IMPROVING THE RESISTANCE OF A SERIES 60 VESSEL WITH A CFD CODE

Transcription

1 V European Conference on Compuaonal Flud Dynamcs ECCOMAS CFD 2010 J. C. F. Perera and A. Sequera (Eds) Lsbon, Porugal, June 2010 IMPROVING THE RESISTANCE OF A SERIES 60 VESSEL WITH A CFD CODE J. M. A. Fonfach *, C. Guedes Soares * Cenre for Marne Technology and Engneerng (CENTEC) Techncal nversy of Lsbon, Insuo Superor Técnco Av. Rovsco Pas, Lsboa, Porugal e-mal: [email protected], [email protected] Key words: Compuaonal Flud Dynamcs, Shp Hydrodynamcs, Free Surface Flow, Turbulen Models, Hull Shape Opmzaon Absrac. An hydrodynamc sudy was carred ou of a seres 60 vessel model usng a CFD RANS (Reynolds Averaged Naver-Soes Equaons) based code, wh he am of calculang he pressure graden and shear sresses of he flow around he vessel, and he assocaed wave ran generaed a he nerface of wo fluds (free Surface), for Froude numbers n he range of 0.18 o The daa were valdaed wh prevous publshed epermenal ess. Dfferen mesh sze was used n he presen sudy o deermne he mos approprae one. The use of a zone wh urbulen properes s a fundamenal aspec n vscous flow smulaon. For he soluon of he governng equaons wo urbulence models for he urbulen vscosy are evaluaed. They are: Shear Sress Transpor (SST) and he K- model. Subsequen o obanng hese resuls, a sudy o opmze he hydrodynamc ressance was conduced, so ha he hull of he shp was modfed by addng a bow bulb, whch were analyzed wh wo dfferen lenghs, obanng he bes alernave

2 1 INTRODCTION The desgn and opmzaon of he hull lnes have radonally been performed on he bass of scaled models esed n owng ans. Ths mehod s oday he mos relable n he predcon of hydrodynamc properes of he shp. Analycal mehods are no used due o he compley of he governng equaons of real flows complcaed by he esence of free surface, vscous phenomena and he comple shp geomery. In hese days wh he developmen of new numerc ools, he advances n compuer echnology and he ncrease capably of daa processng, Compuaonal Flud Dynamc (CFD) has made remarable progress and allowed good resuls o be obaned. The neres and demand of he ndusry o mplemen new mehods s one of he mos mporan reasons ha nfluence he developmen of CFD. Shps have been bul wh bulbous bows as par of he hull, bu he hydrodynamc desgn of bulbous bows s sll dffcul, because of epensve an ess necessary n he desgn of he bows, even a he prelmnary desgn sage. I s val o defne he hydrodynamc performance of he hull, o calculae he engne power, capable o overcome he hydrodynamc ressance produced by he neracon of he hull wh he flow. Thus s mporan o desgn he hull forms such ha hey can operae economcally [1-2]. I s necessary o undersand he complcaed flow characerscs for an opmal hull desgn, whch ncludes a low drag and hgh propulsve effcency. For beer nowledge of he flow around he hull, s mporan o have relable and accurae daa, abou he physcal phenomena n he neracon flow-shp. The daa of he epermenal ess whch descrbe he local flow deals are nvaluable for he valdaon of he CFD models. There have been some epermenal daa of he flow around he shp models avalable for valdaon of CFD. The nernaonal owng an conference (ITTC) summarzed avalable benchmar daa base for CFD Valdaon for ressance and propulson of a shp, for he cargo-conaner shp, seres 60 and urbulen measuremen es case are gven n [3-4]. Prevously wo worshops were presened for he compuaonal analyss flow around shps, HSVA/Dyne aner and a seres 60 model were chosen for he es case [5]. However he progress ha has been acheved n he epermenal ess has no decreased he neres of nowng n deal he flow feld, wh beer nformaon of he near-wall flow, assocaed wh he moon of hull. Ths nformaon s no offered by he epermenal mehod; on he oher hand CFD have a good performance n gvng characerscs of he behavor of he flow ha ofen mprove developmen of he hull form. The cos and me requred for he compuaon are lower han for an ess. The CFD has been negraed n o researchng and he ndusry, for eample s beng used n desgn of shps for he predcon of vscous flow wh free surface around he hull, he flow separaon o desgn appendces and propeller-hull neracon. Vscous flow compuaon for shps began n he 60 s, wh he smplfed boundary layer equaon beng solved. In hs approach, he boundary layer can be calculaed accepably n he hull, however, hs formulaon faled n he predcng flow a sern. In he 80 s a large number of RANS (Reynolds Averaged Naver-Soes) mehods were developed for shp sern flow. The sern flow predcon capables were mproved raher remarably around However, CFD smulaons near he propeller were less sasfacory, due o shape of he boundary layer n he propeller zone. Laer, was realzed, ha he reason for he nably o predc was he nadequae modelng of urbulence. Ths lead o he mplemenaon of more advanced models, such as he -ω urbulence model and he Reynolds sress model [6]. 2

