalstudiesitispossibletobuildupadesigntheoryforbubblebreakwaters. Thisfallsintotw osections,thefirstdealingwiththemagnitudeanddistributionofsurfacecurrentsobtainablefromagivenairsupply,thesecondwiththeactionofagivensurfacecurrentagainstwavesofknownheightandlength.

2 . THEBUBBLECURTAIN

Taylor3,drawingananalogybetweentheverticalcurrentproducedinwaterbyreleasingbubbles,andmairby releasingheat,quotedtheworkofSchmidt9inshowingthat

v* =*9

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998 COASTAL ENGINEERING *UHFACE

FIG. I

W%

14

V h

1 7

II

1 07 5tOSS^09Sv'/5 (__)'

F l < 5 2

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BUBBLEREAKWATERS99Thepracticalengineeri sinterestedin"J0,thequantityoffreeair

deliveredbythecompressorspersecondperfootandthisi s linkedwithd^_bya relationshipgoverned bythedepthofthemanifold( P ) ,andtheatmosphericpressureexpressed a s a headofwaterC P ) .ulson6showedthatEq,(l)canbes e ti n theform

VM =1.46-2feet/sec,. 2 )vp^ /where1"46i s thevalueofKoundbylargescaleexperiment( F i g2 ) .Thecurrentvelocity,V,diminishesapproximatelylinearly withdepth,

untili tequalszero a tadepth -belowthesurface.ulsongivesthefollow-ingexpressionforC\,,

& = 0-32PU^efP+0 ) feet, .. . . ( 3 )- \ P /a s shownmFig 3 .

Whenthesamequantityofairi spassedthrougha varietyoforificediametersandspacingstherei s nosignificantdifferencei n \ ,further,resultsforasinglemanifoldatdepthParenotnoticeablydifferentfromthosewhentwoor moreadjacentmanifoldsaredeliveringthesametotalquantityofa i r .

WhenP =3 4 ft.,theverticalvelocitya t thecentreofthecurtainwhenQa 1 f t3/sec/ftwasfoundt o beaboutthreequartersofthehorizontalsurfacevelocity V , , , . Atypicalcurveofdecay i nsurfacecurrentvelocitywithdistancefromthecentreofthemanifold i sshownmFig4 .

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1000 COASTAL ENGINEERING

6'0

*o

vo

//\ /y/'/

/>//&v03ZP HJe(^)y

IO 20 So0F E E T F l < 5 .3

Feet/ec

V m

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BUBBLEREAKWATERS0013 . COMPLETEWAYESUPPRESSION

Unna10,in194 2,discussedtheactionofatidalstreamonwindformedwaves.ordeepwaterwaveshavingalengthA,thevelocityoftravel,O ,isgivenby

andUnnashowedthatthecriticalstreamvelocity,V,isequalto-ip.Taylor3investigatedthegeneralconditionwhenthewatercannotbeconsidereddeep,andthecountercurrentspeeddecreasesuniformlywithdepth.hecurrentvelocityatthesurfacetocompletelysuppressthewaves,V^wasshowntobegiven by

V.4if t .(5)where

7-Z

6)

and* m istheminimumvalueof o( where(

(""isthespeedoftheorbitalmotioninradians/sec).a .

Taylorgivesacurverelating-and(wwhichisreproducedinFig5 . InX ^ */% verydeepwater,D- " 0an dfromEq.6^Js * 0;then,fromFig5 , A ,^Ki * " t,thevaluegivenbyUnna.

Ifthequantityoffreeairtoproduce i * iis

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1002 COASTAL ENGINEERING

4

s

z

FIO.5

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BUBBLEREAKWATERS003For aknownwaterdepth,",thecurrentthickness*can b efoundfrom

E q . 3 .ora knownwavelength,A ,thevalueof canthenb ecalculatedfromEq.6,andFig5 usedtofind" .hisi ssubstitutedintoEq.8 t ofindtheairsupplyQcr Thevalueof i^_isplottedfor aselectionofvalueso f & and A i n Fig6 ,which graphicallyillustratestheadvantageofsettingtheairpipem a depthofwaterofa tleasthalfthewavelength.( 2 ,risesverysteeplywhenthedepthi ss m a l l .

AccordingtoEq.8, '\0risindependentofwaveheight,butexperimentsshowthatwhenwavesareneithertrulysinusoidal norofmfinitessimalheightthequantitytoproducecompletedampingcanexceedQ(#- I f wedenotethisquantityby $^,Bulsonsuggests a linearrelationshipbetweent" txandthewavesteepnessJ H a sshowni n Fig 7 . * < : * -\

A s anexample,suppposewewish toinvestigatethequantityofairrequiredtosuppressseawaves10 0 f tong,t f t .high,i na waterdepthof5 0 f t . Now,fromEq.3,

d =-32.3ZldjeThen,

= loOZ - 7 T963andfromF i g . 5

* 2 -2 .S u b s t i t u - t i o ni nE q . gives

8 33 3 9 - 6 3f t . (P=3 3 f t .forseawater)

1-66,

Q-ry. =1 3 3cusecsper f t .

