1. Introduction
Duringoperation,ashipisopentodynamiceffectsresult- ingfromspecificsofmarineenvironment.Amongthese effects,winddynamicimpacttogetherwithawavymotion isespeciallyhazardousfortheship.Therefore,thereare applicable criteria, taking the above said situations into consideration,inclassificationsocieties’regulations.Away tocalculateaheelingmomentoriginatedbythewindoper- ation is given in dynamic stability criteria. One may determineanangleofdynamicheelbasedonafunctionof thismomentandrightinglevers’curve.but,assumptions andsimplificationsacceptedbytheclassificationsocieties resultinomissionofsomephenomenaandtheangleof dynamic heel, determined based on theoretical calcula- tions,differsfromtherealone(Moreno,Chaos,Aranda, Muñoz, Díaz, Dormido, 2009). Determination of a real valueofthedynamicangleofheelispossiblebyexecuting modeltestsperformedwithgeometricanddynamicsimi- larityscaletakenintoconsideration.Resultsoftheoretical calculationsandmeasurementsofdynamicangleofheel, executedwithashipmodelof888projecttypeasanexam- ple, are given in this elaboration (Lewandowski, 2010).
Resultsofthepresentedtestsallowformulatingpractical conclusionsthatmaybeusedbytheclassificationsocieties, amongtheothers.
2. Research facility and object of the test
Testsonthewinddynamicimpactonashiphavebeenex- ecutedatafacilitylocatedinthePolishNavalAcademy (Mironiuk,W.2006).Mainelementsofthestandareasthe following:
Modelbasinforsurfaceshipsofinternaldimensionsof LxbxH3x2x0,5m,
—Shipmodelof888projecttype,
—Shipmodelof660projecttype,
—Computerregisteringparametersoftheshipmodel position,
—Devicegeneratingairflow.
Thereisasetoffansfixedinacasingmakingajetofa changeablesectiononthebasin’sshorterside.Dimensions ofthejet’soutletaresufficienttolettheairflowoperateon entireflankofthemodel,withasuitablereserve.Thereare 5bigand5smallfansinthejet’shousing–alltogether,they arecapableofgeneratingairflowfasterthan5m/s.
Ashipmodelof888projecttypehasbeentheobjectof thestudy.Itwasmadeinascale1:50inrespecttoareal vessel.TheschemeofthemodelisshownintheFigure2.
ComparativeAnalysisoftheDynamicAngleofHeelofaShipe 888ProjectTypeDefinedoftheCalculationandModelTests
W.Mironiuk1
©SEECMAR /All rights reserved
Resultsofinitialresearchonairflow’sdynamicimpactonashipmodelof888projecttypearepresented intheelaboration.TheresearchhasbeenexecutedatateststandlocatedinthePolishNavalAcademy.
Theshipmodelof888projecttypehasbeenanobjectofthetests.Resultsofexecutedmeasurements havebeencomparedwiththeoreticalcalculationsforanangleofdynamicheel.Inputparametersfor thetestsandcalculationshavebeendefinedinaccordancewithrecommendationsofPolishRegister ofShipping(PRS)andIMO(IMOInstruments1993,2008,PRS2007).Determinationofaheelingmo- mentbywindoperationhasbeenakeyissue.Theexecutedresearchhasrevealedthatthewaythecri- teriaoftheship’sdynamicstabilityaredefinedbyPRSandIMOtakesacertainsafetymargininto account.
Article history:
Received06June2012;
inrevisedform09June2012;
accepted30July2012
Keywords:
Stability,Warshipmodel, Laboratory,Dynamicheel
A b S T R A C T A R T I C L E I N F O
1NavalAcademy,FacultyofNavigationandNavalWeapons;ŚmidowiczaStreet69, 81-103Gdynia,Poland;tel.+48586262903,e-mail:[email protected], [email protected].
journal of maritime research
ISSN: 1697-4840 www.jmr.unican.es Vol. IX. No. 3 (2012), pp. 33 - 38
Its basic data have been as the following (Mironiuk, W.
