SEAKEEPING BEHAVIOUR OF A FRIGATE-TYPE TRIMARAN

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1 Desgn & Operaton of Trmaran Shps, London, UK SEAKEEPNG BEHAVOUR OF A FRGATE-TYPE TRMARAN W Pastoor, Det Norske Vertas AS, Norway R van 't Veer, Martme Research nsttute Netherlands, The Netherlands E Harmsen, Royal Netherlands Navy, The Netherlands SUMMARY JUt-vpS h G2- c*\x\nl, The moton behavour of a frgate-type trmaran was studed n a jont co-operaton between the Royal Netherlands Navy (RNLN), the, Martme Research nsttute Netherlands (MARN) and Det Norske Vertas (DNV). The startng pont for the study s a seres of model tests for a frgate-type trmaran conducted at MARN. Frequency and tme-doman lnear and nonlnear hydrodynamc calculatons are valdated aganst the model tests. The overall seakeepng behavour ofthe vessel s dscussed and partcular attenton s pad to the rou moton. Parametrc rou s dscussed and test results are presented. The use of passve and actve fns to reduce the rou moton s evaluated n stem quarterng seas. The nonlnear effect on the rou motons of the ntermttent wettng of the sde hulls and the sze of the sde hull volume s evaluated. The paper ends wth a dscusson on seakeepmg and desgn load assessments for trmaran vessels. NOMENCLATURE a fol angle of attack (rad) (3 wave headng (rad) <f> roll angle (rad) y angle between horzon and lne through CoG and sde hull keel (rad) K non-dmensonal rou dampng (-) p densty (kg/m 3 ) flud potental (m/s) Af» fn area (m 2 ) A44 rou added mass (kg m 2 ) B44 roll dampng (Nms) C44 rou restorng coeffcent (Nm) C L lft coeffcent C uy eddy dampng coeffcent C 9 slammng coeffcent F force (N) 44 rou nerta (kg m 2 ) Lpp Length between perpendculars (m) K control gan for actve fn M moment (Nm) p pressure (N/m 2 ) r radus (m) S wetted area (m z ) U VR mean shp speed (m/s) vertcal relatve velocty. NTRODUCTON n the past 0 to 5 years a sgnfcant amount of research and development has been devoted to the appucaton of the trmaran concept for both navy and commercal purposes and ths has been reported n numerous puhtcatons. The trmaran looks smuar to a conventonal monohuu, as the sde-hulls are usuauy very smau. However these sde-hulls can have a sgnfcant effect on the dynamc behavour of the vessel and thus the seakeepng performance and the wave-nduced structural loads. Beng capable of usng numercal tools n the desgn phase of trmaran vessels s of great mportance n order to optmse the vessel for seakeepng performance and to develop realstc structural desgns and weght estmates. The Royal Netherlands Navy, RNLN, operates a fleet of 2 modern frgates of dfferent types wth szes fom 3300 to 6000 tons. Consequenty, there s a contnuous process of study and development nto new concepts and desgns for frgate type shps, lke SES, SWATH and trmaran vessels. Model tests play a central role n vaudatng numercal tools, they provde nsght n physcal phenomena and they are used as verfcaton of (fnal) desgn characterstcs. Developng numercal predcton tools and provdng advanced model test capabltes s key competence for the Martme Research nsttute Netherlands and have thus a long hstory of co-operaton wth the RNLN. Snce 996 has DNV developed the nonlnear shp moton and load program WASUVL t s beng used n seakeepng and desgn load assessments for au knd of vessels ncludng multhuus. VaUdatng the program and further developng the program s requred to provde relable seakeepng and wave load predctons. Ths s used n both shp specfc desgn load assessments, wth full hydrodynamc load transfer to FE models, as weu as the general development of Rules and gudelnes for shp structural desgn. Developng vaudated numercal tools and ncreasng the competence on the dynamc behavour of trmaran vessels s thus of common nterest for the RNLN, MARN and DNV. Ths formed the bass to start a cooperaton between the three companes to use trmaran model tests, [],to valdate exstng lnear and nonlnear numercal tools. The paper starts wth a summary of the model test program after whch parametrc rou, lnear and nonlnear moton predctons are dscussed. Of partcular nterest has been the rou moton and the effect of rudders, passve and actve fns. AddtonaUy the effect of a varaton of the sde hull volume above the calm water on the roll motons was nvestgated. 2004: The Royal nsttuton of Naval Archtects 9

2 Desgn & Operaton of Trmaran Shps, London, UK 2. MODEL TEST PROGRAM n October 996 the Royal Netherlands Navy commssoned MARN to carry out aresearchproject to nvestgate the hydrodynamc aspects of a trmaran. Powerng and seakeepng aspects were consdered n the test program. The test condtons were manly based on the results of the calculatons performed n advance of the tests wth a trmaran verson of a 2D lnear strptheory program, whch ndcated that large rou motons could be expected n stern quarterng seas. The man uncertantes n these calculatons were however the vscous roll dampng and assocated non-lneartes n resultng large rou motons. Varaton n huu spacng of the outrggers and appucaton of passve and actve fns were studed manly wth the am to reduce the rou motons n stem quarterng seas. mounted at 3 m from the base lne, and at mdshp locaton wth respect to the outrggers centre staton. A NACA profle wth span 4.0 m and mean chord of 2.0 m was appued. The actve fn responded wt a gan of 4 deg/deg/s to the rou velocty oftetrmaran. The twn rudders were located at about 2.7 m from the centrelne and orentated 0 degrees from vertcal pontng outwards. The rudder mean chord was 4.25 m and the span was 5.5 m so that the rudder tp was slghtly below the keel lne. The propeuer shafts were supported by V-brackets to the man hull. 2. MODEL DESCRPTON Ths paper focus on the seakeepng characterstcs ofthe bare hull (confguraton 0), the bare hull wth passve