Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Validation of High Reynolds Number, Unsteady Multi-Phase CFD Modeling for Naval Applications
Validation of High Reynolds Number, Unsteady Multi-Phase CFD Modeling for Naval Applications
Pages 423-440
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From page 423... ...
Abstract Un teddy, high Rey old number validation cases for c multi-phase CFD analysis tool have been pu sued Tbe tool, designated UNCLE-M has c wide r mge of applicability including flows of naval relevance Tbis in ludes supercc itating Ed cavitating flows, bubbly flows, Ed water entry flows Tbu far the tool has been applied to c variety of co figurations A isymmehic sheet cavity flow-fields have been modeled in putic jar, m crempt to validate file unsteady r liability of UNCLE M wibb consideration of the effect of cavitati m number, Rey olds number Ed tubulen model has been mad Analy is of the modeled Em teddy fl w field is also mad Ed con lusions regarding the c uses of su cess Ed sho tcom logs m the computational re mlts are d awn Introduction Tbe ctility to properly model unsteady multiphase flows is of g eat impo tance, particularly in naval applications Cavitation may occu in submerged high peed vehicles es well es rotating mcchin y. nozzles, Ed mmmerou of her vend s Traditionally, ca anon on has bad n dative implications associated with damage Ed or noise However, for high speed submerged vehicles, file red ~ tion in d cg associated with c natural or ventilated cavity has g eat pote ticl ben ft.
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From page 424... ...
) he basis of the model is the i pomp~ ble multiphase Rey olds Avereged Ne ier Stokes Equstipms in c homog neous form Each phcse is treeted es c new species emd requi es the mclusion of c sepe cte contimmity equstion Ihree species, ~epresenti g c liquid, c condensable vapor, emd c no pond nsable gas, e e i pluded Miss hem fer betw en fhe liquid emd vapor phcses is cchieved f ough c dffferenticl model ther resee chers have cpplied simile models with c smgle species cpprocch How ver, the multiple species model of multiphase flow is p~esented es c mme flexible physiccl cpprocch A high Rey olds m mber fomm of twocqu~tion models with stemde d wall fu ptions provides tu buie pe closu e he govermog dffferenticl equ~tions, cept m Cc tesiem tensor form e e given es Equ~tion (1)
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From page 425... ...
flux limiter bced on liq id volume frdption is cpplied to th primitive mte pol mts A nom diagord~l pseudo -tim e- deflvat ive prec onditi onmg matrix ~s clso employed Wh~le fhe t~me denvat~ve term mishes from the mixtue contmnity equation es fhe limit of mcompr ss~ble con titu nt phcses is cpprpahed, the effect of pr conditionmg is to redupe the daocidted stiffLess This preconditior r gives rise to c system with w 11-conditioned eigern~lu s which cc mdependent of densdy mtm md loccl volume frd ption This sy tem is w 11 suited to high density rctio, phcse-separcted two-phcse flpws, such es the cavitatmg sy tems of mter st her A t mporally secomd-ord r cocu cte dpal-time scheme was impleme ted for physiccl time integ ction At eah time step, the tmbulerpe trmsport equations are solved mbsequ nt to solution of fhe me m flow equations The multiblock code is inshumented wifh MPI for pmallel execution based on domcm decomposition Du ing umstecdy time mteg ction, to obtarn remits presented her message pcsstog WdP ') cpplied dfter eah symmetric G mss-Seidel sw ep Each imer iterdte ir plved twenty symmehic Gmss-Seidel sw eps, md eah time tep mvolved ffteen imer iterctions This procedu e was s fficient to relialy red p the umstecdy residual by et lecst two orders of mcgmitude However, c pcse by pcse e cmird~tion lik Iy could have redu d fhe expended computatlord~l effort yieldi g remits similar in solutiom fidelity Fu th r detcils on fhe m mericcl method md code are available inKu det cl (199900 Results A isymmehic sheet pavity flow-felds have been mod led in putic dar, m crempt to validate fhe umstecdy relictility of c m dtiphcse, computatlord~l fluid dyrdmms tool w~fh com~demtmn of th dffectr R y olds number md tu bulerpe model hdP beff~ mcde Stecdy, averag, mecsurements of rlevmt cavitation pardmeters tor the shapes chosen have been documentedbyRouse mdMcNow (1949)
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From page 426... ...