Also,H=_Z_ =-04,andfrom F i g . 7 ,JH^L = 1-t,A l o o orthereforethequantityoffreeairrequired,0 ,- I ' M -x13-3 8-6cusecsperf t Thisrepresentsanairpowera t thepipeof 6 4 H P perf o o t .

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1004 COASTAL ENGINEERING

OJitCi/FT.5 .0

40

50

2-0

1 - 0

\\

A*40

. 30. 20- -0E E T

00000 E E T f l

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BUBBLE BREAKWATERS 1005

H A

04

03

01

01

00- 6&0- 2+Flf i

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1006OASTAL ENGINEERINGPARTIALWAVESUPPRESSION

I f lessthanthequantityofairrequiredforcompletesuppressioni ssupplied,therei ssomedampingoftheincidentwave,ulson7proposedanempiricalrelationshipbetweentheheightof thetransmittedwave( n ) ,theheightoftheincidentwave( H ) ,thequantityo f airsupplied( < ? ) ,andthequantity tocompletelykillthewaves(^IM*),o f theformIA&)'*(.)(t"> . ( 9 )

Fig8showsa plotofthisfunctionfor various values o f otethattheamountofdampingfallsasthewavelengthincreases,andthatforwavesgreaterthan100 f t .i nlengththerei s verylittlereductioni n waveheightuntilthequantityofairapproaches t o withina fewpercentof ^^^^

INTERMITTENTAIRSUPPLYBulson8s t o w e dfrommodelteststhatforcompletewavesuppression a n

intermittentairpulseoffersnoadvantageover asteadysupply*thetotalquantityofairsuppliedduringagivenperiodmustbethes a m e .orpartialdamping,however,anintermittentsupplycanbeadvantageous.

Thedegree o fmtermittency i s measured bytheratiosJ j j and t\ ,where

r _imeairvalvei sopen^ j - waveperiod )))Timeairvalve i s closedTimeairvalvei s open . . . ( 1 0 )andFig9showstherelationshipbetweenund hforvariousvalue o f - f e -Thegraphillustratesthati ti s besttouse a slowa valuefor_ _ a sV > Tpossible,when=-75,theintermittentsupplywith X.1 required 50%Hofthetotalair o f acontinuoussupply,andthesupply j . - 2required6 6 % ,Fig1 0showsthecomparisonoftotalairf l o w s .

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BUBBLEREAKWATERS 1007

h H

to

08

06

0- 4

01

\ \ \2 .A=2-o

/2AsoAp

o - a 0-46 oft-o F ia

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1008 COASTAL ENGINEERING

h H

Fl

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BUBBLE BREAKWATERS 1009

H

\ - o

o f,

06

04

02

\\r_

Ol46b- O T O T A tNTEBMITTgNT PLOW TOTALC O N T I N U O U S C L O W F K S0

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1010OASTAL ENGINEERINGTYPICALDESIGNCALCULATION

Supposewe wish t oexaminethefeasibilityofusinga bubblebreakswater i n deepwatertoreduce a rangeofincidentwaveheightsto a trans-mitted heightof 3 f e e t .hreefeeti s assumedtobe the maximumheightthatunloadingandberthingoperationscantakeplace withinthebreakwater.By' d e e p water'wemean that theairpipe o n thesea bed i s a tleastH.belowthesurface.hen,takinganincident wave heightof1 0 feetforthefirstcalculation,andatmosphericpressurer,as3 3feetofseawater,Eq.9givesA

1 5 v V U *J=6

7. "2Hx25-7and fromFig.5 t\\2-1Substituting i n Eq.8 givesQj= t76cusecs per f t .

M 1 0 r t H yAlso,rJ~ = 0-03,andfromF i g . 7~2 =1 -A oW orforcompletesuppression,Qy^ =7 1 cusecsperf t .W 1 0 r t a y Also, =T-Z 0-03,ndromig.7 - =-2, sohatheiruantityA oW

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BUBBLEREAKWATERS011Then,fromEq.12,

GL j=4,260c.f.mperfootofbreakwater.Thequantityofairrequiredisseentobevarylarge.fthebreak-

waterisoperatingagainstth esameincidentwaves,bu tmonly50feetofwater,thequantityisalmostdoubled.orthisconditionEq.3gives

A*M 3 4 0 _.and"7Tx9-63 "62-d - 0-32.33 L

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1012 COASTAL E N G I N E E R I N G

