Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Frequency Domain Numerical and Experimental Investigation of Forward Speed Radiation by Ships
Frequency Domain Numerical and Experimental Investigation of Forward Speed Radiation by Ships
Pages 385-401
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From page 385... ...
ABSTEtAC r b f is paper w p~ese t m e perimental md mm~erical mve tig rti m of f ne mdiati m eft t of c sh p wif h fmward ped m fne fiequency domau~ Ihe te ts were pe founed m c reci ubt 3 water chxmel Foxes, momeris md wave~lwrti m were meas ed m series 60 Ce=0 6 md 0 8 shp mod is m forced heave md pit h osc3kticns A veloci y based fs t crd r Bommdary 3 me t Medhod was dew~lop d usi 3 he forward ped dift ach m radicti m G'en fmctim The cakubticns of f is fmction md its denvrtives as w 11 as it inbr rti m m flat paneL were pef med by conholk 3 bodh fne accmacy md fne c mputational time Ihe Fourier inbr rtion was done usi 3 m Admuti e Simps m medhod wih c p~escubed eucr b whrt m~ns he miace heg rticns, c mix~r43 m m :rical tech iqre (Gmss medhod wih c mmber of pohs whicha~e f nctim of fne ddstar~e betwe fne fleld pomt md fne so :ce paneb md m analytical heg rtion q~eed m fne Stok s fneorem to hansf m fne bommda~y heg al ho c co tour one, fne ~emamsr43 Fouri r inbr cls ~r fne compl:x expone tisl f nchm a~e fnen computed wifh fne same AdmbLve medhod was used Fcr fhe wave prtt m cal 3kticns, m exh mokti m tech iqre was used to obtam improved m3merical ~e 3 ts fcr c fleld poh located m he fie miace INTRODUCTION A pohed out byOkLu 3 mdWff~(1996 md OkLu 3 (199S) , fne compari m of mes :ed md cal 3kt d global forces (cr mohom)
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From page 386... ...
Although the corresponding Green function for seakeeping calculations in the frequency domain around bodies with forward speed is quite difficult to compute and relatively time consuming, the progress of computers during the last years as well as the improvements of the algorithms of computation enable us to develop numerical codes running on a cheap workstation or PC in less than 2 hours for the computation of pressure distribution, forces and moments. The fastest and more accurate techniques of calculation are the steepest descent method, Iwashita and Okhusu (1989, 1992)
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From page 387... ...
f(Hz) ~ F 0 13 2 75 to 3 25 0 22-0 27 0 04 07 25to6 125to27 02 10 25to6 175to38 03 T~ole 3: Te t conddLcns fcr force mesureme ts Th dynamometff used i composed of 3 miniahne force hansd ffS; forces md m me ts a~e uncoupl d by he use of edk s B f ore bei g com~Kted to f ne anslog to d6gital conve ter, eiffhic sig ffS Wff amplffed usi g bmd pass flltffs Sbti w ights Wff used f r caLbrati m to d tffmine fnecaLbratimmahi fcrdned3~'edchon Linmr d6 pEceme t hansd ffS ~eccrd fne moticns Thy a~e not used to mec:ne fne motim amplit d s but to give fne refesnce kg fcr he motion Ho~vff, fne kgs h~ ben confft d fi m parasit kgs inhod ced by fne knesr hansd ffS md by fne dsts acqui iti m t m by fne mms cd phase kgs duri g fne ine tis mes emeris wifh fne k own value of I SO° Fcr fne force mecsureme ts, te ts had to be pe f med twice, wifh fre mod I oscillaimg m a~r ~m dis forces)
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From page 388... ...
, data reduction depends on the number of acquisition points: 6000 for the force measurements and for the wave patterns, 1024 samples were recorded for each channel. The data treatment procedure was as follows: a)
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From page 389... ...
Figures 5 and 6 are for the pitch motion, CM55 and CA55. Conclusions are similar for the heave motion, the effect of the kind of model (value of ~)
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From page 390... ...
Figure 10 Wave amplitudes (pitch motion; F=0.2; f=3Hz) Figure 11 Wave amplitudes (heave motion; F=0.2; f=4Hz)
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From page 391... ...
Figure 14 Wave amplitudes (pitch motion; F=0.3; f=3Hz) The increase of the flow velocity induces the same behaviour: for the CB=0.6 and 0.8 models, figures 9 and 13 clearly show that the wave-amplitudes decrease and the front V-shape pattern is less visible when the Froude number increases; the bow waves are reduced and the region of strong amplitude moves from nearly x/L=0.2 at Fr=0.2 to about 0.4 for Fr=0.3 for the CB=0.8 model.
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From page 392... ...
t/T=1/8 t/T=1/4 t/T=3/8 Cr=1/? t/T=5/E tlT=3/4 t/T=7/8 Figure 17 Unsteady wave pattern during a period for the CB=0.8 model in pitch motion (F=0.3 and f=3Hz)
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From page 393... ...