fns (confguraton ) and wth actve fns (confguraton 2). Model tests were conducted usng dfferent outrgger spacng and desgn, but these results are classfed, and the only numercal results wll be dscussed. Snce the model was free-salng n au test condtons, a twn rudder wth auto-puot was nstaued. Model tests were conducted n the former seakeepng towng tank of MARN, wth dmensons 00 by 24 meters. The research desgn measured 65.0 m Lpp prototype, and was tested to a scale of :35. The shp characterstcs are summarzed n Table. A lnes plan of the trmaran n seen n Fgure. Desgnaton Length between perpendculars [m] Breadth centre hull on waterlne [m] Draught center hull [m] Length sde hull Breadth sde hull [m] Draught sde hull [m] Poston of sde hull wrt centre hull, XfromAP Y from centre lne Dsplacement [tonnes] KG KM (man + outrggers) [m] RoUradusof gyraton (k^) [m] Ptchradusof gyraton 0%) [m] Yaw radus of gyraton (km) [m] Table Man partculars ofthe trmaran Value The stablser fns were attached to the outrggers and ponted nwards, see Fgure. They were horzontauy Fgure Bodylnes of the trmaran wth orgnal and ncreased sde-hull 2.2 MODEL TESTS Pror to model tests, seakeepng calculatons are often carred out to determne the test condtons. f such calculatons are performed wth a lnear frequency doman tool one need to be careful, snce non-lnear effects can ntroduce mportant operablty lmtatons such as parametrc rou whch wu not be predcted. f the shp speed s known, a contour plot showng the encounter frequency as a functon of headng and wave frequency can be prepared. From ths plot the worst headng wth respect to resonant roll can be depcted. Fgure 2 presents the results for the trmaran at 22 knots and wth a natural roll perod of 2 seconds. t ndcates that n stern quarterng seas wth a headng of 65 degrees resonant rou can be expected over a large range of wave frequences. At zero wave encounter frequency (the shaded area n Fgure 2) seakeepng calculatons should be dstrusted when low-frequency (vscous) dampng s not ntroduced. Therestorngforces n the horzontal plane are zero, and wth vanshng potental dampng unrealstc large yaw motons can be expected, whch most lkely wll nfluence the rou motons. The model (confguraton 0, and 2) was tested n regular stern quarterng waves of 75 and 65 degrees headng at 22 and 35 knots. The wave amputude vared from about 0.4 to.2 m, whch led to sgnfcant roll ampltudes of about 0 degrees. n beam wave condton the roll response s sgnfcantly reduced compared to stern quarterng condton, and at ths headng the model was tested n regular waves of about 2 m amputude : The Royal nsttuton ofnaval Archtects

3 Desgn & Operaton of Trmaran Shps, London, UK Natural pottd n «r U0 sf H? > >. '. ' ^ \ -, V\'\\V* \ \ '+ \ \ \ \Y ' f g DO "*. \mmmmxmmsbbsbwg3e* OS WAVE FREQUENCY r»b»] /OUJJWltt Fgure 2 Wave encounter perod as functon of headng and wave frequency at 22 knots forward speed The model was free salng n all tests and appued wth a twn rudder and propeuer arrangement ncludng an autoplot. The auto plot responded to the yaw ampltude and turnng rate, as weu as to the sway moton to keep the vessel at track n the basn. Default auto puot settngs were appued. 23 PARAMETRC ROLL A non lnear phenomenon that can occur for trmaran vessels s parametrc roll n head seas condtons. When large perodc GMt varatons occur, due to for example ptch motons, autoparametrc rou motons can be ntated. The probablty for parametrc rou s dffcult to estmate snce t s assocated wth a threshold value; below a certan wave heght the GMt varatons wu be too smau to ntate the rou motons. From past accdents wth contaner shps severe consequences are descrbed so that t should be nvestgated when relevant [2]. The aft body shape ofthe man hull has a rather Umted draught whch s prone for large stablty varatons. However, the outrggers contrbute sgnfcantly to the overau stablty and even then the manhuu experences large varatons n the wetted surface the outrggers wll prevent large parametrc rou angles, when they are not emergng out of the water. n ths respect the trmaran behaves dfferently than the monohull. When bom outrggers wll become dry n more sever sea states, loss of stablty occurs to a sgnfcant extent The man hull has a KM value of 6.4 m and wth a KG of 8.35 m the trmaran wth emergng outrggers has a negatve transverse stablty. Fgure 3 shows probable crtcal condtons for a GMt of.75 m. The contour lnes are so encounter perod lnes [s]. The fgure shows that around 9 to 5 knots parametrc rou condtons are met, consderng the stablty condton and the shp speed. The threat for stablty loss due to outrgger emergng s assocated wth the shorter waves. Table 2 presents an overvew of the model test results n dfferent condtons. The wave length assocated wth the Speed [Knots) Fgure 3 Parametrc rou n head seas s more lkely to occur when the natural perod of the wave encounter s half the natural rou perod (ths s the soud lne) combned wth large ptoh motons (shaded area "ptch") or loss of stablty due to the outrgger (shaded area "outrggers") peak ofthe spectrum n sea state 7 was 225 m, whch s the 'shortest' possble sea condton wthn the defnton of sea state 7 (sgnfcant wave heght 8 m, PM spectrum type). The tests reveal that parametrc rollng occurred to a smau extent and t s concluded that t does not mpose a severe operablty lmtaton for ths trmaran. Wave condton Sea Headng state rdegl SS5 80 SS6 80 SS7 80 SS7 0 Tp Shp speed M RoU motons rdegl St. Dev Max Max Table 2 Parametrc rou nvestgatons n rregular waves 3. NUMERCAL SMULATON 3. SHP MOTON PROGRAMS Numercal smulatons for a trmaran shp mpose addtonal requrements to the appued tool. Apart from general geometry aspects as hydrostatc propertes, the hydrodynamcs of a multhuu shp requre dedcated calculaton schemes. Strp theory calculatons are based on 2D hydrodyramc coeffcents and wth forward speed an unrealstc overpredcton of the nteracton effects between the man hull and the outrggers should be avoded. Clearly the wave exctaton experenced by the outrggers can be easuy ncluded as weu as the hydrostatc restorng terms. But snce the method s 2D, hydrodynamc nteracton effects can not be taken nto account properly. Neglectng te hydrodynamc nteracton effects s justfable by reasonng that the outrggers are small and that the pressure dstrbuton on the man hull wll not be nfluenced largely by the waves generated by the 2004: The Royal nsttuton of Naval Archtects 2

