Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Modern Seakeeping Computations for Ships
Modern Seakeeping Computations for Ships
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, finik depfh in fhe litk ~ als, md validation md vesificatimm ot codes tm eheme motions I INTRODUCTION Modesn seakeping computations ate used in all asp t ot engineedng tm fhe maine envi~omment They have become a t mda~d d sign k ol; fhey a~e used m sim ulatms; md they a~e used op ~ationally k p edict fhe motiom ot a vessel in ~eal time Mode~n seakep ing computations a~e p ~tmmed usmg a wide va~iety ot techmique fimm simple ship fhemy k ehemely com pie tully mmnlmea~ mmste dy RANS computations To cove~ all asp t w uld ~equue a book, mmt a shmt p~ p ~ Cunsequendy, we a~e going k limit the discus sion to ships at tmwa~d ped This la~gely elimmak s my discussion ot fhe computational k hmiques dewel op d by fhe ottshme oil mdushy in mdez k compuk wave loads md motions ot ottshme st~uctu~e We do mmt w mt k minimie the conhibutions ot the ottshme 1 ind st y which have been subst mtial (some might even a~gue fhat mmdezn computational techmiques have been dkiven by fhe neds ot the ottshme indust~y) , but the to cus ot fhis symp smm is naval hydkodynamics with it emphasis on ships at tmwa~d sped Modesn seakeping computations a~e t'a~ fiom a m~ tu~e engmeedng science Theze a~e seve~al asp ts to ship seakeepmg that m kc it one ot th mo t challeng img p oblems in fhe madne hydkodynamics field it has all fhe compleities ot wave ~esistance m maneuvezmg p oblems wifh fhe addition ot unsteadmess due to in i dent waves The ultimate goal, ot cuut se, is a unified th~ my ot ~ei tance, maneuvezmg, md seakeping Hisk ~i cally md tm a vaiety ot ~esons, each ot the fields have dewelop d indep ndently At p esent fhey a~e till sep~ ~ ated md it will p obably be twenty yea~s betme compu tations a~e huly unified Unto tunak Iy, deign p oblems will mmt wait md designezs a~e constmdy pushing tm bette~ computations in this pape~, we w mt k summ~ ~ie fhe p esent state~t fhe at in seakeeping comput~ tions md then p mt out mym ~eseawh issues fhat ned to be addkessed The mym ditficulties m seakeeping cumputations a~e the mmnlmeadties Theze a~e mmnlmea~ities associ at d with the fiuid in fhe tmm ot viscosity md fhe ve locity squaed te~ms in the p essu~e equation The t~ee su~tace c mses mmnline behavim due k th nat ~e ot the fiee su~tace bounda~y cunditions md the mmnlinea behavim ot fhe mcident waves Finally, fhe body geom eby otkn cmse mmnlmea~ hydkostatic ~esk~mg tmces mdmmnline behavim atthebody/fiee su~taceink~sec tion Ime The only good news is that bee mse ot tmwad sped ships kndto be long md slendez with smmothva~i ations along theu lengfh This geome~ic teatu~e ot typ ical ships is the basis ot m my app ozimations that have allowed a signific mt amount ot p ogtess to dak Recendy, seakeping computations tm ships op ating m fhe littmaMegion have become ot ink ~e t Ot shme computations ae ofien done m finik depfh, but it is ummsual tm ships Most themie md computations have been tm infinik Iy deep wak ~ M my themies could be exknded k finik depfh in a ~elatively shaighffmwad mame~ Fm eample, ~eplacing the deep wak~ Gteen tunction wifh a finite depfh G~en tun tion c m exk nd
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ot 6he desued ~esp nse in othes fields, the RAO is ofien called 6he hans6 fi n tion m the Imea~ sysk m fi n tion At my smgle fiequ~cy, 6he RAO is the amplitude md phase ot the desued ~esp nse to ~egula~ in ident waves actmg on the vessel at the given t~equency In mdez k use 6he St D nis md Piezson app oach, the mput wave sp tmm md 6he RAO's tm 6he vessel must be known Havmg good wave spechal mtmmation is mitical m mdez to obtain good ship ~esponse e timak s Naval a~chik ts usually ~ely on ocea~mg~aphezs k p o vid thismtmmation mdmmch~eseawhhasbeendon in the aea New sak llik ha~king k hmiques a~e bemg d~ velop d 6hat will allow ~eal time wave sp hal e timak s tm my p int in the oce~m Bee mse ot limit d space, we will mmt discuss wave sp ha m this ~ewiew; it will be as sumed that the necessa~y wave specha md m wave time hi tmies ae available The RAO's c m be det ~mmed eithes exp ~ imentally m malytically Almmst all ot the malytic wmk has n glect d viscosity md used p t ntial fiow Ezoept tm some empi~ical viscuus cm~ections, seakeepmg compu tations have all been p kntial fiow until app ozimat Iy th la t five yea~s The 1950's saw the stat ot the d~ velopment ot malytic p ediction t hmiques The fi~ t th ~ies built on 6he 6hin ship app ozimation ot Michell (IS98) The thm ship app ozimation assumes that 6he beam ot th ship is smalHelative k the leng6h md dEafi The 6hin ship app ozimation was exammed mitically by Pek~s mdSkkez(1957)