, f r krge t emplit d s a'e heated r z f r ten~ NUMERICA1 STUDY MettrmeVesd model A velocity besed pMri medhod usi g c so :ce diwbutim wifh fhe diflaction-mdiatimfor~zd ped G'en fwrti m was d velop d wifhout tskmg ho accowt fhe lidi g effects es c fu t tep T r fluid is assum d to be inc mpwss~ble md m v~scous T r f e wuface md 6r watz hri ht are a~umed to be of hfmite e tent A uwMd, fhe tobl fl w mommd c ship wifh c mwz ~t for~zd ped Ux m wa~es m be d ompowd ho c te y fl w, not comid ~ed hme, md ho m um~ady fl w Fz m in obtional fl w, f r velocity pot tial m be uw d We wi3 assume fnat fhe te y md umtedy pa~ts of f r velocity pote tial a~e md prnd t md w only uw he kst r mmd r 6r f m t7,zy,~) e '~ Fl w is described mcoght-hwfled refe~e f~me frced to f r ship T r ~y phrr is he m m undiwwbed fi e miace; x axis is m f r d ecti m of m oh m md thr ~s i vedical m upwzd d ectioa The w,satisl pa~t of f r mm tedy potential mm t wli fy f r mkce equati m mf rfluilf rbodyconddh m mbodyS: (M)
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From page 394... ...
a gi~nby: 1+2tcosq+( I) JI+L,4tcosq,i Ito4 2F~ cos~ q L~ =L~ =I:L~ =L~ = I Wifh th pre ious asumptions md by neglect g fne bommday mt g als m fne fie mia a a fu t cala~lation Bmme t et ol (1993)
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From page 395... ...
md Mal m md Simpsm (19751 whle he heg ati m sbp d ~ses as fne inbg md becomes more osci hti g wih c p~escabed eucr, im~ad of c fom h crd r ~ Kutts medhod Bsch herval is d ided ho 2 parts, fne mt gml on fne whole he~val md fne sum of he 2 heg als mbue 2 sub dom~ns a~e comput dwihc 5 pohs Simps m mehod md fne results c mpared Nor~ew et ol (1997 Th pmcedne is pmsued mtil convergers:e is obtamed it i easy to ~ebte fne eucr m fne whole domam md fne coue pond g eucr m one of fne sub-domams, Gutt m (1983) Th mehod ~ed ces th CPU times md giws accmste ~esult fcr my vahe of fne parameters Never~eless, not only do fne G'en fmction md it fs t denvatives hsve to be c mput d accmutely, but also fne bommdny md co tour heg sls mvolved m fne eq~tion (7 Fcr th bommdxy inbg;ls m panels Kceffcie ts a~ m ~uati m (10)
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From page 396... ...
gives com t ~esults Bett r heg ation is made usl g fne armytical mehod by ~ed cl g fne p~escrll~d euor to IO ~ mdbylncre mg fne mmber of teps dnl g fne ad ,mtative heg ati m to 10000, but o ly ff LS-O I We fnen d id d to compute fne heg als for f is value of z md to exh molate fne values to z=0 Results hsve ben shovm to be nmrly md pmd t of ftse m thod of e xmolatim used We are tdl workmg m ftse lmproveme t of ftse cal-ulati m of fnese hegels Similar dwelopmeris m be also done for fne heg als owr fne wabrllne segme ts Flnstly, eq~ati m (10) led to a linear sysbm of uatlons ft tt m be mve t d gi mg fne so :ce hffuibes m fne panels Afx r ha mg obtamed fnese hff~sities, fne p~ e is computed by eqmhon (8)
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From page 397... ...
Fig e 19 md20 plots dne cdd dmass md dsmpi g cceffici ts wrsus fne m dmff~sional fiequency f =fL/U fcrdneS nesC =08h 11fcr hetwomoticns wifh 490 paneh et F=02 Tne heave amplit d was a/L=0 009 mdfne pit h one ~=1 8° Tne dnhed knes a~e fcr fne m merical ~esults (wi hout fne waterline heg al) md fne symbols a~e fcr fne te t mes eme ts Tnese ~esults show o~ilkdicns prob~oy d e to he e isbnce of imgmk fiequff~cies To ~em dy f is probl m, w h~ cdd d c miace of flat hori or~l md slighdy i mened panels (-O 5% of fne total body le gth)
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From page 398... ...
1~ ..~ 1 Figure 21 Comparison of wave height amplitudes for a series60 CB=0.8 model in forced heave or pitch motion (F=0.2; f=3.9Hz; ~=1.75;a/L=0.009 or ~=1.8°)
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From page 399... ...
