Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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On Submerged Stagnation Points and Bow Vortices Generation
On Submerged Stagnation Points and Bow Vortices Generation
Pages 540-552
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From page 540... ...
AflSTltACT Th mechmi m of the genemti m of bow vertices in two dbm nsi ms, m hbomtory scale, is expkmed on th basis of th :xistence of c subm rged tagrution pomt below fhe fiee smtcce Th t~eam which originctes from fhe submerged tagrution poi t m fhe fie smtcce di ecti m reverses md neut~ali es th mom nt m of mcommg flow ~esultmg m c flee su face separction pomt Th miticl location of fhe submerged stagmtion pomt md subsequently fhe flee smiace separction pomt is cclcubted for fhe case of c s misubmerged horizontal cimukr cylmd r, md fhe ktter is compmed wifh th experime tal results The cgrement is ~ecsonably good Th generction of bow vo tices is ddscussed as c balance betweff~ mertial md gravitational effects Th loss of pressure et fhe b w md th consequent d cg due to b w vertices phffmm mr is calcuhted md is fommd to cgre w 11 with th value fommd by exper ime t A medho do logy for th de sign of efhcient b w contour shap in two dimff~siom whe~e fhe subm rged stagnati m point is used es c conhol hmdle, is p~esented The fheory is clso mplied to nm~egmbr shcpes Ike vetical step md bulbous b w Th results are compared with fhose obtamed by flow computati m md found to be m ~easonably close cg~e ment Firully, c conject re is cd cnced to expkm th genemti m of bow vo tices m the dimff~siom, i e fhe neckk e vo t :x arommd c ship's load waterlme, on the same basis INTRODUCTION Th vo ticcl moti m observed checd of c particlly submerged object tow d m c hyd odynamic tmk is k ow as bow vertices The bow vo tices ~egion is separcted fi m fhe mcm potential flow by c shc,m boundary termed es fhe flee su face separcti m poi t FSSP) , when fhe flow is two dimem iorul Th hyd odynamic flmmes The understmdmg of fhis ph n menon is of di~ect comeq ence to bow wave b~eaki g, which is re pomible for c substmticl c mpone t of c ship's resirtfmce Bcbc 1969)
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From page 541... ...
assigned fhe white water gff~erction phenomffmn to she fl w imtability md subsequent b~eakmg of fhe bow flow, md tudied th same themeticclly md experime tally m g~ecter detail The fiee smtcce cmvatme was concluded to be one of th somces of sh ar fl w benecth th fie surtcce Stability am~lysis, vcrticity shetchi g fheory, md fiee su face boundary kyer fheob w ~e mvolved to expkm fhe exp rimental results, eg velocities, Rey old shesses md b w wave heights Pctel, mdweber md Tmg (1984) cttempted to expkm fhe b w vo tices genemtion on th basis of fhe :xistence of c fie smtcce bommdary kyer, which is c kyer of concenbated vorticity occunmg due to fhe curvat re of fhe fie smiace m fhe fl w of c ~ecl fluid Th cuthors sp cuhted f tt fhe fiee surtcce would move slower f m th kyer benecth it md fhis velocity defect would lecd to c FSSP checd of th body md subseq e tly fhe bow vo tices Fu ther, by assmmmg fnat et th fiee smiace th smtcce tensi m is baLmced by ncrmal viscous shess fcrce, m exp~essi m for FSSF locati m was obtcined by d6'ect mtegmti m of fhe boundary c mdition using th contim ity quctioa The locati m of fhe FSSF was obtcined m terms of fhe slop of fhe fie smtcce Th ~esults so obtamed were cpplied to c cimukr cylmd r md compmed wifh th exp rim ntal values of b'~yo et cl (1982)
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From page 542... ...
e perim ntally Besid s c cacukr cylmd r, th fhecry is clso cpplied to c vertical tep md c bulbous b w shme Th design of m effcient bow contom m two dimff~siom is discussed Pinally, c conject ~e is cd cnced fcr e pkmmg fhe f ee dimemiorul bow vertices generctioa The subseqre t sections of fhis pmer develop th idec md fhe relevmt expressiom m c tep by tep manner ff~dmg with conclusi ms md f t ~e scope of work SSP THEORY AND BOW VORTICES GENERATION The mech ml m of bow vertices genemti m md fhe occmrff~ce of th fie su face separcti m poi t c m be exphined und r fhe fiamework of th proposed SSP th °b as follows A tagrution pomt m fhe two dimff~sional flow pc t c f lly submerged object is clways fhe mtersection of th di id6 g t~eamlme md the body The sheam divides itself mto two parts et this pomt Th pressme on bodh fhe sides of fhe tag,nction poi t d meases The pomt is c maximum of fhe p~essure dish ibution b fhe case of fhe flow pest c partially subm rged object, c tagnation pomt may :xist below th fie su face md may be rightly called c submerged stagnati m pomt (SSP) es show m Pig I It may be conject ~ed fnat m case m SSP does :xi t it should similarly be th mtersection of fhe di id6 g sheamlme md fhe body Accordmgly, the sheam should d6 id itself mto two parts et fhis poi t md ff th fl w is two dimff~sional, one part will flow below fhe object md fhe of her should move upward m fhe d6'ection of fhe fie surtcce This ktter part of th sheam, wi g to th obvious limitation in mo i g upward due to g~avity, ~everses md neabalises fhe velocity of fhe incomi g fl w ~esultmg m m PSSP where fhe two velocities c me m baknce Th reversmg flow tmps c regi m offhefluid(Fig l)
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From page 543... ...