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butthe~ e also sume mt g al k~ms ove~ 6he t~ee su~ tace that make cwaluation ot 6he Ogilvie Tuck coetfi cients ve y ditficult to cumpuk The ~ational app oach to ship 6hemy alsu mvolves ch mges in the tmmulation tm 6he ditfiaction excitmg tmces Bee mse ot the high t~equency (sho t wavelength) ot 6he incident waves, 6he ditfi action p t ntial is mm lomgez slowly va~ying along 6he ship leng6h A solution must be sought as a p od et ot a highly oscillak ~y longit dinal tunction times a slowly va~ymg solution ot the Helmholtz equation T~oesch (1976)
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mWu,eta (1996) These methods have significamtly mm~e unknow s, but the m~ hiz that mu t be in~t d is ve y spase The k tal com putational ettmt amd accu~acy ot the solution ~elaive to pa~el methods d~ends on 6he detals ot 6he code The Neumam Kelvin app oach was fi~st used by the ottshme ind st y sir~e ship theo y could mmt p s sibly wmk fi 6he vessel geomet y typically used in the expimation amd p oduction ot ottshme oil a d gas The miginal codes used lowes mdez pa~el medhods amd the ze~o speed, t~ tace Gkeen tunction m the t~— quency domain Seweza commezcial codes ae avail able, the fi~st p obably being Gadson (197S)
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, md Huamg md Sclavoumms (199S) have used this method m the SWAN 2 cude Both 6he body exact amd weak scak ~ app oaches to seakeepmg computations heat the body bounday cun dition p op ~Iy, but 6he t~ee smta~e bounday co dition has been "linea~ized" m some sense A thud altesnative is to keep 6he tully mmnlinea t~ee smta~e bounday cun ditions Fully mmnlmea computations cam te p ~tmmed in a va iety ot ways Fm sk ady tmwad motion, am ik ~ ative p ocedu~e c m be used in which 6he bounday cun ditions ae initially applied on 6he calm wak ~ pla~e amd the solution ik~at d u til the tully mmnlmea conditions ae satisfied on the exact t~ee su~tace C nve~gence ot the it ~ation p ocedu~e cam te a p oblem but successfi I solutions have be~ obtamed by ammng odhezs Jensen, et al ( I 9S9)
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This is a n w a~ea ot ~eseawh md ~esults a~e just statmg k be p esent d (et Wilsun, et al 1998 G ntaz, et al 1999) Nmmally, RANS codes a~e iktat d until a skady stak solution is obtained n unst dy RANS, it ~ation is still used at each time skp but the global solution is made time accu~ate by using a time steppmg medhod Not e~mugh ~esult a~e yet available to anive at my con lu sions md mmch mm~ k ~em ins k be don Taxonom'Of Seakeping Cnmputations At 6he p esent time, active ~eseawh m 6he aea ot p edicting ship mmtions is contimmmg on panel medhods, bodh tully mmnlinea~ md double body methods, blend ing methods md 6he application ot unsk ady RANS F ~ design pu~p ses a naval awhik t has a wide choice ot methods wi6h which k do seakeping computations; 6he choices a~e mm longez limit d k ship 6hemy md it dezivatives Howeve~, it should be p mt d out 6hat even wi6h 6he av ilability ot a wide selectimm ot computational methods, p obably SO p ment ot all design ~elat d cal culations tm ships at tmwa~d s~ cd ae still m de usmg ship theo y Ship 6heo y has 6he adv mtage otbeing ta t, ~eliable, md able to accommodat a wide ~ mge ot hull tmms it is a meth d that is ha~d to ieat tm con entional ships at mmdezak speds How~weg tm highez s~ed vessels, highly mmn wallsided hull tmms, wave loads m exheme mmtions, 6he compa~isons with exp ~iment a~e much p mes; 6his has ben the p ima~y motivation tm 6he dewelopment ot mm~e ad anced themies n mdez to hy md put some ~elative mdez ink all 6he ditte~ent modem se kepmg computational medhods md main hydkody namics in gene~al, we p esent Figu~e I The goveming equations m 6he fiuid tm 6he gen ezal, th e dfimensional, in mp essible, const mt density fiuid fiow p oblem a~e 6he mntmuity equation md 6he th e comp nent ot 6he Naviez Stok s equations These equations ~esult m a sysk m ot tou~, mupled mmnlin a pa~tial ditfi ential equations tm the tou~ unlmowns ot p essu~e md 6he th e comp nents ot velocity To ob t in a unique sulution ~equi~es bounda~y conditions on all su~taces su~munding 6he fiuid th wett d su~ta~e ot the body, the t~ tace, the botk m, md th su~taces at mfinity On sulid smta~es such as 6he body smtace these a~e tw bounda~y conditions The fi~st is the kin matic condfition ot mm fiow th ough 6he smtace And the semnd is a mm slip condition on 6he tmgential v~ locity These a~e applied on 6he contmuously ch mgmg wett d su~tace ot the vessel On the fie smtace 6heze is a kin matic condition md a dynamic condition ot mnst mt p essu~e with mm shea~ shess The fie su~tace bm nd a~y conditions ae applied on the unlmown t e smtace amplitude, which must alsu be dek~mined as pa~t ot the solution On the botk m bounda~y tm finik dep h these is a kin matic condition, m in infinit Iy dep w~ tes the distu~bance velocities must go k zem At mfin ity, mcident waves a~e p esmibed md the~e is a ~adi~ tion mndition ot m tgomg waves on 6he ship g~at d waves This gene~al p oblem is highly mmnlin a~ m both 6