3 The modern vscous flow codes, whch solve he RANSE, have he ably o smulae effcenly he urbulen flow problems around shps. The wo models mos used n CFD o solve he urbulen phenomena, are he sandard - model and he Shear Sress ranspor (SST) -ω, he performance of whch models was suded n [7] dealng wh he predcon of he reaachmen lengh of flow. The -ω model gave very good comparson o epermenal daa whle he - model predced a sgnfcanly shorer lengh. However, he -ωmodel overpredced he spreadng raes around he free shear layer due o naccurae predcon of eddy vscosy value. Free surface problems such as he wave mang problem were smulaed wh vscous flow codes dependng on wheher he compuaonal grd adaps o he shape or he poson of he free surface. Therefore, wo maor approaches wdely appled o he free surface compuaons are he so-called nerface-racng mehod, e.g. a movng mesh and he nerface-capurng mehod, e.g. he volume of flud mehod (VOF) proposed by Hr and Nchols [8] o deal wh free surface boundary problems. The am of hs sudy s he use of CFD code for a shp desgn. For ha effec, he performance of he seres 60 shp model was mproved as a resul of changes n he hull form. Frs a sudy of he naed hull was performed, whch analyzed he mesh sensvy and valdaed numercal daa. Then wo dfferen bulbs were desgned o reduce he ressance of he hull. The models were calculaed wh he commercal sofware CFX verson MATHEMATICAL MODEL In CFX, he Reynolds-averaged Naver Soes (RANS) equaons for he momenum ranspor and connuy equaon for mass conservaon are equaons governng he moon of a hree-dmensonal seady, ncompressble and vscous urbulen flow. The homogenous mulphase Euleran Euleran flud approach ulzes Volume of Flud mehod (VOF) o descrbe he free surface flow problem mahemacally. The ulzed VOF mehod s a fed grd echnque desgned for wo or more fluds, where n each cell of a mesh s necessary o use only one value for each dependen varable defnng he flud sae, whch can be defned by a funcon α (where q represen he fracon of volume; q = 1, 2,..).The value of hs varable s uny a any pon occuped by flud and zero n he oher case. The average value of α n a cell represens he poson of he nerface of he flud. In parcular, a un value of α would correspond o a cell full of flud, whle a zero value would ndcae ha he cell s empy, so he cells wh α values beween zero and one mus, he conan a free surface. The racng of he nerface s accomplshed by solvng he connuy equaon of he volume fracon. For he q lqud, hs equaon s wren as follow: q α q u where he consrans are gven by: α q = 0 (1) n q= 1 α q = and for ncompressble flows, he frs erm of he connuy equaon s: α q = 0 1 (2) (3) 3

4 The densy of he whole flud n each cell s evaluaed by he volume-fraconaverage of all lquds n he cell: ρ = α ρ q q (4) All oher properes (e.g., vscosy ) are compued n he same way. The momenum equaon s dependen on he volume fracons of all lquds hrough he properes ρ and. The Naver-Soes equaon can be wren n Caresan ensor form as follows: u u 1 p u u = ρ where for seady flow, he velocy-me can be wren as: (5) u = 0 (6) where u s he velocy n he sream drecon,ρ s he flud densy,s he nemac vscosy of he flow and p s he pressure. The Naver-Soes equaon canno be resolved properly for he effecs of hgh frequency urbulence, because he compuaonal resources do no allow he curren generaon of suffcenly fne mesh o properly resolve he small-scale vorce lengh. For hs reason, he effors n Compuaonal Flud Dynamcs are dreced o he soluon of he Reynolds equaons. These equaons are obaned usng he defnon of average me. The flow s separaed no mean ( ) and flucuang (u )componens n he RANS approach o urbulence: = u' (7) he me averagng velocy componen s defned as: T 1 = d (8) T 0 where T s he averagng me of he smulaon, usually chosen o be large compared o he ypcal mescale of urbulen flucuaons. Subsung no he Naver-Soes equaons n seady flow for me averagng, one obans he me averaged Naver- Soes equaons: u 1 p u u = u u (9) ρ where, he sascal averagng of he Naver-Soes equaons gve rses o he unnown erm, s defned n eq.(10): u u 2 u u = δ (10) 3 whch are he correlaon beween he flucuang velocy componens and s nown as he Reynolds Sress erm. The esence of he Reynolds sress means here s no longer 4

