Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
Currently Skimming:
Ship Stern Flow Calculations on Overlapping Composite Grids
Ship Stern Flow Calculations on Overlapping Composite Grids
Pages 910-926
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 910... ...
ABSTRACT A method for predicting the viscous flow aro md ship terns is presented its main cdv mtage is the flexible high-quality g id on which She go coning equations Ed the bo mdary conditions are dircreti:D:d A set of overlapping g ids on the hull surfae are crected either by hyperbolic marchmg from one of the bo mdaries or by cutting the surfae by horizontal Ed vertical plumes Body-ftted vol me g ids are then g own hyperbolically out from the surfae At the outermo t edge of the compnhtioncl domain c bakg o Ed Cartesian g id is chosen Ed c sequence of finer Ed finer Cartesi m g ids is automatically generated to create c s fficiently mooth t msition betw en the coarse edge g id Ed the tine body-fitted g id The algorithm guar mtees duct Here is s fhcient overlap betw en all g ids The Rey olds-Avemged Navier-Stokes equations are solved on the overleaping g id using finite difference discetization The equations are partially tr m formed Ind all variables are co-located Pressure Ed velocities are coupled vie c 5 ah L'L E clgorif m Ed Rhie Chow mte polation is used to avoid checkerboard oscillations Computed results are compared with measured data for th ee different hulls INTRODUCTION The state of She art of Computational Fluid Dynamics applied to ship desig was review d et the previous Symposi m on Naval Hydkodynamics by Larsson et cl (1998) While She obtainable CFD acuray is s fficient for m my purposes, erpff icily when optimizing the hull shape, q mtitative predictions of m my hydkodynamic q mtities must still be regarded with caution Several reasons for She lack of absolute acuray were listed Ed discussed in She review Examples are inadequate g idding, dissipative m mericcl tffhmiquer Ed too approximate turbulence modeling Free surfae representation was also mentioned es m area w re further developments are needed Dming She pest five years effo ts have been mad in She research g oup et Chakmers LOWTECH to improve the state of She art m all four areas The work on g id generation has been reported in Petersson (1997c,b, 1998)
|
From page 911... ...
This c m be done m one of two ways The simplest possibility is to cut the surface by horizontal or vertical plumes to obtain one set of lines The other set is obtained thffecftff by com cting pomts et c given percentage of the total arc lend h along ecch one of these Imes, measured from one of the patch bo mdaries ff g ids of f is type get too skewed hyperbolic marching is used Starting from c patch side, g ids are g ow inwards in c stepwise maimer One step consists of moving all he pomts on one Ime to c new one This is done for ecch pomt by taking c rep et right males to She original line md in c direction t mgenticl to She surface The pomt fo md will generally be away from the surface, so it is moved along the normal doss to the surface Each step length is detemmmed f om the cell area d-fined bv She tart md end positions of two successive points The g id may be forced to follow given lines et She side bo mdaries Having completed the g id generation on the hull, body-fitted vol me g ids are g ow hyperbolicclly outwards from She surface The procedure is c th e - dimens ional generclizat i on of the two - dim ensiomd one just described Points are fir t moved et right males to She hull surface md ah reader et right males to She surface defined by the g id points from She previous step The silos of the step, md She capability of following side bo mdaries are es described groove The description so far concerned the curvilmear body-fitted g ids These are embedded into one or more backg o md g ids, which are normally Cartesi m (cylindkical g ids have also been used) md extend to the bo mdaries of She computational domain When cil component g ids have been generated the o Up algorif m starts Each g id is given a mique priority, She initial backg o md g id always being the loss t The overleaping g id is then constructed m the followmg steps: I Cnt surface holes, i e mark all points outside of the computational domain md Iymg on g id faces that are part of She physical bo mdary as dead 2 Cnt vol me holes, i e mark She remaining pomts that are outside of She computational region as dead 3 Set up exact mtemolation points 4 Ckssffy (i itchy)
|
From page 912... ...
aaiJ = 0(1) md the contimmity equation reeds aul , =0 oi l Us cre the me m v locity components md Xs the space coordinctes P is 6he pressure, v the kmematic viscosity, ~j 6he R y olds shess tensor, md t is the time Cartesi m coordim~tes may be used m 6he backg o md g ids, while the body fitted g ids require cmvilinear coordinctes Tr m forming only the mdependent varibles 6he ctov equationsbecome md a + dt ut + d I ( jt a )
|
From page 913... ...
) The im ff kyer extends f om the surfs s to Ry = 250 Numeneal method A~ = 70 A~ = 2c = 0 418 In order to mske the intffpolstion equations 9 s simple 9 s poss~ble smd to keep 6he m mber of mterpok tion pomts mall some cs e hs4 to be exe six4d when discreti ing 6he equations Fir t 6he discretization stencilhs4 tobe ss small s4 possible, othe wise the ov4rlap regions will be wide Si se 6he equations 9~s second order the ms 11est ste sil possible is 3 nodes wide Second, collocsted storage is req3ired smce taggered storsge givss four mtemolstion pomts per cell Collocsted stora ge s Iso fs silitstes the 3se of Cs tesi m compors4nts so 6~t base v4ctors will not hav4 to be t msfommed when interpoktmg betwsen the g ids Th3s, some medhods I ke higher order 3pwmd differff ses smd staggered g ids cs mot be 3sed, evsn tho3gh they 9 e mmerically sthastiv4 The challenge in the present work is to fud 9 ststle, efficient smd 9 surste sheme with collocated node-cenhed storage wi6h 9 th ee node wide ste sil Anodher requested property of 6he medhod is the capability to sim 31ste thm bo mds y Isyers At model scale the Rey olds n mber for 9 ship h311 is t pically 107 smd st f 311 scs le 109 To resolv4 the corresponding bo mds y Isyffs, g ids with cell 9 spect rstios 3p to 106, Reg trom (1994)
|
From page 914... ...
