BREAKING BOW AND STERN WAVES: NUMERICAL SIMULATIONS
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BREAKING BOW AND STERN WAVES: NUMERICAL SIMULATIONS M. Landrini, INSEAN, The Italian Ship Model Basin Via di Vallerano 139, 00128, Roma, Italy Email: [email protected] A. Colagrossi Ocean Engineering Laboratory, UCSB 6740 Cortona Dr., Goleta 93117 (CA) Email: [email protected] M. P. Tulin Ocean Engineering Laboratory, UCSB 6740 Cortona Dr., Goleta 93117 (CA) Email: [email protected] Ship-generated waves have always fascinated scientists, and played a key role in surface-ship hydrodynamics for con- tributing to hull resistance, generating sounds and radiating very long narrow wakes remotely visible. Some of these phe- nomena originate abeam the ship through extensive breaking of diverging bow and stern waves, forming a wake. In this paper we summarize and extend our recent re- search activity aimed to understand the complex fluid dy- namics involved in bow- and stern-wave radiation, includ- ing wave breaking. The analysis is limited to practical slen- der ships, with a sharp stem, for which basic insight can be achieved by an approximate quasi three-dimensional model based on the idea that longitudinal gradients of relevant flow quantities are small compared with vertical and transverse gradients. A historical recollection of slender-body theory for ship hydrodynamics is given by Maruo (1989), Tulin and Wu (1996), Fontaine and Tulin (2001). In this framework, two methods have been developed at the OEL. One based on a potential flow model, where the velocity field is given through the Laplace equation solved by a Boundary Element Method (BEM), and the evolution in time is obtained by integration of free-surface boundary con- ditions. Specific details of the latest code are documented in Landrini and Colagrossi (2001 a). The method has the advan- tage of high resolution, sufficient to capture breaking, and to trace jet overturning up to the impact against the underlying free surface. Post-breaking evolution is studied by a gridless method, called SPH and developed by Monaghan and co-authors (see e.g. Monaghan (1988)), which we applied to breaking waves since the previous Workshop. In this case, Euler equations for a weakly compressible fluid have been considered. Fur- ther developments led to a code named SPlasH, applied to a variety of free-surface problems, and presented in Tulin and Landrini (2000), Colagrossi et al. (2000). A detailed descrip- tion of the algorithm is given in Landrini et al. (2001 b) The global picture by BEM In the 2D t method, calcu- lations are carried out in two dimensions, vertical and trans- verse to the ship, and successively in time. Fig. 1 shows the three-dimensional steady wave pattern around a Wigley hull reconstructed by collecting successive free-surface configu- rations. Two key features of the flow are evidenced: first, the 0 0.5 1 1.5 2 Figure 1. Wave pattern around a Wigley hull (BL 0 1, DL 0 1, Fr 01) by 2D t (BEM) computations. system of diverging waves radiated at the bow as a result of the collapse of the ”splash”, and second the ”rooster tail” due to the gravity rebound of the free surface just past the stern which, in turn, is the source of another system of diverging waves. A thorough analysis of the genesis of diverging bow waves is given by Tulin and Wu (1996). The collapse of 1
Transcript of BREAKING BOW AND STERN WAVES: NUMERICAL SIMULATIONS
BREAKING BOW AND STERN WAVES: NUMERICAL SIMULATIONS
M. Landrini,INSEAN, The Italian Ship Model Basin
Via di Vallerano 139, 00128, Roma, Italy
Email: [email protected]
A. ColagrossiOcean Engineering Laboratory, UCSB
6740 Cortona Dr., Goleta 93117 (CA)
Email: [email protected]
M. P. TulinOcean Engineering Laboratory, UCSB
6740 Cortona Dr., Goleta 93117 (CA)
Email: [email protected]
Ship-generatedwaveshave alwaysfascinatedscientists,andplayed a key role in surface-shiphydrodynamicsfor con-tributing to hull resistance,generatingsoundsandradiatingvery longnarrow wakesremotelyvisible. Someof thesephe-nomenaoriginateabeamtheshipthroughextensivebreakingof divergingbow andsternwaves,forminga wake.