CONCLUSION We hcve pre t d some experimental md mmencal ~esults m he fiequency domcm conceneng he radicti m fl w ammmd shp mod is of S ri s 60 wih block ccefficie t C =0 6 md 0 3 m fomed oscilhticns of heave cr pit h moti ms Add d~ss md d mpi g ccefficieris were mes cd as well as fl~e m te y fie-suriNce elevati m a ommd fl~e h 11 Ihe mes em nt s sh w c sh o g i fluer~e of he block ccefficie t wh:n compared wih fl~e Froud mmber bo6 m global forces md also fle suriNce elevaticns Fmth mmore, fl~e umte y radicti m wave pattem evoluti m duri g c p riodhas ben analysedby ~emov~ng fl~e m m fle miace eLvatim fl m fl~e mesureme ts Ihe g mh sh w waves, oneried alo g fl~e lo git dinal axis, hahelk g downsheam md sid way fl m he model, boflh starti gfl mfl~efore mdbackpartsoffl~eh 11 Thesewaves moved m Vshme a~s fl~at m be dose~ed m he wave amplit d plots Fcr heave motion, he upsheam md downsheam wave hcve fl~e ~oout same phase kg, wh3e fl~e phase kg is ctout 130° fcr fl~e pit h motioa Close to fl~e ~mhs value of fl~e Brard pa~m ter rO=1/4, fffl~e wave p attem chmges fl m wave h ahefli g m fl~e whok d mam ff ~<1/4to only downsheam wave ffml/4,no ~,mvarictim of fl~e f or ces cceffici ts are fl~en obse~ed Calcukdicns hcve be p fonned wiflh c com mt panel mehod usi g fl~e dff6~cti m ;dicti m wiflh fo ward ped G'en flnctim Boflh he zccmacy of fl~e G'en flmch m md d rivatives but zlso of he i teg ati m m ftat panels hsve ben conh ofled Ihe compari m of zdd d mass md dsmpi g cceffici ts fcr S :ries 60 h fls h ws ~ektive y go d zgreme tbetwe m~ued mdcal-uk4 dvalues Ihe ~esuts obtamed wih fl~e cod dvelop d m fl~e p~ese t sh~dyhsve zlso ben compared wih ofl~er mm~erical ~esults zvaibbk fcr z ftat pkte m forced way moti m md z~e m ~ektizely good zgrem nt hese ~alcukdicns sh w zlso flhe p~eseme of ineg kr flequ~cies zt h h vahes of fl~e ~ed ced flequff~ci s O y fl~e f t inegmk flequff~ci s hsve ben supp~ cd md he tech iq~e usedhas to be improwd Some dfficulti s mpearfor hefle miaceelwatimcal-ukdicns, padicukrly m fl~e wake of he mod I wh ~ess fl~e wzze zmplit ds z~e ovem~edcted by fl~e computatims Neverffiekss, fl~e wave pattem i q~zlitatively conectly ~ep~ese ted by fl~e computaticns Fmth mmore, fl~e fle miaceamplit d z~enotaccmatewhnfl~eflequencyi too clme of m megular cne Finslly, work is m prog ess fu t to improve fl~e tech iq~e used to supp~ess he megmbr flequency, to tudy fl~e seakepi g of ships m regmbr wzzes md to inh od cc he wabrline inbg zl c mputstional cod conhofli g fl~e zccmacy of fl~e i teg zls m he segme ts of fl~e waterkne The i fluer~e of fl~e k4ter will be mve tigated fcr several kmds of boats Ihe ktmg eft t wiflbe zlso inhod ced to dml wih boats m yawed fl ws zs sailmg bosb; cr man~i g ships b 6 is case, inbg zls deali g wih he second d rivati es of fl~e G'en flm ticns hsve to be consid ~ed More c mp ms m z~e to be done boflh m global d~z md kcal ones A sh~dy of fl~e calcubti n of fl~e wz~ zmplit d behmd fl~e h 11 mu t be pmsed m order to und r~md he ovem~edhi m of fl~e fle miace elevati m m flhis zone
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From page 400... ...
end Be M,'~perimental md mmerhal sbady of fne wave mdiatim by c miacepi ml g o~ilLti g md Lwnsk6mg pEte usi g Gre 's 9 nction," P oc Of fne 2 5 mnosi m m Hvd odw~amics. Ho gKo g,Vol 1, 1996,pp 171-176 Nmdekeew U, Be M end Gbflb~md M, "Sol mg c mdiati m probl m wifh fo ward sped usi g c kdi g miace medhod wih c Gren's f mction," A msnace 5 ieme md Tech oloev, No 8, 1997, pp 533-43 Oklmm M
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From page 401... ...
"Prediction of Diffraction Waves of a Blunt Ship with Forward Speed Taking account of the Steady Nonlinear Wave Field", 2 Numerical Towing Tank Symposium NuTTS'99, Rome, 1999. AUTHOR'S REPLY Unfortunately, we have not obtained the paper from Iwashita t11 mentioned by Professor Bertram in spite of asking it from library, so no comparison has been yet made.
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