6, :! CFD7 R ; HI < 4 FG.Spal [6] V ; >,!5a 4 <=( K>; (),*$ +," -.a34+,, Churchfield [7] BTT AUVNO PQ. / 34+,0V K> 34_ `, 1 9:.^UVNO PQ [8] 34+

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1 32 6 Vol JournalofHarbinEngineeringUniversity Jun.2011 doi: /j.isn CFD,, (! ",#$ %& ) :!"#,$%&' N S ()* VOF(volumefraction)+,, -./01! *,2% 34+,567&'$8+,.59:;, <= > ; *?@. AB C!DE FG* <,5 HI+JKELMNO 4, NO PQ R$%S34+,=,BTUVPQ 34+,WXY, Z[(\],^AUPQ 34 +,V E34_ `.abc, ()* VOF+,! 7*, < Z Z. :!;)* VOF!+,;34+,;NO PQ; 7 :U661.31!"#$%:A!&' : (2011) NumericalstudyoftipvortexcavitationusingCFDmethod HANBaoyu,XIONGYing,LIUZhihua (ColegeofNavalArchitectureandPower,NavalUniversityofEngineering,Wuhan430033,China) Abstract:Thenumericalsimulationoftipvortexcavitationissignificantintheprocestoaleviatetheefectsofthe cavitation.thecharacteristicsoftipvortexcavitationbehindanelipticfoilwerestudiedusingreynolds averaged Navier Stokes(RANS)equationswithamodifiedVOF(volumefraction)cavitationmodel.Theturbulencemodel selectedwasanexplicitalgebraicreynoldsstresmodel.inordertoreducethediscreteerorinducedbythegrid, meshrefinementwasappliedtotheareaofthetipvortexcoreinnumericalsimulation.first,theaxisandtangential velocityofthetipvortexflowfieldwithnocavitationwerecalculated.toconsidertheefectofsystemrotationand streamlinecurvature,therotation curvaturecorectionwasadaptedtotheturbulencemodelanditwasfoundthe turbulencemodelaftercorectionincreasedthepredictionprecision.numericalresultsshowthatthecorectededdyvis cosityturbulencemodelsagreedwelwiththeexperiment,whiletheunmodifiedversionsover predictedtheturbulence induceddifusion.basedonthat,thedesinencecavitationnumberoftipvortexcavitationwaspredictedusingtherans methodandmodifiedvofcavitationmodel,andthenumericalresultshowsgoodagreementwithexperimentalresult. Keywords:tipvortexcavitation;modifiedVOFcavitationmodel;turbulencemodel;rotation curvaturecorection; desinencecavitationnumber! N 01! F.!BCD,, B, C.a =!, H I 4! /. [1 4] a N 01! / B.,7 : (): c ( ). *+,-: (1981 ),, C,E mail:hamberg001@si na.com; (1958 ),,, C../*+:. R 4 E 7 "#, S E 4, b$%7 R+J 8!.,$% RANS R ( 4 +J!4/ FG,b! 4 7.RANS Ra < 4 D 7,K>; 34+,;^ 4 = as! +,. Dacles Mariani [5] RANS R=7 ; <,!5 _ " #$,K%& '