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Fig. I Tenors m; of hyd odynamics p oblems fm seakeeping 7
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have stat d us ing unsk ady RANS m ~oll damping computations in the long k ~m, unsk ady RANS will p obably be mak hed with fi lly mmnimea~ p kntial fiow cumputations in the fiu field to give a complek solution The boz labeled empidcal app ozimations undez the viscous fiow branch m Figu~e I is included bee mse d~ signe~s mu t have mswezs md viscous fiow calcul~ tions otk n a~e mmt applicable m a~e k o computationally exp nsive M my empaical methods have b~n dewel op d m which theo y is used to dewelop a t~amewmk with unknown coetficients that must be dek~mined by exp ~iment md tull scale measmements Classic ex amples a~e 1) The maneuvesing simmiation equations that use stability dezivatives to e timak hydkodynamic tmces 2)
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show sume mt ~estmg ~esult tm the sloshing p oblem md the p st b~eaking behavim ot wat ~ waves he mviscid fiow mmdels neglect viscusity com pletely md a~e indicat d by the second majm b~anch ot Figu~e I in this case, the Navie~ Stok s equations ~educe t the Eule~ equations md some ot the bm nd a~y conditions have to te mmdified Namely, the mm slip bounda~y condition c m mm longe~ be met on dgid su~ taces such as the wett d su~tace ot the ship ~ addfition, the bounda~y cundition ot ze~o shea~ ess on the t~ee su~tace is mmt applicable Even this ~educed p oblem is ve y ha~d to sulve md fi ~the~ simplifications a~e neces sa~y Fm mtational fiows, m which vmticity is p ese t, the vo ticity equations md vmt v meth ds c m be used hese t hmiques have tound limit d application in ~oll damping computations md sepa~at d fiows a~ound cu cula~ cylmde~s As indicat d by the second la~ge b~ mch undes Invis cid Flow in Figu~e 1, the mmst widely used t hmique is p t ntial fiow he vmt~ themems show that tm m m viscid, const mt density fiuid sta~t d fiom ~est mm vo tic ity c m be p esent ~ this case, the fiuid velocities c m be w itten m tes m s o t the g~ adient o t a se al a veloc ity p ten tial he govesnimg equation m the fiuid fiow is tound by sub tit tion ot the g~adient ot the velocity p t ntial i to the contmuity equation he ~esultmg Laplace equation is a Imea~ pa~tial ditte~ential equation that depends only on pace va~iables md is mdep ndent ot time Unique solutions ot the Laplace equation ~equi~e bounda~y cun ditions on all su~taces sunoundmg the fiuid domam t g~ ating the Eules equation ~esults m the Benmulli equ~ tion that ~elat the p essu~e to the time de~ivative md g~ dient ot the velocity p t ntial hus, the p t ntial fiow assumption has allowed the p oblem t be ~educed fimm solving tou~ coupled, r~nlmea~ pa~tial ditfi ential equations t sulvmg a smgle linea~ patial ditfi ential equation tm th velocity p t ntial he only mmlinea~i ties lett in the p oblem a~e m the bounda~y condfitions The kinematic body bounda~y condition may be stat d such that at ea~h p int on the hull wett d smtace the mm~mal velocity ot the wak ~ mu t equal the m mal velocity ot the hu11 This cundition is linea except that is must be applied on the exact wett d su~tace This leads to a time vad mt sysk m tm which haditional Imea~ yst m themy is mmt valid The majm mmnlineadties in the gen e~al p tential fiow p oblem a~e in the t~ee su~tace bm nd a~y conditions that irrvolve the qua~e ot the fiuid veloci ties md p oducts ot the fiuid velocities with the unknow t~ee smtace amplitude Cunsequently, the gen~al p tential fiow p oblem with a t~ee su~tace is ve y ditficult to solve md still fi ~thes simplifications have in the pa t been tound necessa~y The mmst obvious simplification is to eliminak all the mmnlineaities by eliminating the t~ee su~tace The boves on the ta lefi side ot Figute I ate use k mdicak these mfinik fiuid p oblems ~finik fiuid p oblems a~e usefi I in m my a~eas ot ma~me hydkodynamics mcludmg subma~ k, p op lle~ w ~k, md the tudy ot fiow amund app ndages Howeve~, in se keepmg ~eseawh they ae ot little use except as mude app ovimations m limitmg values ~ gene~al, the ettects ot the fiee smtace a~e too imp t mt to neglect Only ~ece tly has the comput ~ p we~ been avail able that makes it teasible to atk mpt to sulve the tully mmnlinea~ p oblem usmg the exa~t b dy bounda~y condi tions md the fi lly mmnlmea~ t~ee smtace bounda~y cun ditions As p eviously discussed, ~esults have been ob tained tm a limit d m mbet ot hull tmms m mmdetak seas The p inc ipal ditficu lties hese a~e mm me~ic al