had specubted c simibr scenario as one of th possibilities while cttemptmg to flnd m am~lyticcl soluti m for verticcl or inclit d flat faced bmw shcpes FtESULTS AND DISCUSSION SSP -Evisteue cud Locetiou To confum the e i tff~ce of m SSF md tbs qtt ntly fmd its position should t quit, m genemi, solvi g fhe glavity flmw problem, which of c trse, is very difft uit But it is possible to k ow cbout fhe SSF md evert flnd fhe mitial location of th SSF by amrlysi g the mitial c mdition of fhe probi m Com ider fhe two dimertsimuri flow pc t c horizontci semi tbm rged cit ukr cylinder it is cssum d ft~t fhe fiee t face flow is obtamed by mitistly he i g potential double body flow md removmg th upper flmw suddertly at m imt mt (t = 0+) which may be ttkert as the omet of gm ity flow (Grosenbmgh md Yemmg 19S9)
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From page 544... ...
gives fhe prevailmg p~essme dishibution on th submerged part of fhe cylmder contour at th mset of fhe g c ity flow The maximc md mmimc of fhis p~essme d6 tributi m cm be (~ obtained by fhe cor~ntiorul method ie putti g P =0 dO which leds to cosO ( 3sinO + ~ ) = 0 The points of optimum pressure will be given by 0 = 2 md sin0 = ~ (g)
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From page 545... ...
Accord6 gly, w obtam V2= 4F~ (1 4) So far w hcve ben obtammg fhe t tits just by cnalysmg th imticl condition, es it was pe t tim g to fhe mset of glavity flow m immediately fhereafer; but th next tep i e bahmci g fhe t verse flow cgam t fhe mcommg flow clo g fhe fie trface, is c t suit belongmg to fhe flnal tecdy state, which c m be achieved mly cider severcl smeller tim steps fi m th time t = 0+ onward b fhese steps, th fiee trtcce conditi m is to be cpplied on fhe fiee smtcce, fhe mcommg md reverse flow is to be cclculated clo g fhe ft e su face which itself is m urJmow t Of fhe problem The t n Imearity of fhe ft e smiace c mditi m tdd c futher complicatiot However, sit th cim of fhe p mer is to present fhe fhemy md e pkm fhe m chmism of bow vortices genemtim, md t t to go into det tiled c mputation, w shell tb to obttm some cppro imate re tits so as to get m msight i to fhe phertom nm Accordmgly if ;~ is fhe slope of th fiee smiace w m w ite th balancmg process es COS ;~ = Uz (1 s)
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From page 546... ...
(iii) The th ot tical values for Ft = 0 72 to 12 cm be ssid to be ressotmbly close to th e perim ntal trve keepi g fhe cmde basis of fheu derivati m m mmd luer~dld-Gre titedomtl Effect It is intere tmg to obsetve fhe ch mge m the location of fhe SSF md the FSSF wifh fhe met sse m Ft As Ft is mcressed, th SSF mm s closer to the fie trface md fhe FSSF moves closer to fhe body, Fig 4 Th region, which is obt tined by jommg fhe SSF, th FSSF md F (obt tined by taki g bmw wa~
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From page 547... ...
The sbove fomm is, m s way, c mparsble to th one obt tined by Dsgert md Tulin (I 972, B m 72) One c m slso expt ss CD as s f nction of fhe SSF only md obt tin CD = sin°sss [I + 3 sm 05sS ]
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From page 548... ...
for ~ ve tical step by sol i g fhe gravity fl w usi g fhe method of two pert rbation exp msiom 3 Bow d ag dep nd upon fhe location of fhe SSF, fhe low r fhe SSF th mme is th bow d ag Th location of fhe SSF on th oth r h md is, d6'ectly ~ekted to th p~essme ddshibutim of double body fl w on fhe bow, which m t rn dep nd upon its shme The~efme, th double body p~essme d6 tributi m on th b w md fhe locati m of fhe SSF pro id fhe key to fhe desig of b w co tour for minlmmm b w d ag Bow Cout~mr Deslgu -two dlmeusloual ease A bow contour for th two dlmemiorul case m be designed now for mmlmum b w d ag as foll ws Th total pressure at my pomt of th bow is fhe sum of double body pressure md fhe gm lty p~essme, i e Cp(~ly =cp(d6) +cre The c mdition for fmdmg SSF is given by aCp(b~l)
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From page 549... ...
