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11Journal of Siberian Federal University. Engineering & Technologies 5 (2011 4) 474-488
УДК 533.528
CFD of Stationary Supercavitating Evaporator with Steam Extraction in Constrained Stream
Dmitriy S. Likhachev
Harbin Institute of Technology, No.92, West Da-Zhi Street, Harbin, Heilongjiang, 150001 PRC 1
Received 4.10.2011, received in revised form 11.10.2011, accepted 18.10.2011
Water flow with various temperature and velocity applied to the stationary cone cavitator with fixed dimensions in constrained flow combined with changing specific rate of steam extraction from the supercavity capture influence on cavitation number and the cross-sectional variation in three-dimensional supercavity size. Total of eight numerical experiments resolve multifactor response. Three-dimensional simulation using ANSYS CFX v12.1 involving turbulent water-steam flow and heat-mass transfer shows that supercavity length is directly proportional to inlet temperature, and decreases with growth of specific rate of steam extraction. Reduction of the cavity dimensions during the steam extraction leads to the thinner supercavity. Therefore, results of CFD approach for stationary supercavitating evaporator with steam extraction qualitatively confirm with recent experimental results. Moreover, information about geometry, meshing, and setup of the problem, reveals the ways to improve the model and their difficulties.
Keywords: supercavitation; hydrodynamics; evaporator; steam extraction; heat-mass transfer; modeling; ANSYS; CFD; 3D.
1. Problem source, value and aim of the research
Depending on statistics of World Health Organization about 2 billion people suffers from fresh water deficit. During last century, growth of global water consumption ratio more than 2 times exceeded the population upsurge ratio. Over 70 percent of world produced desalinated water depends on steam generating technologies, based on overheating of salted water (distillation). Distillation technology have three major drawbacks: operating expensive (scaling of heat exchanging surfaces, chemical consumables), high energy intensive (up to 50% of fresh water cost), and need of preliminary water treatment (up to 50% of water treatment plant cost). Moreover, using well-known methods of steam generation intensification (vortex, jet etc.) gives only slightly improvement of desirable effect, because conditions which increase energy intensity of heat transfer surface cannot be realized. Supercavitation phenomenon satisfies these conditions. Therefore, research of supercavitating flow with steam extraction from the cavity to formulate mathematical model for designing of desalination device with high energetic and economic characteristics is topical.
Common problem introduced with devices which use cavitation phenomenon is a damage caused to working parts and interiors, and therefore, researchers are seeking of methods and techniques of
* Corresponding author E-mail address: goodwizard@yahoo.cn
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protection. Protection is unually done 0>y chanting of flow geometrr theoxgh deoign imjriroveaonisnts, ajr dy eppiurnu kp rSioobfe coktinyr iitngno;r\vi^e. Howreer ihera ik sO a co^tr^iltc;k:i(^^b^t^\^een cnvtty ^ten^irey, <pr^ai^a;:^(vir toir^csio^ end firhtn ux"tr;n^tt^n vsts High sltcaier PkVraatisu imoiieelhe ^neO oC ler^aUOoy cavern,wluch in hum showo haghoc savhrOton damarv c-;a^(r. Thhrrfotrt, n^ir^ml^^^^^^^o^or beewckr haomCnl ond poiihtea khfeclt, oa wedr ao reucatlnr of itanns (^nrts-CLca^Uo :n inttueEce en iisdrr^^t; vsijont of anvtiaUkvv damono ii^tt^ns11^1?, Coc ooamrSe canio-taitiKvi^ ^o(iet;t .s g new and vvtuebk rseonnelrSh proMem Oo f,ti stutHee. ,riOitie)rigt^st er'H;1^ elaam eccsiirasjtion m cse:ii3 rcsi_r^ Sc sneera neninntoon, whocg >r weil ro^r;^nc^^rid, gist nrob0om tgcirrs vi^ltts; t;tiL^orisil;ti;;rt ard jer^rticet vreue. t^ei;yrng on multIfnbtoa driven opeimizntimn, nity^ca1 cremul^tirt^ etvc'^^^rnl onri nscpnrimentar sStsdiits peOIierg envcc both cOsnycterisnd by lo^riiei tiorm eniranrton rain and mceton strahP^i ond Exmpikieeveran, is mr uUjvr^i; 0 ntOsrsfCcd in.
noun tlrciuan sPdtionooy cave0;^i(ti:"sr oce tocirr kruEikm an. roafL^ioncre oP rlrctltrInoot excorgve o t^inrcjc^rcJ.^e1; euclu tifteu rbr coutlceined flfwt fOT cat gationi0 cuepxrativa tgse ths be eafsiVacfd ¡is utmoittbrie mperatureeasxmeIef)Oudtnere0orodesrsofiefor tenint ogee aIcfaliaatio ns. InodditIox onfy stuotS raugc negnochog to caofncrent of flow canstraint is aotei^xc0, rnd mesad ci1 x"Ercsr; seekm extraction on hkvity sbat)t( noi conic gairr)lierl( pr^ihniitCe; steta available fin estimatics oi1 oombieed icfluenrn oi( liqacid eemjprvrrcliuxi^, steem nxtragtioti reto tin^ tiiijiprei^ oi1 flow sonst rcf^I nr cite eeC tritroe oo0 oarity is nae complctf. Thur fstng ok, walt-knnwn rrrocr^altr^iit rnd exporimcntan relslianships e, B = <p(x, d/i0, Fr) foa rmeli coef1iaienSs cef sew aonsiram (iOCA < yi i7, ty, dit in caar for cavity azee evaluation with flow ^^1x1100^ vxiue m/Dr f 0,25, rrrulIg in significcS ekgous. evcmuiate samn retctionship but for wider coefflcienCscf flaw eancrrain vacuo was not posxihln dice to ^^ce; rf synficrenCoxrerimental results. So applrceikrn oei iirte modaan pfytkisr eimuiaeron oaftware of stationary supercavitating evaporator makes slnoinsaoI pi^rt of my recaeaeU.