stab i l ity ot the time steppmg method md the local b~eakmg waves In Figu~e 1, the boves unde~ the exact p t ntial fiow p oblem ~ep esent the ditt'e~ent app ovimations that a~e available today The g~eat t deg~ee ot app ovimation is in the bov k the lefi md the least is mm the dght h md side ~ gene~al, computational times inmease as one moves k the ~ight but the~ e mm ha~d md ta t ~ules Fm example, fiat ship theo y is simila~ k the Neumam Kelvin p oblem m computatiom I ditficulty Tw sets ot app ovimations have to be m de The fi~ st deals with the t~ee smtace bounday conditions md the second withthe body bm nda~y cunditions The tou~ set ot ve tical Imes - ese t ditte~ent lewels ot app ovimation to the t~ee su~tace bounday conditions The individual boves ae ditfi ent k hmiques to meet the body bounday condi tion By fiu, the mmst widely used k hmique is to Im emize the t~ee su~ta~e bounday condfition abmt the t~ee st~eam velocity, Uo, amd satisty it on the calm wates pla~e This allows the use ot the t~ee su~tace G~een tune tions amd as discussed m the p cwious hi to y, mamy dit t'esent themies have ~esult d The ditfi ent themies cam be b~ok n dow ink a least tou~ basic app oaches It the beam m dEatt is much smalle~ tham the length, the body bounday conditimm cam be met on a fiat pla~e F ~ small beam the body bounday condition cam be satisfied on the cent qpla~e amd a thm ship themy ~e alt Thm ship themy t nds k p oduce added mass amd damping coet ficients tha ae too small amd is ~aely used Fm small dEat, fiat ship themy satisfies the body bounday cun dition mm the cam wak ~ pla~e The ~esulting equations ae simila k lifimg su~tace themy m ae~odynamics A fiat ship themy (et Lai 1994, Lai amd T~oesch 1995) has been used to solve plammg boat p oblems whe~e cun 9
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with Imea hydkodynam ics Fm h ad seas it app as tha the p imay r~nlmea ities a e the hydko tatic s md the F~ m de K y lov excitmg tmce it a p og~am has these two comp ne ts conect, p edictions tm Iage amplit de mmtions ae imp oved 3 CONTEtMPORARY CALCULATION MEtTHODS At the p esent time, th majmity ot design seakeepmg computations tm ships at tmwad speed p obably still irrvolve the use ot sh ip themy Tha does mmt meam to im ply that the mme adva ed themies that we discussed in sectimm 2 ae mmt imp ~tmt As ship geomet y becomes mme complex amd the design speed in~eases, the d va ed methods will find mm~e amd mme applications This hamsitimm will be accelezat d only by the avalabil ity ot cheapes amd t'ast ~ comput ts Th t hmica lik ~ at ~e on ship theo y, long wave slendezbody theo y amd unified theo y is immense amd we shall mmt discuss them amy tu~thez m this pap ~ Unstead' V's~us Flow As just discussed m Sectfon 2, the viscous fiow about a ship is govemed by the Naviez Stok s amd cunti mmity equatfons ~\ + S~\ S~\ = 0 ~\ whezethe~\,f = 1,2,3aethe~ ,y,amdz comp nent ot the velocity, P is the p essu~e 9\ is the is the com p nent ot the g~avitatfonal accelezatfon g in the ~\ di~ectfon, amd whe~e in acomda e with th Emst in summatfon convention double subscsipt withm a t ~m imply summation ove~ that mdex S~ + pg\+ ~V ~\ (1)
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md (2) mmst satis y a kinematic md a mm slip condition on the body These equations apply to my viscous fiow, lamma~ m tu~bulent As we a~e m tesest d m the fiow about ship with tmwa~d speed in a seaway, th fiow will be tu~bulent ovez substmtially all ot the ship's su~tace Thus, the velocity ~\ mmst ac count tm th k tal velocity including the time dep ndent comp nents at wave encountes fiequ~cy md the t ~bu lent velocity comp ne ts with mmch task ~ iation both t mp ~ally md spatially This ~esults in a computation ally mhactable p oblem tm fiuid volumes the size ot a ship on theoce m's su~tace The commmnly accept d way m which this p ob lem is made hactable is k decomp se the velocities md p essu~es mto slowly va~ying md ~apidly va~ying com p nent D ing this, m~e obtains ~ \ + ~\ md P = P + P', wheze the "ovesbar' ~ - ese ts a Reymmlds avezage taken ove~ a time/ patial scale la~ge ~elative to the scale ot the tu~bulence md the p imed qu mtities ac count tm the velocities md p essu~e at t ~bulent scales Substit tmg this decomp sition ot the velocity md p es su~e ink (1)
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For ~ > l the viscous FSRVM calculations of A44 diverge from the experimental results and converge to the inviscid FSRVM calculations; the B44 predictions diverge from the experiments but do not converge to the inviscid results. The viscous FSRVM predictions of A24 and B24 agree with the experiments for the mid frequencies, but not for either the lower or higher frequencies; they are closer to the experimental measurements than the inviscid FSRVM predictions.