2006):
—Overalllengthofthemodel:Lc=1,444m;
—Lengthbetweenperpendiculars:Lpp=1,284m;
—Displacementofthemodel:D=13,15kg;
—Averagedraughtofthevessel:T=0,078m;
—Depthofthemodel’scentreofgravity:ZG=0,096m.
1,2and3-Valvesforapuncturesimulationinthecom- partmentsPIII,PVandPVII;4,5,6,7and8-Valvesfor flooding the compartment PVI, PIV, PIII, PII and PI;
9,10,11-WaterlevelindicatorsinthecompartmentPVII, PVandPI;12.Indicatorofshipdraught;13.Listindicator.
Attheleveloffloatationline,openings–horizontally arranged–aremadeinthemodel’sstemandsternframe.
Rodslimitingtheship’sdriftcausedbytheairflowopera- tionmaybeplacedintheopenings.Suchanarrangement resultsindefiningafixedaxisofrotationoftheshipmodel.
Infact,positionoftheshipmodel’saxisofrotationisnot
permanentbecause,itdepends–
amongtheothers–ondynamics ofthewindeffect.Locationofthe ship model’s axis of rotation is crucialtodeterminetheheeling moment. The IMO’s stability code (IMO Instruments, 1993, 2008,)provideswithinstructions that the heeling moment’s lever shouldbecalculatedasadistance fromacentreofthetopsidepro- jected area to the centre of the underwaterpartofthehull’spro- jectiononthesymmetryplane,or –approximately–tothevessel’s half draught depth. In this con- nection,resultsofmeasurements of and calculations for the dy- namicanglesofheel,executedin compliancewiththeIMO’srec- ommendations,shalldiffer.
A sensor of the heeling and trimanglesregisteringtheangles withanaccuracyofupto0,01of degreeisinstalledonthemodel.
Signalsfromthesensoraretrans- mitted by means of a cable to a computer.Influenceofthecables connectedtothemodelhasbeen omittedbecauseoftheirinsignif- icantweightandsectionareas.
3. Problem of geometric and dynamic similarity scale Solving the geometric and dy- namic similarity scale problem has consisted in meeting given conditions.Theshipmodelwasmadeinthe1:50scale- thatiswhyallgeometricquantitiescouldhavebeeneasily calculated.Valuesoftherightingleverscurveoftheship modelalsohavebeensubjecttothegeometricsimilarity principle.Theheelingmomentshouldeffectinproportion tothevessel’srightinglevers,i.e.ratiooftheship’srighting leversmaximumvalueandvalueofthewindaffectedheel- ingmoment’slevershouldbethesameforboththemodel andtheship,asbelow:
(1) wherethe“o”subscriptreferstothevessel,whilethe„m”
subscriptreferstothemodel.Figure3makesagraphical mappingofthe(1)dependence.
Windpressureaffectingthevesseldependsonthewind affectedheelingmoment.Therefore,thepressureshould bedefinedincompliancewithasuitabledynamicscalein
Fig. 1.Facilityfortestsondynamicimpactofwind.
relationtothemodel.Valueofthepressurehavingdynamic impactonarealobject,i.e.IMOandPRSregulations(IMO Instruments1993,2008,PRS2007).Itis504Paforshipsof unrestrictedoperationalwaterareasandwindoperating statically.However,avalue1,5timesbigger,i.e.756Pais givenfordynamicwind.Agivenwindvelocitycorresponds withthispressurevalue,andthevelocitymaybedeter- minedwithmanyways.Usingdependenceonthedynamic pressureisoneofthem,asthefollowing:
(2)
Thepressurevalueof756 Pagivestheairspeedof35m/s –atthedensityof1,2kg/m3. Todeterminethewindvelocity inrespecttothepressure,one mayalsousetablevaluespro- videdinpublishedreferences (Dudziak, J. 2006). It follows from them that the velocity should be some 29 m/s for squallof756Papressure.
Theairspeedobtainedfortheshipshouldberecalcu- latedforaspeedforthemodel.Suitablerecalculationsmay bedonewithmanyways.UsingEulercoordinateisoneof them(Grobyś1998),asbelow:
(3) Thepressureof756Paandthespeedof32m/sboth definedfortheshipgivesthewindvelocityof4,52m/s,i.e.
thevelocitythatshouldhaveimpactonthemodel.
