Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
Currently Skimming:
Analysis of Turbulence Free-Surface Flow Around Hulls in Shallow Water Channel by a Level-Set Method
Analysis of Turbulence Free-Surface Flow Around Hulls in Shallow Water Channel by a Level-Set Method
Pages 941-956
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 941... ...
ABSTRACT In fLe presfft st dy on t rbuiffce free sufae problem s m ha low wa er ch mnel, two fluids Reynods ave~ged Navier-Stokes equaions a e solved by using aFinite Volume Method, where 5 MPLEC agondEm is used for velocity md pressure couplmg, md stmdad k cturbulence model is inhoduced for modeling Reynolds stresses A Level-set method is used for capt ring the free-su fa e movement md the influence of the t rbulence layer of fLe free su fa e is implicitly considered For the vaidaion of the present numerica scheme, fLe numffica results for Wigley a d Series 60 Ct =0 6 ships in deep water ae compaed with the expenmffta results Computaions ae made for vaious depth Froude numbers for fLe caculaions of the halow water chmnel flow in the numerica results, fLe presfft solutions show good agreemffts with the experimenta results for the deep wmer ca e, md for the ca e of fLe shalow water solutions with the viscous effect, present numerica results how rea onable physica phenomena in addition, it is demonst~ted fha fLe level-set medhod cm trea the free su fa e flows a ound hulls with a rea onable a cu~cy togedher wifh a simple numerica procedure INTRODUCTION Shalow water ch mnel flow nea fLe critica depth Froude number Fh(=U/~/~) =I is m unsteady, nonlmea phenomenon md ha peculia flow chamctenstics, where h is watff depfh, U is the ship speed md g is fLe gravitaiona a cele~tion At this critica speed, a ship gene~tes tw -dimensiona waves propagaing m fiont of fLe ship, which ae fatff thm the ship speed md show the unsteady flow paten~s These waves a e named solitons or solitay waves The influences of fLe ch mnel wal md shalow wmer c mse the increa e of the resist mce md sinkage of fLe ship a nea fLe critica peed In the experimenta mvestigaions, Thew md L mdweber (1935)
|
From page 942... ...
in file naval hyd dynamics, this method is aprovocative approach md could be used as a robust numerical scheme in file present wodk, d is level-set medhod is introduced for cant ring the freesu face movement md implicitly considermg the influence of turbulence layer of the fi ee su face In o der to validate file present numerical scheme, the expert emol results of Wigley md Series 60 ship at deep water condition are compared wish file present numerical results in file numerical results of the shallow watts flow, the wave patterns, pressure di tributions on file hull md the fiction md pressure resistmces computed at different flow conditions are compared with each of her End pe tmert discussions are included Fr m these numerical results, file validation of file level-set method c m be also checked MATHEMATICAL FORMULATION Governing Equations In the three-dimension problem, the general integral fomms of file time-weraged conservation equations of mass, two-fluid mcompressible Navier-Stokes equations md turbulent kmetic energy dissipation rate c r be Isomer 111 J3t (p(d a)
|
From page 943... ...
Since the characteristics are propagating away from the interface with speed of unity, the appropriate time step according to the CFT (Courant Friedriches Lewy) Ah condition is At = 2 Local Level-Set Method If the level-set function around the interface is an exact signed distance function, the magnitude of the level-set function gradient at the interface must be unity, namely, (17)
|
From page 944... ...
up to time tush Since file chamcteri tics a e propag ting away from the inte face with speed of unity, the appropn te time tep according to the CFL(Courmt Fnediches Lewy) Local Level-Set Method Acco ding to file locality prope ty of the level-set method, it is mffcieDt to calcul te file level-set function only m a small naTow b md around its z~solevel-set for the reinitializ tion procedure By doing so, in file case of tw -dimensional comput non let IV X IV be the number of gad point, then comput tional expense reduces from O(iV )
|
From page 945... ...
g (33) Conclusively, fLe level-set fonm of the tw fluid Navier-Stokes equ tions contains implicitly gas-liquid boundary conditions NUMERICAL PROCEDURE b the discreti tion process, all unknow values md physical prope ties are computed md stored t fLe cent~s of the conhol volume b te pol tion md differenti tion ae necessary to evalu te fLe convective
|
From page 946... ...
eSe (36) The hybrid scheme is used to appr ximate convective fluxes For file approximations of the diff sive fluxes, the gradient ve tor at the cell face c m be calculated fir m the gradients at file cell comers appr ximated by using midpoint r le based on the G mss theor m: Eli (Vq)
|
From page 947... ...
Fig 6 show the t rbulent kinetic energy md eddy viscosity di tributions around the hull of Series 60 hip at FN = 0 316 The fi ee so face turbulence layers in the an md file water region c m be seen The Shot new of file turbulence layer developed around the fore past of file hull boundary on file free su face f ther develops End becomes thicker as it moves backwards Although file numerical solutions computed by file present scheme near the free su face might not be so exact, the calculated t bnlent properties show reasonable physical characteristics For file shallow ch mnel watts calculations, file Wigley hull used previously is taken in file numerical procedure for hallow water ch mnel problems, blockage coefficient 5 = Al /(2wh) = 0 021, a ratio of water depth to the hull d ft It / T = 1 598 md a ratio of chamel widdh to the hull length w/L=20are used, where Aois file ~ross-section area of the hull at mid hip at a given daft Fig I show the definition sketch for file shallow water chmnel problem For file computational cases of Fh = I md Fh =1 5, RN =3 6X10 md RN =5 0xlO are used, respe tively The computational chmnel length x / L = 10, where x / L = 5 head of the hull md x / L = 4 behind the hull in each computation, 210x44x46CVsis used md H-H type grid is employed for the present calculation Computations a e stated at full peed without flow acceleration No slip flow condition is used at the hull boundary md the sidewall of file chmnel, md the symmet y boundary condition is inhoduced at the bottom md also at the center pure of the ch mnel The numerical results are show in Fig 9 Fig 9 (1)
|
From page 948... ...