md fhe con t mt slope Imes of C fm d6fferent vallt s of Ft The i tersecti m of the two slope ttves fhert gives th cmrespond6ng SSF locatiot it c m be seen thct es Ft mcreases, fhe SSF m th ve tical tep moves closer to fhe fie smtcce, simibr to fhe case of c cit ular cylmd r For Ft = 1, fhe SSF lies c little above half th d cid, which is c mparable to th value es show t by Grosenb mgh md Y t g (I 9S9) with fhe flmw computatiot Fig 7 shows fhe sarne for fhe case of bulbous bmw shcpe Owmg to th fi tuent chmges in fhe dbt ction of slop m fhe shap, fhe maximc me not es w 11
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From page 550... ...
fnat th wa~ hekmg is delcyed for c bulbous b w relative to c ve tical step, smce low r is fhe SSF fhe less doml mt is th mertic effect md wa~ brekmg which is duectly Imked wlfh sped is debyed accordmgly Bow Vor~des - tb ree dlmeuslousd eese Th foami g motion or white water observed at fhe b w of c ship md cll clong th load waterline k wn es neckkce vo t x, is th thee dlmff~sional pict ~e of bow vortices if th bow vmtices me genemted in fhe two dim nsicrurl case by fhe presff~ce of m SSF l~low fhe fiee su face, it will be just right to conject ~e fnat m SSF may xist et fhe ship's b w md et th secti ms l~low th fie surtcce b of her wmd, th curve of C omr) vs d aft may have c maximum et th b w md et fhe sections Smce fhe ship has c fmite d cid, its double body flow must acqune c c mpone t of velocity m fhe depfh duection right fi m fhe forward perp ndlcukr down th hull Accordmgly, et th b w fhere is c d mecse of double body pressure fi m forward pemff~dicukr to th kel md et each secti m fi m load waterlme to th bilge, which in presence of gm lty, ~esults m c SSF bel w th fie smtcce givmg rise to c fl w fi m fhe SSF to fhe fie smtcce This upward flow may fmm c jet et the fiee smiace, enbam c lot of air md dismteg ate i to immm rable bubbles at fhe fiee su face ~eflecting mme light owing to their k ge smtcce are md form c white water or c foam lik mpe ance Coueluslous Th problem of b w vo tices genemtion et kboratmy scale is cdd essed h re with fhe mcm clm to e pkm fhe ~esults of fhe experiments on c hml ontal semisubm rgedcacular cylmd r, md fhe mechmism of bow vortices genemti m observed ahecd of fhe cylinder I it is shown fnat fhere xists c tagnation pomt bel w fhe fie suface, ie c submerged sbgnation poi t (SSF)
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From page 551... ...
md (2) should be c mducted fcr odher bow ge mehies with different slop dishibution, e g verticcl step, conventicrur ships bow md bulbous b w et 4 Th conjectme mcde fcr bow vo tices gff~erction in c f ee dimemiorul case is to be verifled by usmg c the dbm nsicrurl arulyticcl body generated by c k own combination of singmbrities The flow past c sphe~e or Rmkine ovul do not serve fhe pu pose es th se me axisymm hic Th c mbination should be such as to result m c hue f ee dimff~sional fl w This will ~equne fhe dishibution to be asymm hic Alternatively, fhe double body p~essmes may be computed m c Wigley hull usi g c higher ord r pmel method so fnat th poi ts et fhe bow c m be tsken as nodes es w 11 as collocation pomts md fhen th p~essme dishibution et fhe b w md at th section should be obbmed Subs quently, fhe SSP et fhe bow md et fhe sections should be calcubted to conflmm fhe genemti m of bow vertices in th f ee dimff~sional case We have worked wifh fhe values of C for double body flow for c series 60 h 11 obtcined fiom "SB P PLOW" but fhese w ~e et th panel cc troids which w ~e cway from fhe pomts at fhe b w contour Owmg to fhe high tmgential velocity m th neighbourhood of bow, fhe C was far bel w th expected value of umty et DBSP We used c four/five deg~ee smiace flttmg but th exhapokti m was not sati factory Refereues Bcbc, E "A New C mpone t of Viscous Resistmce of Ships" Journal of the Socieh of Ncval A chitects of Jcp m, Vol.
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From page 552... ...
M "Splashless Bow Flows m Two Dim psiom", 15th S mposimm on Na~l Hvd odvnamics, 1954, pp 293 3 0 1 Miyata, H Nishimmc, 5 "Fmite Diffe~ep Simulation of Nop Imear Ship Waves", Joup~l of Fluid Mech mics, Vol.
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