4 Desgn & Operaton of Trmaran Shps, London, UK outrggers assumng the dstance between the man hull and the outrggers s not too small and forward speed s relatvely hgh. Snce a trmaran shp s desgned to sal at hgh forward speed the hulls wu berelatvelyslender, whch s benefcal nteabove reasonng. n a 3D method the hydrodynamcs can be ncluded correctly, accountng properly for the hydrodynamc nteracton effects at dfferent speeds and headngs. The 3D lnear frequency doman seakeepng program PRECAL has been developed over the last years wthn the Co-operatve Research Shps framework of MARN. The boundary ntegral equaton s solved usng a free surface Green's functon to calculate the nfluence coeffcents between all panels on the wetted part ofthe hull. The panel code can be appued n seakeepng studes of monohulls, twnhuus and trmarans, wth or wthout takng te hydrodynamc nteracton between the dfferent hulls nto account The latter one nvolves the use of Green's functon that satsfes the exact forward speed boundary condtons. The method appued n PRECAL s the steepest-descent mplementaton, whch stll requres long calculaton tme compared to the zero forward speed Green functon. Addtonal vscous roll dampng can be ncluded based on the keda-hmeno approach [3] combned wth eddy Hampng followng Tanaka [7], or one can mplement measured vscous roll dampng data. Advanced moton control functonalty s mplemented by means of passve or actve stablzer fns and rudders. The forces on the rudders and fns are taken nto account usng a stochastc lnearsaton procedure. The lft slope s calculated based on 3D theory and emprcal data from extensve model tests seres were used accountng for the presence ofthe free-surface and hull n the vcnty of the lftng devce. The contrbutons onteflowvelocty duetothe ncdent, dffracted and radated wave are accounted for when calculatng the angle of attack ofthe fn wth the flow. The computer program DNV-WASM (prevously known as DNV-SWAN) s a 3-dmensonal tme doman program for arbtrary shaped shps (ncludng multhuus) or other marne structures n waves. The shp may have an arbtrary forward speed, the waves can come from any drecton and the responses can be computed n au sx degrees of freedom. The program s based on a three-dmensonal Rankne Panel method, where also the free surface s modeued. The steady flow around the shp s frst solved and te couplng wt the body motons n the shp moton problem s ncorporated. Radaton condtons are treated by ncludng a zone where the free surface condton s modfed such that the waves are absorbed,.e. a numercal beach on the outskrts of the free surface doman. DNV-WASM was orgjnauy developed n a co-operaton between MTT and DNV untl 996. DNV- WASM can be run n both a fuuy lnear mode and n a non-lnear mode. Transfer functons are derved from lnear computatons by harmonc analyss of output tme seres. The mplemented non-lnear opton solves the radaton and dffracton problem stul n a lnear way. The Froude-Krylov and hydrostatc forces are calculated by ntegraton of the ncdent wave pressure over the nstantaneous wetted surface of the hull and gves thus a nonlnear contrbuton. Ths nstantaneous wetted surface can be defned by the nstantaneous poston and orentaton ofthe shp n the ncdent wave or the dsturbed wave profle, whch s bult up by the ncdent waves and the radated and tuffracted waves. Rudders and fns can be added both passve or actvely controued. Vscous dampng can be specfed as an addtonal lnear or nonlnear dampng term, the latter s then gven as a lnear functon ofthe rou amputude. The moton equatons are solved n an Euleran frame thus auowng for large amputude motons. The ncdent waves are modeued accordng to lnear wave theory. rregular waves both long and short-crested can be smulated. The ncluded non-uneartes can gve sgnfcant contrbutons to both global loads and motons n large waves. Further developments of the program nclude slammng and hull flexblty analyss,.e. whppng and sprngng. More detals on the slammng ntegraton are gven paragraph AppUcaton of a tme doman code gves the opportunty to nclude the non-lnear effect of the stablzer fns drectly nto the moton equatons, and to account for the non-lnear hydrostatcs and wave exctaton forces. However, for large ampltude rou motons or hgh forward speed t wll be dffcult to account properly for au hydrrxrynamc fn effects whch become mportant, such as stall due to large angles of attack, cavtaton due to hghforwardspeed or ventlaton due to the nfluence of the free-surface, see [4]. Current state-of-art knowledge s not suffcent to model au aspects correctly for a new desgn. But, usng tme doman smulatons, n combnaton wt lnear frequency doman results and, above au, model test data can provde detaued understandng of the hydrodynamc aspects nvolved n trmaran analyss. 3.2 LNEAR SHP MOTON ANALYSS Fgure 4 presents the heave and ptch RAO n head seas at 22 knots. The model tests were performed n sea state 5. The calculated results compare weu wth the model tests. The ptch resonant response occurs around 0.6 rad/s, assocated wth the natural ptch perod n water determned by restorng, mass nerta and added mass nerta. The rou moton behavour n stern quarterng seas depends on the predcton of the vscous rou dampng snce rou resonant condtons are encounter as concluded from Fgure 2. n PRECAL the emprcal rou dampng method of Bceda- Hmeno-Tanaka s ncluded [3]. Ths method was based on rou dampng data for monohulls and mght not be apptcable for fast salng trmarans. However, no other : The Royal nsttuton ofnaval Archtects