5 5 a closed se of equaons, and urbulence model assumpons are needed o esmae he unnowns o solve hs closure problem Two models were used o calculae he urbulen vscosy. In CFD, he sandard - and Shear Sress Transpor -ω are he wo mos wdely used models n hs caegory. The sandard - urbulence model solves he flow based on he assumpon ha he rae of producon and dsspaon of urbulen flows are n near-balance n energy ransfer. The dsspaon rae, of he energy s wren as: L 3/2 = (11) where s he nec energy of he flow and L s he lengh scale nvolved. Ths s hen relaed o he urbulen vscosy based on he Prandl mng lengh model: ρc 2 µ = (12) where µ C s an emprcal consan and ρ s he densy he flow, applyng hs o he equaons governng flud flow, he equaon of he sandard - model s wren as: ( ) ρ σ ρ = (13) and he equaon: ( ) ρc C σ ρ = (14) based on eensve eamnaon of a wde range of urbulen flows, he consan parameers used n he equaons ae he followng values, 0.09 C µ = ; 1.44 C 1 = ; 1.92 C 2 = ; 1.0 σ = ; 1.3 σ = Shear Sress Transpor -ω wo equaons model was developed as an alernave o cover he defcences of he sandard - model a he walls. The Shear Sress Transpor -ωs smlar n srucure o he - model bu he varable s replaced by he dsspaon rae per un nec energy. The equaons n he Shear Sress Transpor model are wren as: ( ) ρω σ ρ = (15) and he ω equaon: ( ) 2 βρω ω α ω σ ρ = (16) where: ω ρ = (17) Alhough he wo equaon models (-ω and - ) provde a good compromse beween compley and accuracy among RANS models, he applcaons are resrced

6 o seady ype of flow. Thus, soluon s sough o acheve boh compuaonal effcency and he capably of predcng he chaoc naure of flow such as vore sheddng. 3 SHIP MODEL The shp model used for hs sudy s a seres 60 wh bloc coeffcen (C B ) of 0.6, whch s a sngle-propeller merchan ype shp and s a sandard for shp-hydrodynamcs research, and was chosen because, s one of used by ITTC research program. The characersc of naed hull model used for he epermenal and compuaonal es are, gven bellow, and he longudnal profle of he 3D model s shown n Fgure 1. Lengh beween perpendcular (Lbp) [m] Breadh (B) [m] Draf (T) [m] Dsplacemen ( ) [m 3 ] Weed Surface Area (S) [m 2 ] 4 EXPERIMENTAL SETP Fgure 1: longudnal profle of he 3D model. To compare and valdae he numercal resuls, use have been made of he epermenal resuls presened by he ITTC Cooperave Epermen on a Seres 60 Model, a he Shp Research Insue n he sudy Flow Measuremen and Ressance Tes [4]. In he epermens, he ressance es was carred ou under free condon. The range of Froude number (Fn) was 0.07 o 0.34 and s sep s The ressance force was measured by a ressance dynamomeer of he sran gauge ype whch has he capacy of 20g and a olerance of 0.05% of he full scale. The wave profles along he hull surface were measured by phoographs a values of Fn = 0.18; 0.22; 0.25; 0.28; 0.30; 0.32 and The horzonal and vercal scales were drawn on he model surface for hs purpose. The phoographs were aen by he hree 35mm cameras. The vscous flow feld was measured usng 5-hole Po ube, whch s he NPL ype (ape angle s 100 deg.) and s dameer s 5mm. The shp model was fed o he owng carrage n order o assure he accuracy of measurng poson. The Froude number was se o 0.18, for calbraon. The waer condons n he owng an are shown n Table 1: T C ρ gs /m m 2 /s Table 1: The envronmen condon measured n he Towng an. 5 COMPTATIONAL DOMAIN AND GRID GENERATION The geomery of he hull and he volume of conrol of he grd were obaned n approprae eernal sofware, and he molded offses of he ransverse secon of he model were obaned from he polynomal defnon of he cross secon for seres 60. 6