(22) Tcking fhe dismete div Igence D of this equation results m c spa~se Lcplacim DG that will giv solutions wifh chequer boa~d oscilktions its tencil is clso widel f m fhe th ee nodes postokted ea~liel fm mmimi ing fhe ov Ikp legion it clso requi es fuct bo mda~y conditions ~e specified m two kyels Repkcmg the spa~se with the dense Lcpkci m will not effect the mder of fhe scheme, but it will mcke fhe piedictm md cmIectol steps incompabble, so fuct no hue stecdy state whele bodh equations a~e simultmeously satisfied c m be leeched The lemedy is Rhie-Chow interpohtion whele c taggeled tmcge scheme is cpproximated Dffmting q mtities et conhol vol me faces by mbsmipt f fhe pledictm equation is explessed ~s Uf +6t(KU )
|
From page 915... ...
For the continuous problem explicit boundary conditions are only given for the velocity. The pressure boundary conditions are derived by applying the continuity equation on the boundary, except for the outflow where the pressure is constant.
|
From page 916... ...
been made for These two cases Some of These comparisons willbe presentedhere The reason for incorporating both t miners is feet the HSVA hull is outstmdmg when it comes to bo mdary layer md wake measurements et model scale, while the Ry ko Maru date include remits from th ee R y olds mnnberi, corresponding to model ma full scale, es well es m mtemmediete scale More scarce experimentel date have beer amiable for the modem ships, but some comparison between calculations md meesurements has been possible in all cases U fortunately, the modern ships are co fidentiel but permission ht. been g mted to show c few examples f om She container ship The geomet y of the m odern Kore m hulls used in the Gothenburg 2000 CFD workshop was not amiable by the time these celcoktions w re carried out .
|
From page 917... ...
) , Hereby incre6 sing She 6 curacy of She i flow conditions The computation was r m with 6 hybrid first order upwind second order central discretization of the convective tffmr For She turbulence equations the blend was 50/50, while for the moment m equations two blends were tested 20/80 6md 5/95, where She first m mber corresponds to the first order percentage in total 180 iterations were made, 90 with 6 time step of O 1 6md 90 with 6 tep of O 01 In Figme 2 comp6 isons are made between results from the two blend ratios it is en that She dffferff es 6 e ve y smell, bodh m the pressure distribution 6md in the isowakes at the propeller plume it is ml kely that 6 full second order discretization would
|
From page 918... ...
Pressure distribution along the waterline and keel Figure 3. Limiting streamlines.
|
From page 919... ...
Measured data have been reported by Namimatsu and Muraoka (1974) at three different Reynolds numbers, corresponding to model scale, full scale and one intermediate scale.
|
From page 920... ...
Overlapping grid around the aft half of the Ryuko Maru tanker. Top: overview, middle: volume grids at the stern, bottom: surface grids at the stern The hull surface is covered with three overlapping surface grids.
|
From page 921... ...
results. Pressure distribution and streamlines on the afterbody Axial velocity contours at the measurement station for the three Reynolds numbers are shown in Figure 9.
|
From page 922... ...
Surface grids at the stern of the container ship The predicted pressure distribution and limiting
|
From page 923... ...
The overlapping grids used here are best suited to fully explicit methods, where the updating of the solution is done on the structured grids completely separated from the unstructured updating of the interpolation points. In contrast to this the requirement to have an implicit solver that stems both from the incompressible flow and the thin boundary layers encountered, forces us to somehow solve the fluid flow and interpolation equations simultaneously.
|
From page 924... ...
: Viscous Fre Surfae Hydkodynamics Using Unstructured Grids, 22 d Symp on Na~l Hydkodynamics, Wcshmgton, Aug st 1998 Mcs ko, A (1998) : N mericcl simulation of the viscous flow for complex geometries using overset medhod, 3rd Osakc Colloqui m, Osakc Ncm imat su, M md Murcokc, K: Wcke dish ibut ion of full fomm ship, IH E gineering R view, 1974 Petersson, AN (1997c)
|
From page 925... ...
: A L vel Set T - hmique for Computmg 2-D Free Smface Fl ws, 12fh Workshop on Wcter Waves md Floctmg Bodies, Marseille Vogt, M (1997) : A Comparison Betw en Moving kid md c L vel Set Techmique for Solvmg 2-D Free Surfcce Flows ASME Fhids E gmeermg S mmff Meetmg, Varmouver Vogt, M (1 998)
|
From page 926... ...
AUTHOR'S Rb~PLY Ovuall we beheve fh q all viable m hods w 11 give ~ milv resclU he mm differmce bflweec fhe methods h fhal pqIal dhmele qbC h emier oc a smooth qmclmed gnd especiallf if a high order of a mra f h deshed, hLe comerv hOS h easier lo mfome os ag idwithcos overlappkg celh hhUI wvdspefechg wul ppkggrlds Mosllf mooth bosad f, so fhal f w c mpocecl grids aw wqched ald fhe rel qlve eff mpecl oc h I mol qloms Iow High Re reqchhg high ~pe t~aho celh Se h g ids aw emler lo gecuale m ~ pvale mclmed c mposecl g ids No shochs, so the whhoc cm be rewlved ald the h a mrav matlf cm probablf) teceglecled For fhe case of rlgld bodies mwhg relqlve lo ose mother, d ppears fhat d ts more ehiclent to ~se a fh ed R id ~odad ea h bodv fhh case moq of fhe ma hh f reqched h alreadf pesml m al werl pph g grid m hod, while addh g fhh capabllllf lo m m~bmclmed grid method I hes more woh
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.