5 Desgn & Operaton of Trmaran Shps, London, UK Pnca Pajaree nostra o * Pccal - Actve racttra + * E*&-Acfcv*HHKfeft V.4 fr* f frt t? ) WAVE FFEQUBtCf Halre)! a BG Sfl WAVE FREQUENCY lnk*sj Fgure 4 Heave and ptch response n head seas condton, 22 knots dampng data than based on model test results was avalable. The keda Hmeno rou dampng for a shp wthout blge keels results n manly lft dampng and eddy dampng, of whch the lft dampng ofthe man hull s most mportant Other mportant rou Hampng contrbutons wll be due to actve or passve fns, or due to the rudder actvty. The rudders on the trmaran wll respond to the yaw motons to keep the vessel on ts track and course, but the forces on te rudder wll lead to a rou moment as weu. When the rudder actons ncrease n stern quarterng seas, tns effect wll be more and more vsble n the rou response amputude operator. Fgure 5 presents the PRECAL calculated results wth passve and actve rudders and the model test data. Default auto plot coeffcents were used of 8 deg/(deg/s) yaw rate, and 4 deg/deg yaw; no realstc rudder actuator coeffcents were known or reported. The results show the effect ofthe actve rudder on the RAO's, whch are closer to the measured data whch nclude actve rudders as weu. Wth actve rudders the yaw motons decrease and rou motons ncrease, but n absolute sense the dfference (n yaw response) s small. The moton response n the vertcal plane s hardly nfluenced. n the physcal tests effects lke lft dampng of the outrggers and vscous rou dampng due to yaw motons wu be present whch are not ncluded n PRECAL. Thus t was not expected to obtan an exceuent agreement wt te model test. However, the results so far ndcate tat wth a lnear potental seakeepng program trmaran motons can be reasonably weu predcted. A comparson between te model tests and lnear PRECAL calculatons s shown n Fgure 6 for 65 deg headng (from the stern) and 22 knots forward speed. The trend n the rou moton response usng passve or actve fns agrees weu wth the model test data. The span ofthe fns was setto 2.0 m n the PRECAL calculatons whch lead to a lft slope of 2.28 /rad. The model test results ndcate a somewhat lower lft slope snce rou motons are slghtly larger. The effect of the hull on the fn lft HAVE f aeolsmtwjwhs WAVE FREQUEHCrrctlfel Fgure 5 Moton response from model tests (regular waves) and PRECAL calculatons wth passve and actve rudders for 22 knots n headng 65 degrees slope s dffcult to estabush. The PRECAL mplementaton s based on a fn near a shp hull, whch ncreases the effectve spaa The outrggers are smau and the tns are located near the keel lne, so the actual span of the fn (4.0 m) wll ntroduce a too large effectve fn. The effect on the rou motons s sgnfcant; wth 4.0 m span the roll motons wth fns reduce a factor 2. The model test where performed n waves of about 0.5 m amputude, so that the rou angles were about 0 deg. Such rou motons wll ntroduce large angles of attack on the fns, and f ventlaton and or stau occur, the lft slope wll be less than n the PRECAL calculatons whch neglect these effects. Lnear calculatons were conducted wth the DNV WASM program usng passve rudders for 22 knots n 65 degrees headng. The moton transfer functons are shown n fgure 7 and are smlar to the results obtaned wth the PRECAL code. Most devatons occur for the sway and the yaw moton, whch of course are most affected by the rudder control n the model tests. 2004: The Royal nsttuton of Naval Archtects 23

6 Desgn & Operaton of Trmaran Shps, London, UK B-expnofns -*- Exp Passve fns -"-Precalnofns - Preca! Passve 6ns 25- -A- Exp Actve fns -*- Preca! Actve fns a j 0,0 ( ^r^- / --^r!?%t'"''v objectve s to evaluate the effect of the varous components. Wth the man huu beng slender and notfttedwth blge keels the man rou dampng part ofthe hull s assumed to be wave dampng, eddy dampng from the sde hulls, rudder dampng and sde-hull fn dampng. n the subsequent secton the effects of these contrbutons are dscussed and evaluated by nonlnear calculatons. No varatons of wave dampng are studed, but the volume ofthe sde hull above the stll water level s vared. 3.3(a) Eddy dampng Wav«Frequency [recte] Fgure 6: RoUresponsewth no fns, passve and actve fns. Fn span nput s 2.0 m n PRECAL JF *- The work by Zhang and Andrews [5] predcted that eddy dampng s the man contrbuton to the roll dampng together wt appendage dampng for ther trmaran desgn. The eddy dampng was determned vsng the model as proposed by Schmfke [6] based on the work from Tanaka [7]. The latter conducted roll experments wth varous shp sectons to assess the effect of secton shape on eddy-makng rou dampng. The roll resstng force s expressed as, 5 f Tt r ^ a e 0.7 OS. 3 F^prtfsC, eddy () Takng the rou centre at the centre of gravty and decomposng the force, the rou resstng moment s wrtten as, M ^^prjsmrfscvuy =B Mjd p 2 (2) »fcm n.) M a.7 ea Mm***quMuy[r Fgure 7 Moton response from model tests (regular waves) and lnear WASM calculatons wth passve rudders for 22 knots n headng 65 degrees 3.3 NONLNEAR ROLL MOTON ANALYSS RoU dampng s an mportant aspect n seakeepng predctons and assessments and for a trmaran no valdated predcton tools are present n general the rou dampng conssts of wave dampng, skn frcton dampng, eddy dampng, bare hull lft dampng and appendage dampng. n the present paper no attempt s made to develop vaudated predcton methods for the