= 42 In Fig 10, wave profiles caculaed Song file hull su fa e a FN = 0 316 in the deep wme' a the critical speed Fh = I md a file supffscritica speed Fh = 1 5 m the shalow water ale how it cm be seen fha the difference of file wave heights md pmerns between the results for file deep waler md shalow charnel water is somehow considerable By compa ing the wave profiles for file deep water md the shalow charnel of Fh =I whose tw speeds are equivalent, file iagff wave nea the bow md a deep trough nea file steno for the clitics peed ca e, which is of course cat sed by the big pressure ch mges due to the shalow water md ch mnel effects a seen laser in Fig l2, crepes a large him by .-. -I For file three computations ca es, the pressure md faction resistmces acting on the hull are plotted in Fig 11 it cm be seen that the shalow water chat nel effect mcrea es file pressure resist mce md the magnitude of the resistmce ha file ma imum value nea file critical ship speed in the shalow waler ch mnel In Fig 12, the pressure dishibutions on file hull su fa e me plottedforthe fEree ca es Smce file ewe ts of file bottom md side ml is of file ha low ch mnel a e considerable, the magnitude of file pressure difference Song file hull is higher for file critical speed ca e th m that for the deep water ca e When a ship adh-arces in the shalowwmer charnel a ahigh speed, file pressure charges on the ship hull cased by file ewe t of the shalow charnel crepe a large bow wwe with a big trough nea the stem a seen above md a cordmgly, case file severe sinkage md him of the ship, aso resulting a la ge resist mce increa e In Fig 13, the pressure di tributions on file bottom, the cent epl ~ e md sidewal of the charnel a Fh =lae show Becmse of the wave propagation ahead of the hull, a high pressure dish bum on s over the upstream region cat be seen b Fig 14, the velocity distributions md a la velocity contours a x /L = 0 75 a d x/L = I O a e show for file fEree computations ca es Smce the wave heights Song the hull su fat e a d file ma mt des of the fluid velocities for the three ca es a e not a I file same, file a la velocity contours show somehow different shmes Becmse of the effects of the bottom of file ch mnel, the a la velocity contour a the hull bottom a e widens for file ch mnel flow ca e th m fha for the deep waler ca e CONCLUSIONS The level-set apron h to solve the t rbulence fiee su fat e flow a und hull m deep wmer md hallow waler charnel ha been developed The advmtages of the level-set medhod make stable computation procedure, eaw pm ~ [mns~g md aso gives rep onably a curate solutions for the present viscous hee-su fa e flow it seems fha the level of the numenca a curd y obtained by the present medhod is simile to fha of of her methods used with the same turbulent model a file present one Numerica results of the fiee-su fat e flow Sound a hull in shalowwmer ch mnel with file viscous effects show rep onable physical phenomena But in the f ture, it is necessary to compare numenca results wish expert ems for validation md Only out more wstemaic study with vaiaions of parameters, h/T, w/L md blockage coefficient FtEFEFtENCE Bai, K J
|
From page 949... ...
md Chun H H "A Sh dy on the Level-Set Scheme for the A alysis of fLe Free Su face Flow by a Finite Volume Medhod," Joumal of the Society of Nsval Architects of Kores.
|
From page 950... ...
Fig. 1 Definition sketch (shallow water channel)
|
From page 951... ...
Fig. 6 (continued)
|
From page 952... ...
Turbulent hi etic energy Wit A.r Eddy viscosity A.P. Fig8 Turbulent ki etic em & eddy viscosity distributions around hull of S |
From page 953... ...
-(a) FL=l.O, FN-0.316, RN-3.6XIOS Fig 9 Calmiated wave pattems of Wigley hull (1)
|
From page 954... ...
1 1 History of the resistance of Wigley hull at FN = 0.316 in the deep water, and at Fh = 1 and Fh = 1.5 in the shallow water channel with h/T=1.598 and w/L=2.0 (blockage coefficient Sb = 0.021 ) Deep water FN = 0.316 1 4 7 10 13 16 19 22 25 -103.3 -61.9 -20.5 21.0 62.4 103.8 145.2 186.6 228.0 IF.P A.P| / ~ ma\ Shallow water Fh = 1 1 4 7 10 13 16 19 ,/ / ~ 22 25 -270.4 -186.1 -101.8 -I 7.5 66.8 151.1 235.4 319.8 404.1 F.P.
|
From page 955... ...
x/L=0.75 (b) x/L=1.0 Fig.14 Calculated velocity distributions and axial velocity contours at x/L = 0.75 and x/L = 1.0 at FN = 0.316 in the deep water, atFh = 1 and Fh = 1.5 in the shallow water channel with hlT = 1.598 and w/L = 2.0 (blockage coefficient Sb = 0.021 )
|
From page 956... ...
For instauc e, K- P- e quati on on B oussine sq equations. The most benefit by using au unsteady RANS cou d be the better approximation of the wake waves near a transom stem in genera and of the bow waves at high supercntica speed, since the bow waves are very sensitive to the bow shape.
|
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.