Liquid volume fraction contours and corresponding drag history. UNCLE-M result.
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From page 427... ...
The model result used, was, as indicated by the confidence intervals, sufficient for a comparison to experimental, unsteady results. Figure 6 contains a time record of drag coefficient during modeled flow over a O-caliber ogive at a Reynolds number of 1.46x105 and cavitation number of 0.35.
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From page 428... ...
Here, the magnitude of the drag and the amplitude of the unsteadiness may be examined. Figure 9 contains a time record of drag coefficient during modeled flow over a hemispherical forebody and 6
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From page 429... ...
cylmder 6t 6 Rey olds mmber of 1 36xl05 6md c6 itation n mber of 0 25 The Stro~l frequency based on this resflt is 0 0484 Figme 10 contams 6 simil6 time record of d 6g coefficient durmg modeled flow over 6 hemispheric61 forebody 6md cylmd r 6t 6 " ~' R y olds n mber of 1 36xl 05 6md cavibtion n mber of 0 30 The Stro~l fiequency based on 6his resflt is 00622 Figure 11 contains 6 time record of dag 0465 coefficient durmg modeled flow over 6 hemispheric61 forebody 6md cylinder rt 6 Rey olds m mber of 1 36xl05 6md c6 itation mmber of 0 35 The Sho~l f~equency b6 sed on 6his re mlt is 0 0933 in 6 ddition, 6he higher 3, higher fiequency ~esflts co tain sm611er c6 ities in 6hese sit rti ms, c6 ities d ive the over611 msteadiness of the flow, 6md 6he problem of s fficient g id pomts to defme 6m msteady c6 ity becomes 6pp6 ent Th3s, by p3shing the limits of ~easom~ble discretization, 6he limits of effective modeling also 6re te ted Figme 12 contams 6 time lecord of dag coefficient durmg modeled flow over 6 hemispheric61 forebody 6md cylinder rt 6 Rey olds m mber of 1 36x105 6md c6 itation n mber of 0 3 Th Stro~l f~equency based on 6his resflt is 00614 Figme 13 contains 6 time record of d rg coefhcient during modeled flow over 6 hemispheric61 forebody 6md cylmder 6t 6 Rey olds mmber of 1 36xl07 6md c6 itation n mber of 0 3 The Sh o~l f~equency based on this remit is 0 133 Here, 6he stamd6 d t~end of inmeased turbflent cycle fiequency with increased R y olds m mber mpe6 s to have been p~esented Figme 14 contams 6 time lecord of dag coefficient durmg modeled flow over 6 conic61 forebody 6md cylinder rt 6 Rey olds m mber of 1 36xl05 6md c6 itation n mber of 02 Th Stro~l f~equency b6 sed on 6his res flt is 0 0383 As 6mticipa ted, due to the expected stability of c6 ities 6bo 3t this 7 04 _ 044 ll 04 1e 043 043 Figme 9: UNCLE-M res flt Time record of d 6g coefficient for flow over 6 hemispherical forebody 6md cylmderatR D=1 36xlO56md 3=025 ~model mits, D/U~ = 0 136 (s) , physic61 time step, At = 0 0025 (s)
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From page 430... ...
md predicted c Sh o~l f~eque sy of 0 068 Here 6he value is nearly th ssme es 6~t predicted by 6he model using the k~ turbule se mod I Clearly, the t~end based on these results is i sorrect it cppears that 6he current implementation of the RNG model hcs yielded ~esults consistent wi6h the k-7 model st one savitation m mber, 5=0 30, but et c 1ower value, the cycle f~eque sy is far g ester 6 m the t mdard k-7 modeled ~esult or 6he measured data it seems probable that wi6h finer time s &ilO 15 ~o t (s) Figme 13: NCLE-M result Time ~ecord of d cg coefficient for flow c r c hemispherical forebody md cylmder ctReD=1 36xl07 md 5=0 3 Inmodel mits, D/U~ = 0 136 (s)
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From page 431... ...