A = 4605lt>0IO

IUA.CONTNUOU >

a. L //oau.Ulu 5 80x10*

'/IL-L

71

540'/ 1 //

o40x10 /

/2fe0/7/A

0 ^ ssx

\iNTe(MITT!N T

4H IIE E T F I G I

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BUBBLEREAKWATERS013Intheseconditionsitwouldbedifficultforasmallvesselto

approachthebreakwaterfromth eseawardquarter. Itwouldbenecessarytosailaroundandapproachfromleeward. Similarly,alighterorsmallcraftleavingthebreakwatercouldnotsailoutacrossthebubblecurtainwithoutconsiderablehazard.

b SurfacecurrentswithinthebreakwaterTherewouldbeaconsiderableconfluxofsurfacecurrentswithinthe

breakwater. Intherangeofbreakwaterdesignsconsideredinsection7,thesecurrentswouldbeatleast12knots,andmightcausedifficultyinmooringandcontrollingsmallcraft.

c .irsupplyItwasdemonstratedabovethattoreducewaves10feethigh,

34 0feetlongtoaheightof3feetrequiresacontinuousairsupplyof34,260c.f.m.perfootof breakwater.hi sisunderidealconditionswhenthedepthofwateris170feet(In50ft.ofwaterasupplyof59,700c.f.merfootisneeded). Atbestthen,theoutputof57largecommercialcompressorsisrequiredforeveryfootofbreakwater,alternativelythereareverylargeenginedrivencentrifugalcompressorsavailablecommerciallywithacapacityof30-40,000c.f.m. ,bu ttheseweighover20tonsandconsume2 15gallonsperhouroffuel. Onthisbasisa50 0yardlongbreakwaterwouldcostabout100,000perdayinfuelandinvolveacapitalexpenditureforai rsupplyof20m.

d .ntermittentsupplyAnintermittentsupplycansaveair,bu ttheengineeringproblems

inprovidingonecouldbedifficulttosolve. Interruptingthesupplyfromthecompressorsseemsalesslikelysolutionthandirectingth eai ralonglengthsofpipealternatelybymeansofavalvesystem.arewouldbeneededtoensurethattheairfeedlinestothesevalveswereclearofthehullofanyvesselwithinthebreakwater.

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1014OASTAL ENGINEERING8 . CONCLUSION

Theexperimentaland theoreticalstudiesduringthepast25yearshavemadeitpossibleforareasonablyaccurateestimatetobemadeoftheairquantityrequiredtooperateabubblebreakwater.hequantityisastron-omicalandcostlytosupply.hepracticaldifficultiesofoperatingafullscalesystemareimmense. Itisdoubtfulwhetherany novelideasofbubbleformationandsizecanproduceeconomies,andhighcostisboundtobeth ebasicfeatureofanyapparatusofthistypewhichisdesignedtocombattheenergyof thesea.

R e f e r e n c e s

1 .rasher,P. ,CompressedAi rMagazine,vol.20,1915,p.752.2 .hite,CM.,AdmiraltyReportATR/MSIC/1685,1943.3 .aylor,SirGeoffrey,Proc.Roy.Soc.A. ,vol.231,1955,p466.4 .ulson,P.S.,DockandHarbourAuthority,vol.XLVIII,No.550,June1967,p.41.5 .vans,J.T.,Proc.Roy.Soc.A.,vol.231,1955,p.457.6 .ulson,P.S.,DockandHarbourAuthority,vol.XLII,No.487,May1961,p.15.7 .ulson,P.S.,Dockand HarbourAuthority,vol.XLIV,No.516,Oct1963,p.191.8 .ulson,P.S.,Dockand HarbourAuthority,vol.XLIV,No.514,Aug1963,p.129.9 .chmidt,W. ,2Aug.Math.Mech.,vol.21,1941,p.265.

10.nna,P.J.H.,Nature,vol.149,19 42,p.219.

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BUBBLEREAKWATERS015Notation

Celocityof travelofwavesM,hicknessofcurrentK .eightoftransmittedwavekoefficienti nformulaforcurrentvelocityt\atiooftimeairvalvei sclosedtotimei ti s openpimeairvalvei s openV n ,urfacevelocityofcurrentVriticalstreamvelocityV * murfacecurrentvelocityt ocompletelysuppresswaves0 depthof manifoldbelowsurfaceH heightofincidentwaveP atmosphericpressureexpresseda s headof waterQ quantityofairemergingfromorifices,perfooto f pipe(X0 quantityoffreeairdelivered bycompressors,perfootofpipeY-quantityoffreeairtoproduce n ,,perfooto f pipe

(J^^quantityoffreeair tocompletelysuppresswavesoffiniteheight,perfootofpipe& ,j quantityoffreeairsuppliedintermittentlyperfootofpipeT waveperiodZ