In this paperwe summarizeand extend our recentre-searchactivity aimed to understandthe complex fluid dy-namicsinvolved in bow- and stern-wave radiation, includ-ing wave breaking.Theanalysisis limited to practicalslen-der ships,with a sharpstem,for which basicinsight canbeachieved by an approximatequasithree-dimensionalmodelbasedon theideathatlongitudinalgradientsof relevantflowquantitiesare small comparedwith vertical and transversegradients. A historical recollectionof slender-body theoryfor shiphydrodynamicsis givenby Maruo(1989),Tulin andWu (1996),FontaineandTulin (2001).
In this framework, two methodshave beendevelopedatthe OEL. One basedon a potentialflow model, wherethevelocity field is given throughthe Laplaceequationsolvedby aBoundaryElementMethod(BEM), andtheevolution intime is obtainedby integrationof free-surfaceboundarycon-ditions. Specificdetailsof thelatestcodearedocumentedinLandriniandColagrossi(2001a). Themethodhastheadvan-tageof high resolution,sufficient to capturebreaking,andtotracejet overturningup to the impactagainsttheunderlyingfreesurface.
Post-breakingevolution is studiedby a gridlessmethod,calledSPHanddevelopedby Monaghanandco-authors(seee.g. Monaghan(1988)),which we appliedto breakingwavessincethe previous Workshop. In this case,Euler equationsfor a weakly compressiblefluid have beenconsidered.Fur-therdevelopmentsled to a codenamedSPlasH, appliedto avarietyof free-surfaceproblems,andpresentedin Tulin andLandrini (2000),Colagrossiet al. (2000).A detaileddescrip-tion of thealgorithmis givenin Landrini et al. (2001b)
The global picture by BEM In the 2D�
t method,calcu-lationsarecarriedout in two dimensions,verticalandtrans-verseto theship,andsuccessively in time. Fig. 1 shows thethree-dimensionalsteadywave patternarounda Wigley hullreconstructedby collectingsuccessive free-surfaceconfigu-rations.
Two key featuresof the flow are evidenced: first, the
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Figure 1. Wave pattern around a Wigley hull (B � L � 0 � 1,D � L � 0 � 1,Fr � 0 � 1) by 2D
�t (BEM) computations.
systemof diverging wavesradiatedat thebow asa resultofthecollapseof the”splash”,andsecondthe”roostertail” dueto the gravity reboundof the free surfacejust pastthe sternwhich, in turn, is the sourceof anothersystemof divergingwaves.
A thoroughanalysisof the genesisof diverging bowwaves is given by Tulin and Wu (1996). The collapseof
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Figure 2. Evolution of the splash at the bow of a Wigley hull (B � L �0� 2, D � L � 0 � 1, Fr� U �� gL � 0 � 4) by 2D
�t (BEM) computations.
splashat thebow is detailedthroughFig. 2: thefree-surfaceflow is notmuchdeceleratedbeforethestem,but uponreach-ing it, is deviatedsharplyupwards,riseson andeventuallylevels off andfalls down. An entirethin sheetis formedinthisprocessandappearsasasplashoneithersideof thehull.The relaxationof thesesplashesis the prime sourceof di-verging waves. In thepresentcase,radiatedwavesarelargeenoughto break,following thetypicalevolution: crest-rising,front-steepeningandjet formation.