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becomes (9) In Rmkin soume method, finik depth will m mease 6he computational time because ot 6he additional unknowns n essa~y k meet the bottom bounda~y cun dition, but 6here is mm in ~ease m computational ditfi culty Flat botk ms a~ y easy k comput smce m image syst m c m be added k the mfiuence mahiz tm ~elatively small computational cust n the othes h md, wi6h 6he typical G~een tun tion app oach, the finit dep h Gkeen tunctimm is signific mtly ha~der k cumpuk 6h m m infinit dep6h G~een tun tion Fmik depth Gkeen tun tions a~e almmst always desived tm fiat bottoms so thtt a~biha~y botk m cuntou~s c m mmt be accummmdat d n the mst mtaneous fiee su~tace bodh 6he kin matic md dy namic conditions mmst be satisfied he kmematic cun dition is ~ = Vf Vg Uo(t)
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md others have di~ecHy applied a Sommerteld typ ~+ diation condition 7his w ~ks well m tw dimensional Imea~ p oblems, but m 6 ee dimensions va~ymg wave di~ections md obtainmg accu~ak estimat ot the local phase speed c m c mse ditficulties Seweral mthms have used makhing bounda~y cun ditions (tm example see Dommermubh md Yue 19S7 m Lin, et al 1999) k makh a Rankine im~ solution to a Imea~ solutimm in 6he ouk ~ domam that is modeled with t~ee smtace G~een fi nctions, 6hus satistymg 6he ~adi~ tion cundition bee mseot 6he fiu field fiee su~tace G~een tunctions 7his makhing ~equi~es 6hat 6he p kntial, it mm~mal derivatives, md the wave height ag~ee at 6he bounda~y between the i mer md ouk ~ domains How cwer, achievmg 6his mak hing betwe~ 6he mmnlmea~ m ne~ solution md Imea~ ouk ~ sulution c m be a p oblem P obably the most commmm t hmique to p cwent wave ~efiection is to use absmbmg bounda~y conditions, m beaches Evha tesms a~e dded to 6he t~ee smtace bounda~y conditions, either one m both ot (10)
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used a desingmladzed method m which the soume panels a~e locat d outside 6he fiuid domam md 6hus 6he kemel m th goveming inkg~al equation is desingula~ ized in addition, bee mse ot the desingula~ization 6he panel dishibution c m be ~eplaced by simple p int smgu la ities he use ot p mt singula~ ities g~eady ~educes 6he complexity ot 6he comp t ~ code bee mse the mt g~als ove~ panels that mm~mally have k be cwaluat d k set up the infiuence mah i a~e ~eplaced by simple summations Rega~dless o t 6he method u sed to set up 6he i fi u~ce m ~ hiz, 6he ~esultmg system ot equations must be solved at each time st p This typically t kes app ozimak Iy one halt ot 6he CPU time As p cwiously discussed, depend ing on 6he size ot the p oblem, di~ect sulvess, itesative solvezs, m mdez N methods might be mmst app op iat Fully mmnlinea computatiom have adv mtages in that 6hey mk matically including tmwa~d speed ettect md mmnlmea~ mt ~actions No sp ial heatment such as th m: k~ms indhebody bm nda~y condition m the mmd ified t~ee su~tace bounda~y condition in 6he double body app oaches a~e needed k mclude tmwa~d speed ettect Nonlmea~ ettect such as added ~esistance, me m dkifi tmces, m 6he dit6~ence between the hogging md sag gimg midship bending mmment 6hat mm~mally ~equi~e ex tensive additional computations nat ~ ally tall out ot tully mmnlinea~ cumputations The p oblem wi6h tully mmnlm ea~ computations is wave b~e king md 6he stability ot 6he time steppmg medhod ~ theu miginal w ~k, L nguet Higgms md Cokelet (1976) encountesed a sawk oth m stability ot 6he t~ee su~tace md employed a smmothmg t hmique to supp ess its g~ow6h Fm azisymmehic p ob lems, Dommezmmth md Yue (19S7)
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( 1996) shows the hydrodynamic force acting on the modified Wigley hull III used by Journee ( 1992)
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Figures 6 and 7 show the added mass and damping coefficients as a function of frequency for the modified Wigley hull III at a Froude number of 0.3. Figure 6 is for forced heave and Figure 7 is for forced pitch.
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0.3 -064 9,~1 3 4 5 6 7 0 03~ -0.5 + + ~ ~ o + 2 3 4 5 6 7 Fig. 6 Experimental and theoretical added mass and damping coefficients for forced heave of Modified Wigley hull III, F~ = 0.3, x3/L = 0.00833 (from Scorpio, et al.
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, 0 ~ 2 3 034L/g 5 6 7 Fig. 7 Experimental and theoretical added mass and damping coefficients for forced pitch of Modified Wigley hull BI, En = 0~3, X5 = 1.5° (from Sco~io, et al.
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An equivalent time domain code, SWAN 2, has been extended to nonlinear ship motions using the weak scatterer formulation. Figure 8 from Huang and Sclavounos (1998)
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Derived Quantities Derived quantities are those responses of a ship that are a result of ship motions or the radiated-diffracted waves. These include factors such as accelerations at the bow, green water on deck, slamming, structural loads, and added resistance in waves.
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The ship motion amplitudes and phase angles relative to the incident wave were taken from the experimental results. The Froude number is 0.3 and for this particular case of maximum motions in head seas, >/L = 1.2.
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The second contribution results F p from the interaction of the radiation-diffraction waves with themselves.4 Such approaches to added resistance prediction were necessary in the days when strip-theory methods were the only means of predicting ship motions. With the advent of three-dimensional methods for the prediction of seakeeping, it has become feasible to pre dict added resistance by means of direct pressure integra tion over a ship's hull surface.
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From page 24... ...
The two figures show the vertical-bow accelerations in head seas for a tumblehome model in regular waves with a A/L of 1.0 for two wave steepnesses, 1/45 and 1/30, and at a Froude number of 0.21. As can be seen, the accelerations appear to be inverted trochoids, with the steeper waves providing "sharper" troughs.
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From page 25... ...