varous components. nstead, exstng methods are used orreformulatedand appued for ths trmaran case. The The estmaton of the coeffcent C eddy depends on the secton shape and s a rather uncertan factor to estmate. Secondly, the effect of the flud veloctes due to the ncdent and dsturbed waves s not consdered, only the roll moton nducedrelatvevelocty at the blges or keel s taken nto account Ths model s used here as well but no attempt s made to predct the eddy dampng as accurately as possble but nstead a lower and upper value were estmate for the eddy coeffcent, resultng n two dampng values, whch are used to evaluate the nfluence on the roll motons. n the DNV-WASM program the vscous roll dampng can be added by usng a non-dmensonal dampng curve as a functon ofthe rou amputude, Here K s a non-dmensonal dampng gven by, (3) B K = (4) 2^/44 + AU )C M : The Royal nsttuton ofnaval Archtects

7 Desgn & Operaton of Trmaran Shps, London, UK Wth the roll dampng formulaton n equaton 2 and the estmated upper and lower values for C^, two K curves are obtaned, wth K 2 =0.005, K and K X = 0.0. When usng both K curves n a nonunear DNV WASM analyss the rou amputude RAOs are derved and shown n fgure 8. As seen the varaton of the rou response vares from a few percent up to 20%, manly due to dfferent rol veloctes, encounter frequences and a tme dependent added mass formulaton' n DNV WASM. n the lemanng calculatons ofthe paper tc 2 was set to M : '-T- AUUSM UD0M L*._ L*- * * t - *., * " ft -4-. L [ A +" * % +! * 4 *. * * t L l + t, L l > r~ ' ' " f --+ > l_ q» too Wm«aquancy[*tt! Fgure 9 WASM frst harmonc RAOs wth two sets of autopuot gans, 35kn 75 degrees 3.3 (c) Passve and actve fns The modellng of a stabtsng fn n the DNV WASM program s done by a lft formulaton, M'^Q^pt/^XO (6) «<LS.0. t.».4 Fgure 8 Eddy dampng varaton on WASM frst harmonc RAO, 22kn 65 degrees 3.3 (b) Autoplot model The model was self propeued wth rudders actng on an autoplot. The exact settngs of the autopuot gans were not reported. The DNV WASM calculatons are most often conducted wth an autopuot model based on an ordnary PD type controuen Sfy^kflr + kw (5) The values ofthe gan coeffcents are of arbtrary choce as usuauy no specfc values are avalable for the vessel under nvestgaton. Fgure 9 demonstrates that the effect of the gans on the rou motons s sgnfcant. Two dfferent set of gans wth both stable autoplot settngs gave an average dfference of 5%. f the autopuot model s extended wth a proportonal sway term the effect can even be larger dependng on the moton reference pont as rou contrbutes to the sway moton. The comparson between DNV WASM and te model tests for ths 35 knots case s not as good as for the 22 knots case of fgure 8. Possbly the sde hulls, beng very slender, gve extra rou dampng by actng as low aspectrato wngs upon asymmetrc nflow due to occurrng drft angles and sway and yaw motons. Secondly, the average number of measured oscllatons for the tests at 35 knots was just 4, whue for the 22 knots case ths was over 9 gvng morerelable harmonc results. Here a s the angle of attack, whch s determned by the relatve velocty normal to the lftng surface. n case of actve fn control te demand angle s determned by a control model. n the present calculatons a smple term proportonal to rou velocty s used, a^,{t) = K j(t) wth K = 4 deg/ deg/ s The Uft coeffcent s user nput and t s a rather dffcult task to select a value as a lot of aspects have an nfluence on the fn performance: Profle thckness Aspect rato Fn submergence BUge radus Boundary layer thckness Fn hull nteracton Fn oscuaton (Theodorsen functon) The fns were defned by a NACA profle wth a 2D Uft coeffcent of n the nnetes a 3 years R&D project was carred out by the MARN Co operatve Research Shps programme on moton control of shps, [8]. Based on ths work, an estmate has been made ofthe lft coeffcent, compensatng for the effects as lsted above. However the present fn confguraton s not easly comparable wt fns nstaued at the buges of ordnary shps. When takng the aspect rato as s/c or 2s/c (based on the actual dmenson, or assumng the hull as an end plate) the estmated lft coeffcent vares from 2.2 to 3.2. An average of 2.7 was used n the DNV WASM calculatons. (7) 2004: The Royal nsttuton of Naval Archtects 25

8 Desgn & Operaton of Trmaran Shps, London, UK n fgure 0 the rou moton RAOs are shown for the vessel salng at 22 knots n 65 degrees waves. Good predctons are obtaned for the bare hull and the hull ftted wth passve fns. An under predcton of 30% s seen for the actve fn modellng. n the WASM calculatons no delay was modeued for the behavour of the actve fns, to what extent a delay was present n the model tests s unknown. n contrast to the lnear predctons shown earler a nonlnear smulaton does capture the trend n the model test results. The two clear response peaks are weu predcted. Why the results for the actve fns are not as good as the passve fns s not known. The nteracton between the huu and the fns can possbly be mportant. Van Walree [9] has shown that the nteracton between the hull and control surfaces can be large. f mportant, ths would recjure a modfcaton of the DNV WASM program to nclude a lftng surface model n the boundary value problem. For the regular tests at 22 knots n stern waves from 65 degrees tns hull form was smulated wth WASM and the rou moton RAO s shown n fgure t A- 0' <y A' rv' * ~ - r -,* l --- l l l - r _ - r - ~ r " r _ tav*%9mnqrfhjfoj - -Exp. -*-WAaw. amm «fc hub * WASW-l»9>H*hl*«. - rv\- r ^L-*\ V \ +" -4, \ * ". * W Fgure Nonlnear WASM frst harmonc RAOS, 22kn 65 degrees The ncrease of the sde hull volume clearly shows a reducton of the rou moton ampltudes. The beneft s however small for wave frequences around rad/s. For these wave frequences the correspondng