Simulation of wave-body interactions in viscous flow based on explicit wave models

Transcription

1 Smlao of wave-body eracos vscos flow based o eplc wave models Roma Lqe, Berrad Alessadr, Perre Ferra, Loel Geaz Ecole Cerale de Naes LMF/EHGO, UMR 6598 d CNRS,, re de la Noë, F-443 Naes Cede 3, Frace rodco Today wave-body eraco problems ca be solved mercally by sg sofwares based o Reyolds Averaged Naver-Sokes Eqaos (RANSE). So s possble o ake o acco vorcy ad vscosy effecs wc ca flece ydrodyamc loads ad srcre of e flows. However mercal smlaos der vscos flow eory sll lead geerally o large CPU mes becase of grd reqremes o esre a good propagao of cde waves e mesed par of e fld doma. Moreover sccessve wave reflecos o e body ad e oer bodares ca affec e comg wave ra ad redce e seable drao of e mercal smlao. To overcome ese dffcles a orgal meod cosss solvg e dffraced flow oly (Ferra e al., 3). Ts RANS Eqaos are modfed by splg all kows of e problem a sm of a cde erm ad a dffraced erm. Te cde erms are eplcly descrbed by flly o-lear wave models based o poeal flow eory : reglar waves are obaed by a algorm based o e sream fco eory of Reecker & Feo (98) ad rreglar wave ras by a specral formlao (Ferra e al, 3b). Ts oly e par of e grd e vcy of e srcre eeds o be refed ad a sreced grd allows a effce dampg of e dffraced flow far from e body. Here e splg of kows defed prevosly s appled o a vscos flow solver (Alessadr & elommea, 995). Modfed RANS Eqaos verfed by e dffraced flow are amed SWENS (Specral Wave Eplc Naver- Sokes) Eqaos ad ave bee developed prevosly (Ferra e al., 3a). e followg ad 3 resls are preseed order o sow ables of e prese meod. Te flow of a reglar wave ra o a mmersed crclar cylder s frs sded see Ferra e al. (3a) or Lqe e al. (3) Te a 3 case of a vercal cylder waves s sow. bo cases prese resls are compared w mercal ad epermeal daa. efo of SWENS Eqaos for e dffraced problem To cosder e sgle dffraced problem, prmve kows (Caresa compoes of velocy ( ) pressre p ad free-srface elevao ) are decomposed as follows : w {,,3}, = p = p p = {,,3 } Varables w e sbscrps ad represe cde ad dffraced varables respecvely. Ts decomposo s e rodced e se of al eqaos assmg a e cde wave flow flfls e Eler eqaos ad o-lear free srface bodary codos poeal flow eory : - Traspor eqaos : ν ( ) p ( ) ν ν ν ν = ν ν ( ) ρ - Mass coservao : =

2 - Free-srface bodary codos : () kemac codo 3 3 = ()ormal dyamc codo ( ) ( ) g p g p = ν ρ ν ρ ν ρ ν ρ () ageal dyamc codo ( ) = prevos eqaos e erms defed by cde varables (veloces, velocy grades, free-srface elevaos ad free-srface elevao grades ) are eplcly comped kowg kemacs ad erface poso of e cde flow. Ts se of eqaos wll be amed e followg SWENS (Specral Wave Eplc Naver-Sokes) Eqaos ad s solved by a flly-copled vscos fld solver developed by Alessadr & elommea (995). resls A o-lear reglar wave ra propagag above a mmersed orzoal crclar cylder deep waer s smlaed ere followg e mercal sdy of Scøberg & Capl () ad measremes by Capl (). Parameers of compao are ormalsed by akg e cylder rads c ad (c/g) / as leg ad me scales respecvely. Ts e cylder sbmergece s d/c=.5, e aglar freqecy kc=.56 ad e amplde of e fdameal freqecy compoe a/c s.7. W ese parameers, e Kelega-Carpeer mber s KC=.5. Fgre : deals of e grd Fgre : Lef : Free-srface profle beea e cylder (ceered a =). Rg : Forer compoes of e free srface elevao. Symbols : measremes from Capl (); dased le : compao from Scøberg & Capl (); sold le : prese compao.