2 6, :! CFD7 R ; HI < 4 FG.Spal [6] V ; >,!5a 4 <=( K>; (),*$ +," -.a34+,, Churchfield [7] BTT AUVNO PQ. / 34+,0V K> 34_ `, 1 9:.^UVNO PQ [8] 34+, K> _ `,Y <.!+,, [9] $%23!+,+ J * [10] % ) * VOF (volumefraction)+, [11] +J NACA66*41, 5!FG, 7D 5 B 67T8*. 91& 5 NACA160201, -./0 15 8,2%UVNO PQ 67& '$834+, 014 FG, Z*.abc,%)* VOF+, +J : 7;! /, 7* ρ t + x j (ρu j )=0, (1) t (ρu i)+ (ρu x j u i )=- ρ + j x i [ ( ) ] ρ (μ+μ x t ) u i + u j - 2 u k δ j x j x i 3 x. (2) ij k 4 = NO4 13 _ \,$%_ 34+,+J 4 FG ZWX.5 <,Walin [12] Y = X > 6 7 & ' $ 8 +, (EARSM),?+, * B!>,CD =. E 4 T8 $, &'$8 $ EL>, F 34. G W4 N 4 H IJK NOA 5L E4 FG, M4= 3 N9.5 O 5L $, Walin [13] Y= )%S EARSM34+, NO PQ R,9:KE 3 _ `. [14] V %/ +, 6 EARSM+, * NO PQ, 34+, J.BTUVPQ EARSM 3 4+, < Z\ 34+, Z[( ].b5 P, 9 <=Q%UVNO P Q EARSM34+,. 1.2 RP Bakir [11] Y=,S( TU V,W X 3 F.YLS( : 1 ρ=. (3) (1-y d -y v )/ρ l +y d /ρ d +y v /ρ v X U. (%; mg ),YL X F75 7,@ ρ m,g 5 1 ρ m =. (4) (1-y d )/ρ l +y d /ρ d >=:ρ5@,y5 F7,; dg X,lG 0,vG V,y =ρ /α /ρ.?s( 5 t (ρ mα m )+ x j (ρ m u j α m )=S l. (5) >=:α5 ZF7,V ZF7 α v =1-α m ;S l= -S v,5s( V [ \].X ( ^ _ S l G">,`>(1)~(5)a,- V ZF7. Fbc/X V, v S =Nρ v 4πR 2 br b. (6) >=:R b 5X,N5 ZEX 7. RP Rayleigh Pleset,CD *$ _,, R b = 2 p v -p sgn(p 3 ρ v -p). (7) 槡 l >=:p v p ρ l F 5X!W8 4 W8 { 3α d α 4πR 3 m,p v -p>0; b N = (8) 3α v,p 4πR 3 v -p 0. b RP>(6)~(8), Sl =-F c Nρ v 4πR 2 b 槡 2p v -p sgn(p 3 ρ v -p).(9) >=:F c U L7,%SPQX.a>(4)~(9)=,y d R b F c 5U 7.RP 9 [10], p v -p>0d,f c =100; p v -p 0D, F c = <=!5 y d = ,R b = m. 2 9 <+, 1& 5 NACA160201/ -./01,1 C=0.475m, l

3 L=0.7125m. [1] a 0 =2, %& m 1.14m. 4 V= 10m/s,cS 4 &' ,1 α=10. 5 < R HI, 9 <.1. a1r = >, = 1 F 5 2.5C,10.0C. < L M4= IJK NOA 4 7?,a+JE4 D,$ % H67&'$8+,(EARSM)+, UNO PQ 34+,(EARSM CC) < Z WX. 3 4F x 3 > E (U/U ) (V t /U ) z FG < Z Z. 1 Fig.1 Domainusedincomputations RP < /, 9 % H,; < * ; F, 2. F / 1 E4 E,5 \HI +J E4, 9$% O,; 1 I ; * >,Y ;,. ; y + a 1~30[. (a)x/c= Fig.2 Overalviewofcomputationaldomaingrid TSKE \,5 9:? 7, 9 K ; *?@, KE ; 7" 50 50, < ; a, 45 &' 7.1, * W Pa, $ m/s, > %, _ 5 5;= kg/s; 1G < ;G 5,. <a % CFD CFX=2. (b)x/c= < 014 FG, V? R,.abc $%!+,! *. (c)x/c=0.3 3 :; Fig.3 Profilesofvelocityintipvortex

4 6, :! CFD7 R 705 3=, =,a x >,AUPQ 67&'$8+, WX S Z, a x/c=0.3d S 4, Z. 5 ; B, IJK NO?, _ ` 9 :,ÂUPQ 34+,V E3 4_ `, 1E 9V.ÛVNO PQ 67&'$8+, 9 3 _ `, ai x/c=0.1> Z[( ].^? >Q! C E,5! C Y. 4, =,UVNO PQ 34 +,HI = x > FG, Z[(\];ÂUPQ 34+, V, Z WX. Z, =,am4i x >, z<0d,e4 awx, T.9 [15]!5H 01 *, <H I+J= * %. (c)x/c=0.3 4 : Fig.4 Profilesoftangentialvelocityintipvortex 55$%PQ 34+, < F (ω x C/U )a x/c= > ( 5 ; ), =, *. =, =,a x/c=0.1>* \, \WX, 4 < Z=,. ; B,* BCF, ( =. T8, 6 =, = 5 ω x C/U =100,* 5 ω x C/U =-20. (a)x/c=0.1 (b)x/c=0.2 5 <=>?@ Fig.5 Formationandrolupofthetipvortex