wave length s about twce the shp's beam. t then happens that one sde hull s wetted n a wave crest whle the other s dry or nearly dry n an opposte wave trough not gvng any restorng or dampng effect A snapshot of ths moment s shown nfgure 2. Wnh««vl^ Fgure 0 WASM frst harmoncs RAOs, 22kn 65 degrees, wthout and wth passve and actve sde huu fns 3.3 (d) Varyng sde hull volume The model test program used a prelmnary trmaran desgn wth sde hulls beng very slender up to the cross deck structure. An actual desgn wll most lkely have more volume n the above water part for proper load transfer between the sde hull and cross deck structure and for other reasons based on stablty or desgn characterstcs. n a later model test seres, the present hullform was tested wth sde hulls havng more volume above the stll water level Although ths provdes a sgnfcant ncrease of the GZ stablty curve, a sgnfcant ncrease of te roll moton was observed. Apparently the wave exctaton on the sde hulls, nducng rou motons, can be domnant over the restorng and dampng effect due to the extra volume. f analysng the moton behavour of a trmaran wth a nonlnear seakeepng tool such a phenomenon can be quantfed. No detaled data was avalable of the actual hullform wth ncreased sde hull volume, therefore a modfed hullform was developed as part of ths study, see fgure. Fgure 2 WASM Snapshot of trmaran wth ncreased sde hull volume, headng=75deg from the stern,,=.02, COFO.90 rad/s Wth the headng changng more towards beam seas the effect becomes more pronounced as fgure 3 shows for 75 degrees headng. Around.0 rad/s almost a doublng ofthe rou moton s calculated : The Royal nsttuton of Naval Archtects

9 Desgn & Operaton of Trmaran Shps, London, UK * A ' -'* - -Bq -*-WAHM - «Wml M Ml ' - - WfWM'lngaaMahJb /%.... ^q^u..:! OM O.W " wjau JS fl TO J0,jB * Fgure 3 Nonlnear WASM frst harmonc RAOs, 22kn 75 degrees 3.3 (e) A nonlnear dampng model n DNV WASM An addtonal opton n the DNV WASM code s to nclude slammng loads. A pre process calculaton s then conducted for a set of 2 dmensonal strps of the hull usng a 2D BEM program, developed by Skee and Helmers [0], as part of the MARN Co operatve Research Shps programme []. The theory of ths program s based on work carred out at NTNU n Trondhem ncludng verfcaton by experments, see [2]. The results from the 2D BEM program are subsequently used n the nonlnear WASM smulaton. Thus nonlnear contrbutons for dampng and added mass are ncorporated for te *above stu water part\ Thetotal pressure s then formulated as, p(x,t) = /> V R V(x,h)+ pc, (x,h)vj (8) Here the nvarant potental soluton and the slammng coeffcent are only functons ofthe poston on the hull and the mmerson depth. Durng the WASM smulaton the relatve veloctes and the mmerson ofthe secton n the wave are calculated. The slammng coeffcents and the potental solutons are extracted from the slammng database and the pressure s calculated and mapped on the panel model. Experence has shown that some nonlnear smulatons wth only the Froude Krylov and hydrostatcs as nonlnear components show unrealstc shp moton behavour as the moton behavour lacks an amount of nonlnear dampng. Sometmes ths behavour can be charactersed by a "chttd on a trampolne" as the nonlnear Froude Krylov and hydrostatc term are sprng terms and nsuffcent dampng s present n the dynamc system. Experence wth the ntegrated slammng has shown that for cases where no slarnmng occurs ths model can gve an mproved moton behavour of the vessel as t adds nonlnear dampng to the moton equatons. Ths model s used here for the sde huus to add nonlnear dampng due to the ntermttent wettng of sde hulls. When evaluatng the results, only a few percent less rou amputudes are obtaned and thus rrelevant to show n an addtonal fgure. As the encounter frequency s rather large, above 9 seconds, the veloctes are too small to cause any substantal nonlnear dampng due to the sde hulls. 3.3.(?) Summarsng dscusson The calculatons n the prevous paragraphs show that lnear and nonlnear calculatons can predct the motons of a trmaran vessel weu. The rou motons as observed n te tests were large and for dstnct headng and wave length very large. RoU moton control s thus of paramount mportance for a trmaran vessel. The model tests and calculatons proved that the actve use of rou dampng fns gave the largest reducton of the rou motons. ncreasng the volume of the sde hulls can reduce the rou motons n some condtons whle t can ncrease t at other dstnct headngs and wave perod combnatons. n addton to te use of sde hull fns are other Uft devces possble, lke T fols or fols extendng from the man hull to te sde hull. The work by Grafton, see [3], addresses these dfferent confguratons as well as varatons n the dmensons and aspect ratos. Ths s of mportance for mproved modellng of Uft devces n numercal shp moton predctons for trmaran vessels. 4. MOTON AND LOAD ASSESSMENT The fnal goal wth numercal smulatons of trmaran motons and loads s to support the desgn of these vessels, to provde suffcent documentaton to prevent the rsk of volent motons, to optmse the seakeepng performance and to provde relable predctons of structural desgn loads. Based on the prevous studes a dscusson on the applcaton of lnear and nonlnear snp moton analyss s gven for both seakeepng and wave load studes as part of a trmaran desgn development 4. SEAKEEPNG PERFORMANCE ASSESSMENT EspecaUy n case of a combatant trmaran development the seakeepng behavour s an mportant aspect, as the performance or avalablty of sensors, weapons or personnel deterorates wth ncreasng motons. n an early stage crtcal response characterstcs are to be dentfed and properly addressed n order to optmse the seakeepng behavour. As shown n the paper a lnear shp moton tool can assst n ts process. RoU stablsng fns can provde a sgnfcant reducton n rou motons and good results were obtaned wth the modellng of these devces n Lnear shp moton analyses. Nonlnear predcton tools can provde addtonal predctons for phenomena not captured n lnear theory. EspecaUy the sde hull volume above the calm water level showed to have a surprsngly large nfluence on the rou moton response. ncreasng the sde hull volume gves ncreased statc stablty however for dstnct headngs and wave lengths the ntermttent wettng ofthe sde hulls shows a domnant behavour of the roll exctaton gvng a sgnfcant ncrease of rou motons. 2004: The Royal nsttuton of Naval Archtects 27