7 The modeled surface of hull was compared wh he epermenal model; he dfference was only 0.2%, and hus was consdered ha he surface was modeled opmally by he generaed mesh. The volume of conrol was chosen o be of bo shape. The hegh of he compuaonal doman s 1.25L bp and s wdh s aen o be of 1.5L bp due o he symmery of he problem. The doman nle boundary s a a dsance of 1.5L ahead of he shp, whle he oule boundary s locaed a 2.6L bp from he shp sern. The grd generaor ICEM CFD was used for meshng he compuaonal doman wh unsrucured erahedral grd and dfferen mesh szes were consdered for he analyss of ressance n naed hull condon. The mesh sze for he hull and free surface are summarzed n Table 2 and are shown n Fgures 3 and 4. Mesh sensvy sudes were performed o eplore he effec of dfferen opology and local refnemen o observer accuracy on he resul, In ICEM CFD he opon Low ranson was chosen o refne he mesh gradually n he zone of neres unl a remoe zone of he doman. nsrucured erahedral grd was chosen because s easly adusable o comple geomery; however hs ype of mesh ncreases he compuaonal cos. Mesh N Hull Sze F.S. Sze Doman N Node Mesh N 1 2%L 2%L 425,940 Mesh N 2 0.5%L 2%L 596,313 Mesh N 3 0.5%L 1%L 1,874,160 Mesh N %L 1%L 2,391,549 Table 2: Dfferen sze mesh used n he hull and Free Surface (F.S.). L s he Lengh beween perpendculars. In he free surface and hull surface a prsmac layer mesh was appled (see Fgure 2), wh an eponenal ncremen beween layers. The nal hegh and he number of layers are presened n he Table 3. The parameer seleced was ha he oal layer hegh n he nerface zone s wce he draf of he hull, and he oal hcness around o hull appromaely equal o one quarer of draf. The prsmac layer mesh has been used n he all cases ecep for mesh N 1. Iem N Layers Inal hegh Hull F. S Table 3: Parameers for Prsm layer mesh appled n he hull and Free Surface. Fgure 2: Scheme of grd used n he compuaonal doman. 7

8 Fgure 3: Compuaonal Grd on Seres 60 surface, a dfferen sze mesh. Fgure 4: Compuaonal Grd on Waer surface around Seres 60 shp model, a dfferen sze mesh. 6 BONDARY CONDITIONS AND SIMLATION CRITERIA For free surface calculaons, he ar and waer flow around he seres 60 shp model was smulaed usng he sandard homogenous Volume of Flud (VOF) model (or free surface model) avalable n CFX In he VOF model, a sngle momen equaons s shared by he flud volume fracon of each of he fluds n each compuaonal cell s raced hroughou he doman, surface enson was no appled n he models. The coupled volume fracon soluon algorhm was used o mprove he convergence. The sn and rm of he hull was no aen no accoun, hus was consdered ha he hull was fed and he compuaons were run seady n me. The sandard - and shear sress ranspor -ω urbulen model was employed n he CFD smulaons wh he sandard coeffcen. Boh urbulence models are wdely used n he marne and hydrodynamcs applcaon and hese models have a good performance for hgh accuracy boundary layer smulaons. The waer condon was modeled as n he epermenal es, whch means fresh waer a 21.5 Celsus degree, (Densy = 999g/m 3, Dynamc Vscous = 1.137E- 3g/m/s). The ar was assumed compressble (for compuaonal sably reason) and was modeled wh a molecular mass of 28.96g/mole and a Dynamc Vscosy of 1.8E-5 g/m/s. Buoyancy forces due o flud densy dfference were modeled n he analyss. The boundary condon was employed o smulae he condon on he owng an. A velocy nle boundary condon was used upsream; he flow velocy was consdered equal o he velocy epermenal of he model usng he cases of epermenal measuremen o wave profle. The free surface elevaon was fed a he nle. A hydrosac pressure oule boundary condon was used downsream; he hydrosac pressure a he oule was calculaed assumng an undsurbed free surface. Smooh walls wh a free-slp condon were assumed for he op, floor and he sde wall, only half of he model was consdered n he smulaons by usng a symmery plane condon a Y = 0. Smooh walls wh a non-slp condon (u, v, w = 0) were assumed n he enre hull. 8