Diverging breakingwavescanbe radiatedalsoby tran-somsterns.This is shown in thecaseof a Wigley hull, suit-ably taperedto have a deeptransomstern(cf. top-plot inFig. 3). The computationis performedasin previouscasesup to the last section. We thenassumethat the transomisdry and the potential is continuousacrossit, this providestheinitial conditionsfor thefollowing free-surfaceevolution.The resultingwave patternfor Fr=U �� gL 0 � 3 is shownin the center-plot. Besidethe alreadymentionedbow wavesystem,herewe observe a sharproostertail, surroundedbysteepbreakingdivergingwaves.Theanalysisof theflow fieldshows that the roostertail is causedby i) the inwardmotionof thefluid in proximity of theshipassociatedwith thecon-tractionof thehull crosssectionandeventuallycolliding aftertheendof theship,andii) thegravity reboundof thefreesur-face. Both featuresarealso detectedin the caseof Fig. 1,but for a dry transomsternthecavity left in thefreesurfacegivesrise to a strongerrebound.Thegrowth of sternwavesis bettershown in theperspectiveview in thebottomplot. Atfirst, the freesurfacemove inwardsandupwards,creatingasortof triangularhump.Later, themainbulk of fluid startstocollapsedown, leaving athinnerandthinnerjet, andacoupleof steepwavespropagatingoutwardsemerge,breakingsoonafter.
Post-breaking analysis through SPlasH In practicalcasesship-generatedwaves break, and further analysisby BEMwould requirespecialtreatmentof thefreesurface,oftenun-physicalor notpractical.Thereasonsfor shipwavesto breakcan be found in ship geometry(bow-flare, transomstern),higherspeedof advance,interactionwith ambientwaves.
The gridlesscodeSPlasH hasbeendevelopedto han-dle thesebreakingcases.The evolution of a breakingbore,shown in Fig. 4, gives an idea of the capabilitiesof themethod. The flow is generatedby a piston moving hori-zontally with constantspeed. After a while an energeticjet appears,impactingwith the underlyingfree surfaceand
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Figure 3. Wave pattern around a modified Wigley hull with a transom
stern by 2D�
t (BEM) computations. Top: ship cross sections; center:
wave pattern; bottom: detail of rooster tail and breaking waves past
the stern.
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Figure 4. Breaking bore and splash-up cycles forced by a piston
moving from left to right in finite depth water. Computations by SPH
method.
creatinga cavity andthereforecirculation(hereclockwise).The strongsplash-upI appears,center-plot, evolving into acounter-rotatingvorticalstructureandanotherforwardsplashup II, bottom-plot.Thestrengthof theplungingjet is crucialin determiningthatof thefollowing splash-upandtheentireresultingprocess,which for the breakingborehereconsid-eredis characterizedby several splash-upcycles,Tulin andLandrini (2000).
We have discovered similar featuresin breakingshipwavesby analyzingpicturesof modeltesting(picturestakenby PennaandGuerraat the INSEAN modelbasin). In par-ticular, Fig. 5 shows the bow wave generatedby a frigate(DDG51-type of the US Navy) with a strong flare. ForFr 0 � 41,thesplashreadilyevolvesinto aplungingjet, creat-ing thesplash-upshown in theenlargeddetailwhich revealsalsothesurfacescarassociatedwith thebackwardfacingjetto becomparedwith thebottom-plotin Fig. 4.
We appliedSPlasH in a 2D�
t fashionto studythepost-breakingbehavior of shipwaves.We first discussthecaseofa Wigley hull. The initial evolution hasbeenalreadyshownin Fig. 2 and, in this case,the computationsare initializedby thoseBEM results. This proceduresimplified the mod-eling, increasedthe efficiency andallowed an optimal reso-lution of the computation,with a high numberof particlesclusteredinto the jet. Thethree-dimensionalwave patternisreconstructedin Fig. 6, whereonly the upperlayerof parti-clesis represented.Only the portionaroundthe breakingis
Figure 5. Breaking bow waves in model testing. INSEAN Model
2412 of the US Navy DDG51 (Fr=0 � 41).
shown, with the ship centerplanelocatedat y 0, andthemid-ship crosssectionat x 0. The impactingjet gener-atesa splash-up,evolving into i) a vortical structureleft be-hind thecrest,andii) remainingparticlesriding on thecrestemerging after thebreakingwhich resemblethesteadyeddyusedby CointeandTulin (1994)to modeltwo-dimensionalsteadyspilling breakers. This flow patternis bettervisiblein thetwo-dimensionalbottomplot, andis remarkablysimi-lar to picturesof (two-dimensional)breakingwavesshown inMelville (1996).