Avemged mstecdypressure computations mdmeaeuredGtc Rouse mdMcNown 1 948) Severcl parsmeters of ~elevance m 6he charcterization of cavitation bubbles inchde body dismeter, D, bubble ienf h, L, bubble dismetb, dm, md fomm d cg coefficie t cssocicted wi6h th cavitator, Cd Some smbig ity is mherent m both the expb imentcl md computatmrurl dehmhon of the ktter th ee of these parsmeters Bubble closme location is difficult to defne due to mstecdmess md ~ts dependence on diterbody d6smeter (which c m r mge from O [isohted camtator]
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From page 432... ...
Here, Strouhal frequency is shown over a range of cavitation numbers. Computational results are given for hemispherical, 1/4caliber, conical, and 0-caliber forebodies.
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From page 433... ...
Figure 23 contains a comparison of the spectral content of results for flow over a hemispherical forebody and cylindrical afterbody, with ReD=1.36xlO5 and o=0.3, for three, successively smaller, integration step sizes. Here, the computed flow resulted in a Strouhal frequency, Str=0.600 with a physical time step, ~t= 0.005, Str=0.0622 with a physical time step, ~t= 0.0025 seconds, and Str=0.0680 with a physical time step, At= 0.001 seconds.
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From page 434... ...
usmg UNCLE-M have been foumd to be quite comistent with arithmeticclly averaged timedependent results This ~esult is expected to be u eful m expeditmg the fuu e mtemretation of complex 6 eedimensional flows in cddition, reel si gle phcse flows, et the R y olds numbers considered, over these axi mmetric bodies cc in fct umstecdy Howewx, with the g ids md level of modeling cpplied he~e, 6he UNCLE-M solutmns tended to be stecdy it seems poss~ble that in recsed resolution md in omorction of low R y olds number tmbulen e modelmg w mid resolve 6his issu Conclusions The effect of Rey olds m mber on the ~esults for 6he h misphericcl cavitator was not mticipated it was cssumed that with the cppropricte mplication of the high Rey olds number tmbul nce model et th wall, the inviscid extenurl flow would dominate the flowfield, determinmg cavity shape md si:D: (ie suLce pressue) How ver, it cppears that shong flow-field interacti ms du to the highly tmbulent separcted closure ~egion are impo t mt to determming 6he umstecdy mode To some extent, based on the avemge re mlts, these phenomena are being ecu stely ccptmed How ver, there are shortcommgs m 6he cunently employed level of single-phcse tu bulen e modelmg The validstion cases e smmed have demon trsted the ccpabilities of UNCLE-M over c rmge of importmt flow conditions The most promin nt ~esult for validation is that th umstecdy flequ n ies obtain d in mmmericcl remits cppear to be boumded by 6he experimentcl data of Stmebrmg (1983)
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From page 435... ...
& MeNown, J S., Covitotion and Pnessu~e Dut ibuLon, Heod Forms ot 7em Angle of Y w, Studies in E gmeermg Bulletin 32, State University of lowc, 1 948 Sehdichting, H., Boumdarv-Lawv Theorv, M GmwHill, N w York, 1979 Stindh ring, D.R., Bdlet, M.L., & Holl, J.W., An Inrer tigotion of Covi y Cycl ing for Vmtilot d ond Noturol CoviLes, TM 83-13, The Pemmsyl mic State University Applied Research Laboratory, 1983 Sthdhrhg, DR., Sccling of Ccvitation Dcmcg, M S Thesis, The Pemmsylv mic Sbte Uniwvsity, University Park, Pemm yl mi~, Augu t 1976 Taylor, L
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From page 436... ...