9 Convergence was assessed by plong he flowng parameers agans he number of eraon: Resduals for mass, momenum and urbulence (arge crera = 1E-4) and Drag forces (X drecons). The mamum number of eraons was equal o 500. However, f he convergence crera are reached for all resduals, he smulaon was sopped before reachng 500 eraons. For mos smulaons, convergence of all resduals forces and monorng pons was acheved n around 300 eraons [9]. 7 NMERIC RESISTANCE VALIDATION OF THE BARE HLL The oal ressance coeffcens were obaned from he numercal resuls and compared wh he epermenal value. No blocage correcon was made for epermenal daa [4]. The speed relave o waer s used n he calculaon. The oal ressance coeffcen s: R C = (17) 2 0.5ρ. S where R s he oal ressance. The oal ressance coeffcen for dfferen mesh and urbulen model are show n Fgures 5 and 6. Fgure 5: Toal coeffcen a mesh N 1 and N 2 for -ω and - urbulen model, for dfferen Fn. Fgure 6: Toal coeffcen a mesh N 3 and N 4 for SST urbulen models for dfferen Fn. To valdae he resul he percenages of dfference beween he numercal and epermenal daa, were calculaed and are summarzed n Table 4. Fn / Mesh N Mesh N 1 (SST) Mesh N 1 (-e) Mesh N 2 (SST) Mesh N 2 (-e) Mesh N 3 (SST) Mesh N 4 (SST) Table 4: Dfference n percenage beween C num and C ep 9

10 The wave paern generaed for he shp when advancng n calm waer, whch generae he waves on he dsurbed ar-waer nerface (free surface), s due o he shp ha has o supply he energy connuously o generae he wave paern ha followng he shp. Thus, he shp should overcome he drag nduced by he wave generaon on he free surface. The so-called wave ressance (drag) relaes o hs mporan phenomenon. The comparson beween he numercal and epermenal resul of he wave profle along of he hull wh dfferen Froude number and mesh sze are shown n Fgures 7 o 9 and he global vew o he wave paern are show n he Fgure 10 and 11, a Fn = 0.32 for he dfferen mesh sze. Fgure 7: Predced wave profle for Fn = by CFX. Fgure 8: Predced wave profle for Fn = by CFX. Fgure 9: Predced wave profle a Fn = by CFX. Fgure 10: Epermenal and predced wave conour for mesh N 2, a Fn = Fgure 11: Predced wave conour for mesh N 3 and N 4, a Fn =

11 From he obaned resuls, was observed ha he use of prsmac mesh mproves he predcon of he urbulen boundary layer, where he SST model was he bes appromaon. In hgher Froude Number, he predced ressance s more eac, defnng a velocy range where he CFD code gves accurae resuls whou requrng a grea compuaonal cos. For he lower Froude Number, s necessary o use a fne mesh capable o consder small dfferences n he graden of pressure and free surface deformaon. The fne mesh n he nerface of he flud perms a good appromaon of he wave paern by he shp. However he fne mesh n he hull mproves he predcon of he ressance beer han he fne mesh n he free surface. 8 DEFINITION AND PERFORMACE OF THE IMPROVED CASES The man obecve s o mnmze s he oal ressance of he Seres 60 model shp, n calm waer a dfferen speed for ranges of Froude number beween 0.18 and The bow of he shp was modfed ncludng wo bulbs wh dfferen lengh. The frs layou of he bulb was consdered as cylnder, n whch he ransversal area of he cylnder was esmaed as 20% of he md shp secon area and he lengh was consdered beween 0.04L bp <<0.06L bp, from he fore perpendcular. Laer he shape of he bulb was modfed unl he proper desgn was acheved. The wo desgned bulbs are shown n Fgure 11 and are compared wh he naed hull. Fgure 11: Perspecve vew of he bow and bulb geomery, naed hull, hull N 1, hull N 2 The used mesh for he hull was mesh N 2, whch was used n he numercal smulaon of he naed hull. For he bulb a fne mesh accordng o mesh N 4 was used, as show n Fgure 12. The boundary condon was he same as n he prevous case. Fgure 12: Mesh on he hall and free surface for he opmzed cases. The bulb reduces wave generaon around he bow regon. The wave generaed by he bow bulb under free surface neracs wh he wave generaed by he desgn waerlne. The wave ressance can be reduced f he bow bulb s properly locaed. The analyss of he hull wh bulb, was compared wh he naed hull smulaon, he parameers consdered n he analyss were he oal ressance coeffcen, he wave paern, he wave profle along he hull, pressure n he hull and sream lne n he hull, ha were repored n he Fgures 13 o 18 and Table 5. 11