, m exknsion ot thee p Iymmmial app m imations k the tmwa~d ped ~ diation ditt~action Gken fi n tion will be mme com plicat d th m 6hat ~equued tm the steady mmtion md zem sped ~adiation ditfiaction G en tun tions How cwez, it such m aB oach could be successfi lly dewel op d, 6hese app ozimations could signific mdy ~educe the cumputational time tm evaluatmg the tmwad ped diation ditt~action Gken fi n tion Noblesse md tw co m6hms have p oduced a mmm bez ot pap ~s Noblesse, et al 1997, Chen md No blese 1998 Noblesse, et al 1999, Chen 1999) p ~ senting a unified Fou~iez/sp hal th ~y ot the G en tunctions tm the 6 e p mcipal p oblems ot ship hy dkodynamics 6he stedy Kelvin wake p oblem, 6he t~equency domain zem sped ~ adiation ditt~ a~tion p ob lem, md the t~equency domam fi wa~d sped ~adiation ditfiaction p oblem Noblese, Ymg md Chen's w ~k employs the same tmm ot G en tunctimm tm each p oblem, only the disp ~sion fi n tion in 6he kem I ot thei~ wave mmmbez inkg~als chmges Noblesse, Ymg md Chen call 6his Fou~iez/sp hal ~ep esentation ot 6he Gken fi n tion the Fomies Kochm ~ep eentation Theu - esentation is a gene~alization ot a commmn ~ep ~ sentation ot th Gken tun tion tm 6he steady Kelvin wave p oblem 6hat ~esults tmm a kin matic malysis ot the waves m the Kelvin wave patt m Like 6he sk ady 25
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From page 26... ...
t hmique to fi ~6hez spa~si y the mahiz equation 6hat mu t be sulved md sped the computation Thi s t h ique u ses F T convo lution ove~ 6he spati al gdd to compuk 6he p tential ovez the field due k 6he smgu laitiesdishibut dove~theg~id The p kntialatdistmt field p int is still cwaluat d by multip le accelezation King,etal (1999) ~ep ta~ecutiontimeswith6hepF T app o ach 6hat a~ e 3 6 k 5 3 p e ent o t 6he ti mes obtamed usmg a haditional high density BEM solvez Unstedy RANS calculations a~e exhemely time consumimg It my computational etficiency is gomg to be attained, unste dy RANS calculations ned to em ploy multig~id mmltiblock t hmiques How~wes, even wi6h these methods, unsk ady RANS will contimme to be exhemely time consuming It may well be 6hat 6he most app op iak app oach k the unstedy RANS p ob lem will le to couple the RANS solution nea~ 6he ship to a p t tial fiow solution away t~om the ship This could be done by the ml ed souee t hmique cu~endy employed m LAMP (Lin, et al 1999)
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From page 27... ...
show simila~ finit pikes in 6he added mass md damping coetficients at r = 1/4 tm both a subme~ged sphe~e md a Wigley hull tmm Large Amplitude Motions ~md Cap 4zmg The Navy is concemed with lage amplitude mm tions fimm tw p ~spectives Fi~st, m mmderat Iy high sea tak s th concern is with habitability md csew et tectivmess ~ exheme sea tak s, th concem becomes ship smvivability This latk ~ cuncern has become a sig nific mt issue wi6h 6he consideration ot t mble h me hull tmms tm DD 21 (Holze~ 2000) Accelerations due k ship mmtions attect hum ms by cmsing t'atigue, loss ot p ~tmmance md exheme dis comtmt md m ilk ess An assessment ot 6hese p t ntial ettects c m be obt ined by applyimg the mik da ot ISO Stmda~d 2631/1 md /3 (ANSI 1935a, 1935b)
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From page 28... ...
Tatmo, et a 1990, Umeda, et al 1990, Vezme~ 1990) Dynamic loss ot stability occurs when roll motiom become so lage that the rightmg am becumes zero m negative md the ship capsizes this usually mvolves mmnlinear seakeep ing Broaching iraolves la ge headmg excursions trom the desued course, md the ship capsizes bec mse ot dy namic loss ot sta ility m at high ermugh speeds, the mm mentum ot the ship c m tmce exheme roll due to high resist mce to lat ral motion O hez tactm s a e issues such as wak r on deck that result in a loss ot static stability, shit ing cago, m exheme wmd loads in leam seas Dynamic rollmg as a c mse ot capsizmg is m asym mehic mll that results trom all siz modes ot motion b~ ing coupled The ship takes on exheme mll k leewad when on a wave crest in tollowing m quatedng seas, md rolls back k wmdwad m the wave hough This cycle r~eats with inmeasmg roll amplit de duhng subseque t wave encounk r s, until it capsizes Dym mic roll result fimm the loss ot stability on wave crest that is mmt com p nsmed tm m the houghs Dynamic mll will typically occur at wave p dods signific mdy greaer th m the roll nat ral p dod Senjamvi6 (1994)
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From page 29... ...