3 A very refed grd abo 6 pos per waveleg for e rd armoc (fgre ) as bee sed o compe e ger order armoc compoes of e free srface properly. Sc a compao w a 5 odes srcred mooblock grd akes oe week a PC w a processor of.5 GHz. fgre o e lef saaeos free-srface profles obaed by prese compaos are compared w poeal flow compaos made by Scøberg & Capl (). Tese profles are ploed a e sa a wc e dsrbed wave feld wold ave a zero p-crossg a =. Te agreeme s qe good b ere are oceable dffereces : e vscos wave profle as a small pase lag ad s local mama are smaller. Capl () cocldes a vscos effecs wold mpose a ressace o e fld moo wc s lkely o delay e rasmsso of e wave over e cylder, eplag e small pase lag. Fgre o e rg sows e spaal varaos of e frs ree armoc compoes of e free srface elevao. For several locaos e mercal wave ak ese compoes ave bee comped sg a Forer decomposo of e me sory of e free-srface elevao sgal a movg wdow of oe wave perod log. Prese compaos are good agreeme w Capl's epermes especally for e frs armoc compoe (e mos fleced by vscosy effecs). 3 resls Z Z Y X Y X free srface cylder cde wave ra Fgre 3 : Vews of e mes arod e rcaed cylder 3 compaos ave bee r for a rcaed vercal crclar cylder o-lear reglar waves (see e grd o fgre 3). Te perod s.8 s, wave eg.37 m ad wave seepess abo 4.6 %. Te grd as 5 odes ad e reqred CPU me s abo 9 mes CPU per wave perod o a PC w oe processor of.5 GHz. Wave rps (fgre 4) ad armocs of orzoal forces ave bee compared w o-lear poeal flow resls from XWAVE code (Ferra, 998) ad/or epermeal daa from Kroksad & Saberg (995) w a very sasfyg agreeme. Force compoes (N) F (N) F (N) F3 (N) No-lear poeal eory Epermes SWENSE compaos

4 . Wave rp, T=.8 s, H=a=.37 m, β=.5 wave elevao (m) me (s). Wave rp, T=.8 s, H=a=.37 m, β=π/.5 wave elevao (m) me (s). Wave rp, T=.8 s, H=a=.37 m, β=π.5 wave elevao (m) me (s) Fgre 4 : Wave Rps (β= : p wave, β=π/ : sde, β=π : dowwave po of e cylder waerle) dased le : prese meod, sold le : No-lear poeal flow resls Coclso Te dffraco of o-lear reglar wave ras or 3 cases as bee sded w a orgal approac combg a vscos flow solver ad a eplc descrpo of e cde waves. sead of compg e wole velocy, pressre ad free srface felds, e dffraced flow oly s comped solvg SWENS Eqaos (RANS Eqaos were varables ave bee decomposed cde ad dffraced varables). Frs resls are ecoragg ad sow capably of e meod o well smlae wave-body eracos by sppressg sal mercal problems of wave geerao vscos flow solvers. Refereces Alessadr, B., elommea, G. (995), A mlgrd velocy-pressre-free srface elevao flly copled solver for calclao of rble compressble flow arod a ll, 9. Cof. Nm. Me. Lamar ad Trble Flows, Alaa, pp Capl, J. R. (), No-lear Wave eracos w a Sbmerged Horzoal Cylder,. Offsore ad Polar Eg. Cof., Savager, Vol. 3, pp Ferra, P. (998), Flly olear eracos of log-cresed wave packes w a ree dmesoal body, d ONR Symposm o Naval Hydrodyamcs, Wasgo. Ferra, P., Geaz, L., Alessadr, B., Le Tozé,. (3a), A Poeal/RANSE Approac for Reglar Waer Wave ffraco abo Srcres, Sp Tecology Researc, vol. 5, o. 4, pp Ferra, P., Le Tozé,., Pelleer K. (3b), No-lear me doma models for rreglar wave dffraco abo offsore, eraoal Joral for Nmercal Meods Flds, press. Kroksad, J.R.; Sasberg, C.T. (995), Rgg loads model verfed agas epermes, OMAE'95 Coferece, Copeage. Reecker, M.M.; Feo, J.. (98), A Forer appromao meod for seady waer waves, J. Fld Mec. 4, pp Lqe, R., Alessadr, B., Ferra, P., Geaz, L. (3), RANSE Aalyss of flow abo a sbmerged body sg eplc cde wave models, 6 Nmercal Towg Tak Symposm, Rome. Reecker, M.M.; Feo, J.. (98), A Forer appromao meod for seady waer waves, J. Fld Mec. 4, pp Scøberg, T.; Capl, J.R. (), Compao of No-Lear Wave Reflecos ad Trasmssos from a Sbmerged Horzoal Cylder,. Offsore ad Polar Eg. Cof., Savager, vol., pp.8-87.

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