10 Desgn & Operaton of Trmaran Shps, London, UK Seakeepng operablty studes are often conducted and usuauy based on lnear shp moton results. Further studes nto the rou moton predctons should evaluate to what extent lnear shp moton theory can be appued n a seakeepng operablty assessment dependng on the actual sde hull confguraton. Nonlnear smulatons are very tme consumng for the smulaton and postprocessng of a complete scatter dagram for all relevant headng and speed combnatons. 4.2 DESGN LOAD ASSESSMENT Consderng the predcton of desgn loads more gudance s avalable on how to apply nonlnear predcton tools and ths s necessary as no rules for trmaran vessels are avalable. DNV provdes a separate chapter on "Drect Calculaton Methods" n the Hgh Speed Lght Craft Rules. As there are no rules avalable for trmarans t s recommended that a trmaran wll have to be evaluated fouowng a so-called "level 3- alternatve rule analyss". Nonlnear hydrodynamc analyses are then requred wth load transfer to a FE model for structural strength analyss. A prncpal ssue for hgh speed craft s the use of a speed/sea state curve descrbng the maxmum operatonal lmts of the vessel. Ths speed/sea state curve forms the bass of te nonlnear load assessments. A pror t s not known, whch speed/sea state combnaton s most crtcal nor whch wave perod gves worst responses. For some vessels/responses a lnear shp moton and load analyss can be suffcent to dentfy the worst headng, speed and sea state combnatons, whch s subsequently used n a nonlnear desgn load analyss. However n case of unknown behavour or sgnfcant nonlnear responses t s advsed to perform a nonlnear analyss to dentfy the most crtcal sea state, whch serves then as desgn sea state. Preferably rregular nonlnear analyses are conducted and used to derve the load statstcs from the tme seres, from whch expected extremes n 3 hours can be estmated. The appucaton of a regular desgn wave approach s to be Umted to cases, where ths has proven to be relable;tn'ss not the case for a trmaran vessel. t s mportant to conduct the rregular smulaton suffcently long for relable statstcal post-processng; any extrapolaton s preferably to be avoded. Most often the shp crew estmates the wave heghts by vsual observatons, whch ntroduces an uncertanty wth respect to the operatonal lmts set by the speed/sea state curve. n addton the desgn sea state mght be encountered more often durng the lfetme ofthe vessel. Consequently, the determned expected extreme n 3 hours cannot serve drectly as bass for the structural desgn. Based on experence and studes a safety margn s therefore ntroduced, by demandng a desgn value at % exceedance ofthe extreme probablty curve. n case of a lnear response process ths would mply a safety factor of approxmately.25 on top of the expected extreme n 3 hours. Ths factor s adopted for nonlnear responses a weu. The use of ths drect load procedure s weu-estabushed over the years and supported by operatonal experence and measurements. However the needs are changng and future developments are lkely on several areas. Frst of au DNV s amng at the development ofrskbased rules andtsaffects the drect load procedures as weu. More attenton should then be focused on the statstcal dstrbutons of both the extreme loads and the ultmate capacty n combnaton wth acceptance crtera. Secondly, the use of a speed/sea state curve sratherarbtrary and perhaps can be replaced n the future by drectly accountng for the operator behavour n wave load analyses. EspecaUy n case of an unusual shp lke the trmaran, where comparatve data s lackng a speed/sea state curve s dffcult to specfy. A procedure to account drectly for the operator behavour n severe weather s then preferred and a summary s gven hereafter. 4.2 (a) Shp behavour assessment usng realstc operatonal profles At MARN smulatng realstc operatonal behavour s conducted to provde desgn assstance and decson support for desgners and owners. Ths technque evaluates the progress of a shp on ts route on the bass of hstorcal wnd-wave nformaton. The results gve a detaled nsght nto the nature of fuel consumpton, effcent salng strateges and the rsk of exceedng a target trp duraton, see DaUnga [5]. At DNV puot studes have been conducted to evaluate desgn load analyses usng reaustc operatonal profles, see Pastoor [4]. The bass ofthe procedure s to defne shp response crtera and defne envronmental and operatonal condtons such tat these crtera are not exceeded. The fouowng steps are then fouowed: a. Defne crtcal responses Defne whch responses are used by the crew to change headng and or speed,forexample: - Green water on over the bow or the cross deck - Slammng on the cross deck - Sde hull emergence - Etc. b. Defne response crtera Crtera values are avalable for many responses and are used n seakeepng performance assessments. Consequently these can be used as a startng pont. Another opton s to use "expert opnon" from shp crews. c. Defne operator actons A defnton s necessary on what actons shp personnel take. These actons depend not only on the prmary parameters,.e. responses, speed and headng, but also on secondary aspects lke a possble delay on the voyage tme schedule, possble manoeuvrng restrctons, etc : The Royal nsttuton ofnaval Archtects