ht e show bitut ation in beam ses, whtve 6he ~oll will jump fimm a modttak Itwel to capsizmg cun ditions undtt slight p tu~baions Sa hez amd Nayteh used amaog comp tations k ¢udy the mil btht im ot a shipaswt eslop amdt citationt~tqut ywtvevaied They p esent 6he bifi cation dfiag~ams tm 6he mmtions nea tesona e, tm simmiations wi6h mm ~oll bit md tm ~oll withbiasesoti6° Thebit es le dk quit ditfi t~t beht im t~om tha wi6h mm bias amd fimm et~h otht t F~a~cescutto amd Nabe~go; (199 ) study m ideal ized mmnlinea ditfi t~tia tquation tm 6he ~oll ~esp nse ot a ship They htve a cubic k~ esponding k 6he hydkostatic tesk ~img mmmt~t amd 6hey subjt t the sys t m to na~ow bamd t citation As is to be t p t d, th y obttin tesp nse at both 6he Imea nau~a t~tquency amd a subha monic t~t quency at app ozimat Iy one 6hi~d 6he nat ~ al t~t quency Theu so lutions demmnsh at the c l as sic bitueations 6hat tquations with mmnimea dampmg t hibit Atthe samt timt, Falza am amd T~oet h (1990)
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From page 30... ...
dP5 comput s si deg~ees ot t~eedom ship mm tions tmd wt e loads in Ittge amplitude wt es The mtthod tmploytd is a ml td t ume tmmmlftion, whtve th fiuid domam is dividt d mto i mt t tmd out ~ domams, sepaatdbyamathmgsu~tt e ~theimttdomam,the body, fiee su~tt e, tmd mat hing boundtty we all dis metized with Rankine singult titles Th i mt t domt in ttee t ~tt e pobltm is t Ivtd undtt the wtak scatt ~ ing assumption, whtve it is ast mt d that the ~adittion ditfit tion wt t we small cumptttd t the mcidt~t wtves The body boundtty cundition is satisfitd on the in ttmtmt us wett d hull undt t the incident wt e p o file At et h timt st p, local fiee su~tt e elfwations we ustd t ht tmm the body gt met y int a computt tional domam with a detmmt d body tmd a fiat t~ee su~ tt e Bylmettizmgthefieesu~tt eboundttyconditions about this mcidt~t wt e t ~ttce, the solution is simpli fitd in the outf t domtin a linett p oblem is solvtd us inglmettizedtteet ~tt ebtmsientGteentunctionsdis hibut d only mm the mat hing t ~ttce in this app ot h th cm~t t hyd ostitic tmd Fmude K ylov wt e tmces we ~e dily includt d This t t nsion is imp ttmt esp cially tm h msom st m ships tmd wht the amplitude ot the incident wt e is Ittge As th mat hmg bounday is fiztd mdnevet detotmtd, thecorrvolution mt g~als ovtt past time t te gteatly simplifit d tmd tccelt tat d Vit ous tmd lit ing ettt ts t te mcludt d m LA! dP us ing semi~mpaical tmmulas At etch timt step, vit ous tmd lit ing tmces md mmmt~ts t ting on the ship ae cal culat d tmd includtd in the tquations ot motion as pttt ot the tmcmg tUf tions A P D |
From page 31... ...
employ a finik ditte~ence sch me k sulve 6he Eulez equations undes a shallow wat ~ fiow assumption They p esent tw md th ee dimensional fiow calcul~ tions which compa~e quit tavmably with mmdel scale exp ~iment Fekken, et al (1999) use a volume~t fiuid method to hack 6he location ot 6he t~ee su~tace m a sim ulation ot the Naviez Sk kes equations tm 6he fiow ot wates on deck They p esent cumpadsons ot wave p o files md p essu~es fimm exp ~iment md cumputations tm th ee dimensional fiow on a mmdel tmedeck Horizontal Plane Motions We have chosen k ~e6 k 6he subject ot hmizontal plane motions tm 6his section bee mse we wish to em phasize the coupimg between ship maneuvezmg md se~ keeping Two issues come to mmd immediak Iy the fi~ t is 6he use ot 6he ~uddez k p ovide ~oll stabilization in lieu ot ~oll fins, md 6he second is 6he ~elation ot b~oach ing to su~ging, with the loss ot di~ectional conhol, le d ing to p ssible capsizing R dder RoU Stabi izaion Baitis (19SO)
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From page 32... ...
all mclude finit dep6h ettects bee mse the b dies a~e ott n so la~ge that the ~adiation tmces mmst mclude bottom ettects cwen it the mcident wavelemgths a~e shmt e~mugh that they may beconsideredasdepwak~ waves Fm ships, shipth~ my p og~ams a~e easily modified fi finit depth ettect by ~eplacmg the mfinik depth, tw dimensional G en tunction submutmes wi6h 6hose tm finit depth The finik depth p og~ams t kc longer k ~un, but the com puk~ time is still shmt Kim (196S) , Takski (197S)
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From page 33... ...
ae as tollows Verificaion 6he demmnshation 6hat the code is "~easonably" bug fiee md 6he output is mmmezically cm ~ect Fm complex codes vedfication is ve~y ditficult b~ c mse 6he cm~ect mswezs a~e mmt k ow md 6heze a~e litesally thous mds ot p ssible cases to check Usually codes a~e vedfied usmg ink ~nal consistency md cunve~ gence checks, computmg k own malytic solutions tm simple k st geomehies, md t tmg agamst othes c des None ot 6his c m gua~ mte a bug fiee code tm all p s sibilities (m tact, 6he fi~ t law ot computmg is 6hat all lage codes contam bugs) , but hop tully 6he bugs that do em am a~ e mconsequential Va idaion 6he cumpadson ot the mmmezical p ~ dictions with physical ~esult Validation is usually done by compait n wi6h d tailed t p dment O occasion tull scale t pttiment ctm be used tm validation, but tull scale ~esults tte usually mmt t cu~at tmough The ttquited p t ision ot 6he t p dments ctm mmt be ovt t emphasized It 6ht te is a ditfi t e between 6ht y tmd t p dment the confidt e Itwel ot the t p dmental tt suits must be t ch 6hat one ctm be t ~e that 6he p obit m I ies w ith the 6ht ~ etic al p edictions Tht te we mtmy hm ~m sk dt ot wasted ettmt t ying k find tt It with 6he mmmt tical computf tions, only k discovt t that the t p ~ imenttl ~esults wt te int u~ak In the idt tl wmid thtve should be a synergism between mmmt tical cumputitions tmd t p dment so 6hat both we imp oved m pt tallel At reditaion 6he cc tification thtt a specific code is t~ceptable tm a cc tam typ ot design p oblem Attt t t medititionthec dectmbemadet ailabletodesignets to t Ive 6he t medit d typ ot p oblem Acmeditition must be vety sp ific m 6ht te will be a k ndency k apply the code k p oblems tm which it was mmt mt nded 33
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From page 34... ...