On this ground,in breakingship-wave patterns,we candistinguisha TYPE I breaking,resultingfrom lessenergeticbreakingwaves,andresemblingthesteadyspilling breakingobservede.g. pasthydrofoilsat small incidence,anda TYPE
I I breaking,with strong(possiblymultiple) splash-up,caus-ing largerair entrapmentandvortex generation.
TYPE I I breakingis (usually) generatedat the bow of
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Figure 6. Top: perspective view of 2D�
t computation by SPlasHof the wave pattern generated by a Wigley hull (B � L � 0 � 2, D � L � 0 � 1,
Fr� 0 � 46); bottom: two-dimensional view of late evolution.
shipswith pronouncedflare,andthenumericalsimulationbySPH requiresthe modelingof arbitrary curved boundaries.Thisextensionof SPlasH hasbeenrecentlyaccomplishedbygeneralizingtheconceptof ”ghostparticles”,anda prelimi-nary resultis givenin Fig. 7 for a frigate-typeship (usedbyO’deaandWaldenin their analysisof deck wetness).Theflareis lesspronouncedthanin Model2412,andthecollapseof thesplash,topplot, causesaweakerbreakingthanthatob-served in Fig. 5. The resultingthree-dimensionalwave pat-ternis reconstructedin thebottomplot.
Resultsfor Model2412andfor thepost-breakingevolu-tion of sternwaveswill bediscussedat theWorkshop.
ACKNOWLEDGEMENTSThis work hasbeensupportedaspart of a programfor
the simulationof ship breakingwaves by the Ship Hydro-dynamicsProgramof ONR, initiated by Dr. Ed Roodandnow supervisedby Dr. Pat Purtell. The researchacitiv-ity of M.L. is also supportedby the Italian Ministero deiTrasporti e della Navigazione through INSEAN ResearchProgram2000-2002.
REFERENCESR. CointeR., M.P. Tulin ”A theoryof steadybreakers”,
J. Fluid Mech., Vol. 276,1994.A. Colagrossi,M. Landrini, M.P. Tulin ”Near Shore
Bore PropagationandSplashingProcesses:GridlessSimu-lations”,Monterey (CA), OEL Tech.Report00-224,2000.
E. Fontaine,M. Landrini, M.P. Tulin On modelingthepost-breakingphase:splashing.Proc.of 15th Int. Work. Wa-ter Waves Float. Bodies, Eds.T. Miloh andG. Zilman,2000.
Figure 7. 2D�
t computation by SPlasH of wave pattern around a
frigate. Top: the collapsing splash at the bow; bottom: perspective
view of the resulting wave pattern.
E. Fontaine, M.P. Tulin ”On the prediction of free-surfaceflows pastslenderhulls using the 2D+t theory: theevolutionof anidea”,Ship Tech. Res., 2001.
M. Landrini, A. Colagrossi”TwoDPT: a 2D+t codeforshiphydrodynamics”,OEL TechnicalReport,2001
M. Landrini,A. Colagrossi,M.P. Tulin ”Gridlesssimula-tion of sloshingflows in tank”, OEL TechnicalReport,2001
H. MaruoH. ”Evolutionof thetheoryof slenderShips”,Ship Tech. Res., Vol. 36,pp.107-133,1989.
W.K. Melville W.K. ”The role of surface-wavebreakingin air-seainteraction”,Ann. Rev. Fluid Mech., Vol. 28,1996,pp.279-321,1996.
MonaghanJ.J.,”An Introductionto SPH”, Comp. Phys.Comm. 48,pp.89-96,1988.
M. P. Tulin, M. Landrini ”Breaking wavesin the oceanandaroundships”Proc.of 23rd ONR Symp. on Naval Hydro-dynamics, Val deReuil,France,2000.
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ONR Symp. on Naval Hydrodynamics, Trondheim,Norway,NationalAcademyPress,Wash.D.C.,pp.99–117,1996.
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