11 Desgn & Operaton of Trmaran Shps, London, UK d. Varaton study of crtera values As the response crtera are most questonable they should be vared from low to large values n order to nvestgate there effect. Such results provde addtonal nformaton to make proper choces for the crtera values. Even better would be to model the crtera as uncertan quanttes wth a probablstc descrpton. A smple approach would be to consult a group of experts to defne a "maxmum crteron value" and a "mnmum crteron value" and use these to develop a standard normal dstrbuton.'n ths way the uncertanty of the crtera values can be evaluated ntermsof desgn load varatons, whch n turn helps to evaluate whether approprate crtera values can be selected or not 5. CONCLUSONS A summary s presented of model tests conducted wth a frgate type trmaran. Man attenton has been gven to the rou moton behavour. Both lnear and nonlnear shp moton calculatons have been conducted to valdate the numercal tools. These calculatons showed that lnear and nonlnear predctons gve good comparsons wth model test results and can thus be used n trmaran desgn and desgn load assessments. Large rou motons were observed n the model testng and ths needs to be addressed properly n the desgn process to acheve an acceptable level of rou motons. Lft devces seem most promsng andreasonabletogood predctons were made wth the shp moton programs. However te modellng of the lft behavour s an ssue, whch needs to be addressed further as the fn confguraton and local flow behavour on a trmaran sde hull s not drectly comparable to conventonal blge keel mounted fns. n addton t s expected that the sde hull can gve addtonal roll dampng as t s very slender and asymmetrc flow occurs when havng a drft angle. t was shown that the sde hull volume above the calm water level can have a sgnfcant effect on the rou motons, changng the condtons were and extreme response occurs. For wave lengths n the order of twce the shp's beam the rou exctaton s a domnant factor as te sde hulls are opposte wet or dry. Further model testng wth varyng lft devces and sde hull varatons are recommended to ncrease the knowledge on the physcs of these phenomena and ther effects on the rou moton. Secondly, t s desrable to further develop calculaton schemes for lftng devces and nonlnear exctaton and dampng for mplementaton n shp moton programs. A dscusson on the appucaton of these tools for trmaran seakeepng and wave load assessments completes ths paper. 6. ACKNOWLEDGEMENTS The authors would lke to express ther grattude to the Royal Netherlands Navy for the permsson to use and publsh the model test data. 7. REFERENCES. FEKEMA, G.J., 'Seakeepng tests for a 65m trmaran', MARN report no ZT, Vol. & t, LEVADOU, M., PALAZ2J, L. 'Assessment of operatonal rsks of parametrc rou', Proceedngs of World Martme Technology Conference, SNAME, KEDA, Y., HMENO, Y., TANAKA, N., 'A predcton method for shp rollng', Techncal report 00405, Department of Naval Archtecture, Unversty of Osaka Prefecture, Japan, GAUARDE, G. 'Dynamc stau and cavtaton of stablser fns and ther nfluence on the shp behavour', Proceedngs of the FAST conference, Napels, ZHANG, J.W., ANDREWS, DJ. 'RoU dampng characterstcs of a trmaran dsplacement shp', nternatonal Shpbuldng progress, Vol 46, no. 448, SCHMTKE, R.T., 'Shp sway,rouand yaw motons n obuque seas', SNAME Transactons, Vol. 86, TANAKA, N. 'A study on the bflge keels (Part 4 - on the eddy makng resstance to the rollng of a shp hull', Journal ofthe Socety of Naval Archtects of Japan, Vol. 09, DALLNGA, R.P., DOEVEREN, A.G. van, 'CRS Moton Control: Physcs of fn stablzers - emprcal model of lft and drag', MARN Report no OE, WALREE, F. van, 'Development, vaudaton and appucaton of a tme doman seakeepng method for hgh speed craft wth a rde control system', 24* Symposum on Naval Hydrodynamcs, Fukuoka, Japan, July SKEE, G., HELMERS, J.B. (999) 'Slarnmng n SWAN - usng 2DBEM as a pre-processor', Techncal report no (nternal), Det Norske Vertas.. SKEE, G., KVALSVOLD, J., NESTEGARD, A., 'Computer program CRSLAM for predcton of slammng pressures', Techncal report no , Det Norske Vertas, : The Royal nsttuton of Naval Archtects 29

12 Desgn & Operaton of Trmaran Shps, London, UK 2. ZHAO, R., FALTTNSEN, O., AARSNES, J.V. 'Water entry of arbtrary two dmensonal sectons wth and wthout flow separaton', Proceedngs, 2th symposum on Naval Hydrodynamcs, Trondhem, Norway, GRAFTON, T., "The trmaran concept and trmaran roll dampng', Presentaton held at the London branch ofthe RNA, PASTOOR, W. 'Ratonal determnaton of nonlnear desgn loads for advanced vessels', Proceedngs of the FAST conference, Napels, [5] DAUNGA, R.P., DAALEN E.F.G. van, 'Desgn for servce', MTA Conference, October 2003, Rotterdam 8. AUTHORS BOGRAPHY Wouter Pastoor Ph.D. s workng as a senor engneer at Det Norske Vertas. He s workng on R&D projects to mprove predcton and assessment methods for shp motons and loads for both fatgue, ultmate loadng and seakeepng assessments. Other actvtes are concentrated on consultancy studes on behalf of clents and DNV Classfcaton. Raan van ' t Veer PhJD, s workng as project manager n te seakeepng group at the Martme Research nsttute Netherlands. After graduaton at Delft Unversty on hydrocrynamcs of catamarans, hs PhD work was devoted to the same topc (998). Currently he s nvolved n many research projects on advanced seakeepng and damage stablty ssues. Hs work combnes model testng and numercal developments. Eelco Harmsen M.Sc s workng n the hydrodynamcs group of the department MUtary Martme Technology ofthe Royal Netherlands Navy : The Royal nsttuton of Naval Archtects

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