~ep ts on m ettmt to assess sott wa~e tm stability calculations A16hough the ettmt d~ sm ibed is only ~ elat d k hydko static s , the~ e a mm mbes ot conclusions that a~e ~elev mt k la~ge amplit de mm tion p edictions, pa~ticulady bee mse hydkostatic tesk ~ ing tmces a~e su sigmfic mt to m my comp nent ot ship motiom The 6 ee conclusions that app a mo t sig nific mt a~e 1) A g~aphics capability tm ve~ification ot the geomeby should be m mdato y, 2)
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From page 35... ...
Le (1992) A localized finit element medhod tm mmnlinea t~ ttce wt e p ob Itms,P'oc 19thSy,p NavaiHydio, pp 9~114 Baids, A
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From page 36... ...
Atht letical tmd t p d ment tl investigttion ot bt tge mil dampmg P'oc 4thIntL Cont Stab Ships & Oce~ Vehic, Naples, Italy, pp 253 60 36 Bunnik, T
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From page 37... ...
Bitut ation tmalysis ot a vessel slowly t mmg in wtwes Proc 4th Ind Cont Stab Ships & Ocean Vehic, Naples,lttly,pp 647 52 37 Falzarana, J M
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From page 38... ...
The Gteen fi n tion method tm ship motions at tmwttd sped Ship Tech R s Schifft h ik, 39 3 21 Jensen, G., V Bertram & H Sbdng (1989)
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From page 39... ...
Yue (1990) Numt tical solution tm Iagt amplitude ship mmtions m the time domam P'oc 18thSymp NavaiHyd~o p p 41 66 Lin, W.-M., S
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From page 40... ...
Ship mmtions by a thee dimt sional Rmkme pt al medhod Pmc 18thSymp NavaiHydm~pp 21410 Nayteh, A
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From page 41... ...
(1990) Ship motions by a 6 t~ dimtnsionaMmkin ptnel medhod Pmc 18th Symp NavaiHydm, pp 21410 Sdavaunas, P
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From page 42... ...
P ob abilistic st dy on ship capsizmg due to pute loss ot stt bility in u~egulf t quttt ~mg seas Proc 4th Int'L Cont Stab Ships & Ot~ Vehic, Naples, Italy, pp 32S 35 Vassaltr, D
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From page 43... ...
AmmtticaHt ettchotmmn Imett body wt e int ~t tons P'oc 18th Symp NtDnd Hyd~o, pp 103 18 APPENDIX—CORRECTION TO THE ADDED RESISTANCE OF LIN AND REED (1976) Tht te is tmt tm~ indhe~tmges otint g~ tion mthedefini tion ot (Z:.F~)
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From page 44... ...
p et inaccuracies in the far-field wave predictions that m t rn would lead to deficiencies in the .. a ve load predictions on She second hull DISCUSSION L En In tit to Superior Tecnico, Spain The mthors definition of verification: 'The dem onsh ction that the code is retsorLthh hug free Ed that the output is mmmerically correct" suggest the following comments: Although w are aware That there is still c lot of debate on She proper deli n On of verification, the present d it con on does not mention the need to qu notify the en or Ed or the uncertainty of the verification procedure, which w believe to be essential in such c process It could also be mentioned in She paper that the verif cation of c complex flow is not c trcight fo ward exemise Ed Nat, m geneeal, it is very costly Ed time consuming AUTHOR'S REPLY L E c tises the issue of mmmericcl error Ed uncertainty m the verification process We agree that She quantification of mmmericcl enors Ed unce tcinty are imperative for verification Ed validation of c code Whedher error analysis belongs in verification or validation is not that import mt She key is that is must be done in reality, it probably should be part of both processes DISCUSSION M Tulm University of Calffomic, USA I just w mt to con r~mh~e Bob Beck on His ve y valuable paper Ed th mk him for its preparation I say That particularly bee mse of She clear emphasis mdfocushegavetok geamplit de motions Ed She complexities of that regime He mentioned SPH particle tracking methods)
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From page 45... ...
Ed She importance of date it is trrilrmg how much date w have in the smallest amplitude regimes Ed so little (vat ally no yst matic date) for very Urge ship motions AUTHOR'S REPLY M Tulin lauds SPH Ed endorses our observation that thele is c pmcity of Urge cmplit de motion date for validation Ed verification purposes We are pleased that he supports our position Nat much more validation of large cmplit de ship m otions must be done SPH hr.
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Key Terms
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