5 ABC; DE Fig.6 Iso surfacesofnormalizedaxialvorticity < ZX,a <01I F GD, 9 % 34+, ;,.a bc, 9 )* VOF+,, 01 7 /*.! C 4 =XK /, V,TSXK.LD,^ +,cs!a / YL, b?+,a! CV a <.a = C 7 \,^ 7 \5L, b % 7 5 BC H7. C,, b$% +, 7.L,. 7501a 7 σ= D V ZF7 α v =0.1 < Z. =, =,a? 7E,01(=T!,^ A=T. 7 % 9:,.9 [16]! 5 " 1~3mmD!5!, 9 2mm5 P. 7" 2.6~2.7D,? % " 2mm,bD,L 5, 7a5! 7 σ d, < [1] Z σ d =2.65[(\]. (c)σ=2.7 (d)σ=2.8 7 FGHIE (α v =0.1) Fig.7 Iso surfacesofwatervapourvolumefraction α v =0.1indiferentcavitationnumber 4 9 $ % RANS R < 1 & 5 NA CA160201, -./014 FG, ( )* VOF!+, *, =; : 1)a <IJK NOA 4 D, AUNO PQ 34+,V M4 = _ `, 1KE 9:V.^ UVPQ 67&'$834+,\] )* < Z, [(\]. 2) 9$% 7 RHI = E * EL, Z,5 Lc. 3)$%!+, 7,, Z [(\]. JK!": (a)σ=2.5 (b)σ=2.6 [1]FRUMANDH,DUGUEC,CERRUTTIP.Tipvortexrol upandcavitation[c]//19thsymposiumonnavalhydrody namic.washingtondc,usa,1992: [2]ARNDTREA,ARAKERIVH,HIGUCHIH.Someob servationsoftip vortexcavitation[j].journaloffluidme chanics,1991,229: [3]ARNDTREA,MAINESBH.Viscousefectsintipvortex cavitationandnucleation[c]//20thsymposium onnaval Hydrodynamic.WashingtonDC,USA,1994:

6 6, :! CFD7 R 707 [4]MAINESBH,ARNDTR EA.Tipvortexformationand cavitation[j].journaloffluidengineering,1997,119: [5]DACLES MARIANIJ,KWAKD,ZILLIACG.Onnumeri calerorsandturbulencemodelingintipvortexflowpredic tion[j].internationaljournalfornumericalmethodsin Fluids,1999,30: [6]SPALLRE.Numericalstudyofawing tipvortexusingthe Eulerequations[J].JournalofAircraft,2001,38(1): [7]CHURCHFIELDM J,BLAISDELLGA.Nearfieldwingtip vortexcomputationusingthewind code[r].washington DC:AIAA,2006. [8]SPALARTPR,SHUR M.Onthesensitizationofturbu lencemodelstorotationandcurvature[j].aerospacesci enceandtechnology,1997,5: [9]HUANGSheng,HEMiao,WANGChao,etal.Simulation ofcavitatingflowarounda2 Dhydrofoil[J].JournalofMa rinescienceandapplication,2010,1: [10],,. *41!4 7 +J [J].0 8 *,2009,24(6): HANBaoyu,XIONGYing,CHENShuangqiao.Numerical simulationofcavitationaround2 dimentionalhydrofoil[j]. ChineseJournalofHydrodynamics,2009,24(6): [11]BAKIRF,REYR,GERBERAG.Numericalandexperi mentalinvestigationsofthecavitatingbehaviorofaninduc er[j].internationaljournalofrotatingmachinery,2004, 10: [12]WALLINS,IOHANSSONA.Acompleteexplicitalgebra icreynoldsstresmodelforincompresibleandcompresi bleflows[j].journaloffluidmechanics,2000,403: [13]WALLINS,IOHANSSONA.Modelingstreamlinecurva tureefectsinexplicitalgebraicreynoldsstresturbulence models[j].internationaljournalofheatandfluidflow, 2002,23(5): [14],,!.34+, " J [J].#,2010,31(12): HANBaoyu,XIONG Ying,YEJinming.Efectofturbu lencemodelsonnumericalsimulationoftipvortexflow fieldbehind3dwing[j].actaaeronauticaetastronauti casinica,2010,31(12): [15]ARNDTREA,KELLERAP.Waterqualityefectson cavitationinceptioninatrailingvortex[j].journalofflu idsengineering,1992,114: [16]$ %,&$=. ' (;)[M]. : \ =,2004:68. [LM'N:O ]

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