Incasethefollowingdependenceonthewindaffected heelingmomentisapplied(PRS2008):
(4) Where:
Fw–topsideprojectedarea[m2],
zw–distancefromcentreofwindprojectedareatowa- terline positioned at height of T/2 above basic plane,atgivenloadcondition[m],
j–angleofheel,
vw–windvelocityatheightofwindprojectedflank’s geometriccentre,definedwiththefollowingfor- mula(PRS2008),
(5) Where:
v10–windvelocityatheightof10metresabovewater- line,v10=80knotsisacceptedfortheshipsofunrestricted operationalwaterareas.
Thewindvelocityis4,51m/sfortheshipmodel.
Thepresentedsolutionsfortheproblemofdynamic similarity scale follow to similar results of the air flow speed.Therefore,itisprobablethatthecalculationsforthe windvelocityhavebeendonecorrectly.
4. Execution of the tests
The study’s programme has been executed in several stages.Determinationoftheairflowspeeddistributionhas
Fig. 3.Determinationofwindaffectedheelingmomentlever’svalue
forshipmodel.
Fig. 2.Dispositionofelementsinthemodel oftheshiptype888.
beenoneofthefirstactivitiesattheresearchstand.Meas- urementsoftheairflowspeedhavebeenexecutedin18 points.Resultsofthemeasurementsforthespeedofthe airflowgeneratedonlybythebigfansaregiveninTable1.
Average value of the speed of the airflow affecting the modelhad4,52m/s.
Table 1.Resultsofmeasurementsofairflowspeed.
Nextstageoftheresearchhasbeentodeterminethe dynamicangleofheel.Testsatthestandhavebeenexe- cuted,amongtheothers,forthefollowingvaluesofthean- glesofheeltowardsthewindwardshipboard:6°,15°,18°.
Valuesoftheseanglesresultfromcalculationsofweather criteriaexecutedfortheshipprojectoftype888inaccor- dancewiththeregulationsofIMOandPRS.
Thefanshaveworkedwithconstantvelocityduringreg- isteringtheanglesofheelwhatcorrespondswithconstant characteristicsoftheheelingmoment.Resultsofthemeas- urementsoftheregisteredanglesofheelsaregiveninFig.4.
Fig.4. Measurementsofdynamicangleofheelafterdeflectingmodeltowards windwardshipboardtoangleof:a)6°;b)15°;c)18°.
Table2containsalistingoftheresultsforthemeasure- mentsexecutedatthestand.Thebiggestvaluesofthedy- namicangleofheelhavebeenobtainedwhenthemodel hasbeendeflectedtotheangleof18degreestowardsthe windwardshipboard.
Table 2.Valuesofdynamicanglesofheel.
5. Theoretical calculations
Calculationsfortheship’sdynamicangleofheelhavebeen executedfortheheelingmomentdefinedinaccordancewith theIMOandPRSrecommendations.basedonthem,lever ofthedynamicallyoperatingheelingmomenthasbeende- terminedassumingthatthedistanceofthetopsideprojected area’scentrewasmeasuredfromthehalfdraughtdepth.The prospectedleverhasbeencalculatedwiththefollowingde- pendence(IMOInstruments,1993,2008,PRS2007).
(6) where:qv =504Pa–windpressure;
Fw –topsideprojectedarea[m2];
Zv –measuredperpendicularly,distancefromcentreof topsideprojectedareatocentreofunderwaterpart ofhull’sprojectiononsymmetryplane,or–ap- proximately–tovessel’shalfdraughtdepth[m];
D –ship’sdisplacement[t];
g –9,81m/s2;
andforthedata:
Fw =533m2; Zv =6.46m;
D=1643.7t,
toresultinobtainingvalueofthewindaffectedheeling leverequal0,162m.
Forthisvalue,thedynamicanglesofheelhavebeen readonagraph(Fig.5)andplacedinaTable 3.
Table 3.Valuesofdynamicanglesofheel.