12 Fgure 13: Toal coeffcen for bare hull and Hull N 1 and Hull N 2. Fn / Hull N Hull N Hull N Table 5: Dfference percenage of oal coeffcen beween bare hull and hull N 1 and hull N 2 Fgure 14: Predced wave profle for hull N 1 and N, a Fn = by CFX. Fgure 15: Predced wave profle for hull N 1 and N, Fn = by CFX. Fgure 16: Predced wave conour for hull N 1 and N 2, a Fn = Fgure 17: Pressure n he bare hull, hull N 1 and N 2, a Fn =

13 Fgure 18: Seam Lnes n he bare hull, hull N 1 and N 2, a Fn = The ressance n boh mproved hulls was reduced when a Froude number over 0.28 s used. Ths s observed on he compued wave paern, as he dsrbuon of wave feld by he cussed bow bulb s globally sof and has a smaller bow wave. The low amplude of waves s an ndcaon ha he wave ressance componen of he shp s ressance was reduced. Boh mproved models reduced he amplude of he bow wave, alhough hs s more noceable n hull N 2. In addon, he seepness of he frs wave and he frs rough around boh models are sofer. Wh he bulb volume a low pressure feld shows mprovemens n he pressure coeffcen dsrbuon. The pressure paern on he bow vares more genly and he pressure gradens are reduced n he modfed regon. In he wo new cases he slope of he sream lnes are larger. Fnally a lowes ressance was calculaed from he sream flow bulb when ncreasng he lengh bu hs dfference s margnal beween boh bulbs. The sgnfcan dfference wh he nal desgn s caused only by he pressure ressance, because he hree cases have he same frconal ressance. 9 CONCLSIONS Ths wor shows he poenal of Compuaonal Flud Dynamcs applcaons n shp hydrodynamc desgn. CFD s an effecve ool allowng he opmzaon of he hull, whch decreases he cos n he frs sages of desgn. The vscous flow wh free surface around Seres 60 Model Shp was smulaed for wo dfferen urbulen models a dfferen Froude number. A comparson of hese resuls wh epermenal daa showed good agreemen. The accuracy of he naed ressance predcons s ncreased when s usng a mesh fner han a 0.5%L n he hull. The obaned resuls are whn 10% of he epermenal resuls. Two dfferen bulbs were esed n CFD and provded an mprovemen n he hull ressance a hgh Froude numbers. REFERENCES [1] Emlo F. Campana, Danele Per, Yusue Tahara and Frederc Sern, Shape opmzaon n shp hydrodynamcs usng compuaonal flud dynamcs, Journal Compu. Mehods Appl. Mech. Engr.196, (2006) [2] W. J. Km, S. H. Van and D. H. Km, Measuremen of flows around modern commercal shp models, Epermens n Fluds (2001) [3] Suzu H, Suzu T, Myazas S, Turbulence measuremen n sern flow feld of a shp model sere 60, C B = 0.60, Kansa Soc Nav Arch, (1997) [4] H. Taesh, T. Hno, M. Hnasu, Y. Tsuada and J. Fusawa, Flow Measuremens and ressance Tess, ITTC Cooperave Epermens on a Seres 60 Model A shp Research Insue, Proc. 17 h Towng Tan Conference, (ITTC), (1987) 13

14 [5] Berram V, Chap K-Y, Lammers G, Laundan, Epermenal valdaon daa freesurface flow for cargo vessel. In: Kodoma Y (ed) Proccedngs of CFD Worshop, Toyo Japan, (1994). [6] Zhang Zh-rong, Lu Hu, Zhu Song-png and Zhao Feng, Applcaon of CFD In shp engneerng desgn pracce and shp hydrodynamcs, Chna Shp Scenfc Research Cener, Wu , Chna (1996) [7] Wlco D C, Turbulence Modellng for CFD, DCW Indusres Inc., Calforna, (1993) [8] Hr, C. W and Nchols B.D., Volume of Flud (VOF) mehod for he dynamcs of free boundares, Journal of Compuaonal Physcs,39, (1981) [9] C. Craddoc, A. Lebas, and A. Ganguly, se of CFD For hull form and appendage desgn assessmen on an offshore vessel and he denfcaon of a wae focusng effec, Proceedngs RINA Marne CFD Symposum, Souhampon, K, (2008) 14