misohopy between mom Rey olds sin ss compor nts, Ed (iii) turbuler e-erJkmced mass tr m fer across the phase interface, should be emphasized The second issue is related to the r ed for ~ solvmg the liquid-vapor boundary with due accuracy This issue is difhcult to h mdle bee mse the interface's location, shape, Ed velocity must be computed es part of the solution, resulting in c syst m that doesn't have either c pa determir d co figuration geometrically, or c fixed mass, momentum Ed en rgy budget withm its domain A accurate Ed robust interface tracking sch me c m help improve She performance of the present CFD tool The third issue is related to the mmmericcl ebments, in luding feet res such es dynamic cdaptation of the grid to help mcmtam den tble resolution, satisfactory conhol of mmmericcl dispersion Ed dissipation in view of the highly cormective multi-phcse flows, Ed way to e.
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From page 437... ...
It would appear that ccpt rmg the largesccle motion of the re-entr mt jet would be e;senticl in predicting he conect delayed r covery of the pressure I would fhmk Nat the "steady" calculations would predict c more cbmpt recovery In eon lusion, I find She mthors' work to be truly representative of the i~a~e-ol:~h -art in cavitation mod leg Only She extension to thee dimensions Ed the validation thereof is required b:fore c high-fidelity tool for unsteady cavitation prediction will emerge Author's Reply: Professor Edwards makes insightful commentary regarding the th ee-dimensiorslity Ed tr msient nature of sheet cavitation it is clear that he has spent c greet deal of effort studying Ed modeling such flows Responses to his th ee questions me listedbelow: l Subsequent to the comments of Professor Edwards, She mthors have begun to undertake some f ee-dimensior~l modeling of the ogive cases that w re originally mecsured experimentally by Rouse Ed McNow Farticlly completed results me included here in Figure A These results seem to indicate the preser e of thee-dimensiorsl modes How ver, c complete study, in luding sen sitivity to smell mgles of attack, was not reedy es of the time of the deadly for this reply The rate equation used for mass h msfer is c w ok Imk m our model However, it hr. been applied m c consistent maimer The rate coefhcient was original y chosen empiricclly es or which produces cppro imately correct stecdy-state cavity si e for c given ogive et c specific cavitation mmmber After this initial calibration, She rate coefficient hr.
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From page 438... ...
Please di cuss He relative merits of advanced turbuler e modeling versus mass tr msfer mod in g in improving the prediction of the unsteady cavity dynamics Author's Reply: The mfhors me pleased to receive such fa vorable commentary fiom Dr Farrell it was due to his expertise in the field of cavitation in eption Ed cavitation modeling that it was suggested that he be m in ited discusser Regrettably, the mthors have not been Cole to advance She physical quality of mass h msfer modeling beyond the simple rate coefficient based model presented in the text it is hoped that m in eption model may be developed with physics based on the Jaundice of cavitation mmclei in She flow This might be similar to work] thathcsbeendor byDr Farrell[1]
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From page 439... ...
Here liquid volume fraction, id, is solved for in the liquid volume continuity equation as a dependent variable. It appears in the momentum equations via the formulation of Am and m Mass transfer from liquid to vapor and from vapor to liquid takes place due to source terms in the continuity relations.
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From page 440... ...
D Thesis, D putment of Mech miccl md Nuclear E gin ermg, Pemmsyl mic State University, August 2000 2 Wilcox, D C, Turbulen e Modeling for CPD, DCW Indushies, Lc Canadc, Californr, USA, I 99S 3 A ndt, Song, et cl, Inst bilih of Portiol Covit tion: A Nurnericol/Experirnentol Ap prooch, ONR 23 Symposium on Naval Hyd odynamics, val de Reuil, Pmnce, 17-22 Septermber, 2000
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