Theresultsshowthatthevaluesofthedynamicangles ofheelobtainedfromthecalculationsareseriouslybigger thanthevaluesobtainedfromthemeasurements.Thefact thatleveronwhichforceofthewindpressureoperateswas definedfromtheship’shalfdraughtdepth,insteadoffrom theoperativewaterline,isoneofthereasons.Shouldone
Measurement Place of measurement and Average value
height value of speed [m/s] [m/s]
1 2 3 4 5 6
35,5cm 4,57 4,68 4,69 4,16 4,10 4,53 4,46 18,5cm 4,67 4,86 4,77 4,53 4,16 4,65 4,61 8,5cm 4,33 4,63 4,60 4,65 4,65 4,10 4,49 4,52
No. 1 2 3
Angleofheeltowardswindwardshipboard[deg] -6 -15 -18 Dynamicangleofheel[deg] 23 29 31
No. 1 2 3
Angleofheeltowardswindwardshipboard[deg] -6 -15 -18
Dynamicangleofheel[deg] 33 40 43
a)
b)
c)
take this note into consideration, the wind affected dy- namicleverlwshallequal0.111m.Anextgraph,givenon Figure6,allowingdefiningthedynamicanglesofheel,has beenexecutedforthiscase.Obtainedvaluesoftheangles arepresentedinaTable4.Moreover,alinewithvaluesof thedynamicstabilityanglesmeasuredatthestandhasbeen added-toenabletocomparetheresults.
Table 4.Valuesofdynamicanglesofheel.
This time, the results of the dy- namicangleofheelcalculationsand measurementsareverysimilar.Differ- encesarefrom10to16%.Itispossible to obtain more similar results after dampingofmovementandsizeofthe windexposedarea’sprojection,which changesduringtheheel,aretakeninto account.
6. Summary
Theexecutedinitialresearchonthe dynamic influence of the wind af- fected heeling moment shows high convergenceofthetheoreticalcalcu- lationswiththemeasuredvalues.The obtained results prove that the way thewindaffectedheelingleverisde- terminedhassignificantimpactonthe valuesofthedynamicanglesofheel.
Theshipmodelhashadthefixedaxis ofrotation,positionedinnotwaving waterplane.Therefore,ithasnotbeen possible to compare the measure- mentsresultswiththeresultsofcal- culationsforthedynamicangleofheel accurately,ifdeterminedbasedonthe heeling moment imposed by IMO.
Further research on the described issueshallallowexecutingmoreaccu- rateanalysis.
7. References
Dudziak,J.(2006)Teoria okrętu.Gdańsk:WM.
GrybośR.(1998)Podstawy mechaniki płynów część 2.Warszawa:PWN.
IMOInstruments(1993).Code on Intact Stability of All Types of Ships.Lon- don.
IMOInstruments(2008)International Code on Intact Stability.London.
Lewandowski,G.(2010)Badania modelowe stateczności dynamicznej okrętu projketu888 poddanego oddziaływaniu wiatru.Gdynia:AMW.
Mironiuk,W.(2006)Preliminaryresearchonstabilityofwarshipmodels.Pro- ceedings of the 9th international conference on stability of ships and ocean vehicles, 23-30September,RiodeJaneiro,brazil,pp.345-352.
Moreno,D.;Chaos,D.;Aranda,J.;Muñoz,R.;Díaz,J.M.;Dormido,S. (2009) Applicationofanaeronauticcontrolforshippathfollowing.Journal of Maritime Research. Volume6,Issue2,August,Pages71-81.
Pawłowski,M.(2004)Subdivision and damage stability of ships. Gdańsk.
PRS(2007)Przepisy klasyfikacji i budowy statków morskich, Część IV.Gdańsk.
PRS(2008)Przepisy klasyfikacji i budowy okrętów wojennych, Część IV.Gdańsk.
No. 1 2 3
Angleofheeltowardswindwardshipboard[deg] -6 -15 -18 Dynamicangleofheeldetermined
forZv=4.49m[deg] 25 32 36
Dynamicangleofheelmeasuredatstand[deg] 23 29 31
Fig.5. Determinationofdynamicanglesofheelforshipof888projecttype–forZv=6.46m.
Fig.6.Determinationofdynamicanglesofheelforshipof888projecttype–forZv=4.49m.