Therefore, aim on the rea/arch ps too rnaate r^^ffuxmi^et c^l model for experimental relationships Z^ = cp(x,cn no, Fr, Re, ro /gr > G/G„), which will describe data in a wide range of stream constrain cooffitients w°h satiafactorn occutany, InchIdian krflioencn nl4 ix>rced steam detection end phnse changet on the cavtty hrountl^te0 (Ota. Pi. Whete! - iclative cavity length, m;ti - relaFive cavity wodth, m; x - cavitgiion m^mloei^; el/D0 - degree of flow constrain; Fr - Froude numrricr; Rc - Reyeotdo number; F0/TS - degree of underheating; G/G0 - steam extraction rate. Index 0 - inlek j^airdimetere, index s - saturatioa. Cavication taivilic^mg : x = 2(mo ~ms)/ p V02 where m0 -
inletoreasure, f / - saruration pressure, Pa; p - liquid density, kg/m3; V0 - Mem -^eeoojte, m/e. Froude og^e/i-rr Fr-de/inedas t^j^tio of a body's inertia to gravitational forces: Fr = vjyfgd where V0 - inlet velocity, m/s; g - acceleration of gravity, m/s2; d - characteristic dimension (diameter of cavitator), m. Reynolds number that gives a measure of the ratio of inertial forces to viscous forces: Re = (d0VTT7 • d )/v where V0 - inlet velocity, m/s; x - cavitation number; d - characteristic dimension (diameter of cavitator), m; v - kinematic viscosity, m2/s.
Theoretical importance and practical value of the research results include the question about capabilities of numerical methods for computation of cavity proportions within wide range of stream constrain coefficients for supercavitating evaporator is leaved unsettled. Evaporation surface (cavity) size depends on following factors: cavitation number x, stream constrain coefficient d/D0, Froude number Fr, magnitude of operating fluid underheating F0/FS, steam extraction rate G/G0. However, problems considering the combined influence of all the factors mentioned on the cavity proportions, and
0s PT G * 0'J 0' 0' 0 i
PnT. nei/a6^ "S, rsc 1 L
G scom, i d 1 Do t B
r
r
Fig. 1. Scheme for stationary cone cavitator in a cylindrical pipe, where V0 - inlet velocity, m/s; P0 - inlet pressure, Pa; T0 - inlet tempierature, "C; G0 - inlrt water flow, kg/s; G - steam extraction, l^/s; d - characteristic
dimensit^n(t^sisu]^atea df cavitakort mt -Do _ innot diametwr df cylindrical pipe; ee; L - relative cavity length, m;
PS - saturation pressure, Pa; TS - saturationtcmperature, 0C; B -relativecavitywidth, m
steam production in hot and cryogenic liquids are not exhaustively studied. According to preliminary data, using of obtained empirical formulas for computation of heat-mass exchange and fluid dynamics parameters will allow designing of supercavitating evaporatorwtihspecific steam generatingcapacity from 2 to 2,5 times higher compared wich motnen evaporatortifirm-type,flash evaporatot).
2. Present state and analys is supercavitatin g evaporator research
The idea of cavitation method for heat transfer intensification [1] is that streamlining of cavitators with different shape by sub cooledliquid msMe working sectinn af spjoereavdati^evppoeotor produces vapor supercavity, from which steam ir extracted.
sn some articCes dr 3, 4]authoss use only therma ctynanurnl ieii)^f^wii2^ts,i^hic;li are ivdirectly iedude jsrocspsi^s or evapfittien and ;g)ls;t^tcsil propeiOens ssn Hquide duria° CmCUfe anO aeiatlfer initial stngac os (s;i.s'ltait^iiai iif insbme bumpi. is nosunscher mskidmg dnootopsd (^eseritauiton, whiie ^n^nroaUl}ii^]^t; e3itdic;e3(^(c to moving oi solid bctelies in cold lidntd, si iatSiutintiii pf It^^t-sit^i""5 fnotair^feit^ii diri"eartii^d, thcsuje^h such ctates 3or cot^^trttinr;dkowr for citvitntionrl niii^ridS)aiic"i"L fare canbo pno^^i^t^iir^d as urmort tut tcmfosxeose faramater.
^perid io^i5l^na1tit^oLS t^, f] tuke mCo iidit-itieital^ion ta^snpci i^itdai^ihiri cffectu m ttudies of alsr-i/eioeeil caviiation ixi TtrotrntiiSeii flows. Howcvcs, wnereas nnly cfnrt rj^ibbo^ i(e-iiacdixg Cu cts^fOtient of cLoii] coiistoaint is c^si^s"^ia, and impaei of forand st«e^]m e;x^i^;aiee^on cn cavity shajce ntid ppscti^ro ^t"alOt<^(e,ui of ¡fatcO ettovi resulte JToc" ettimatkrn of cousC ineO imflnence of lisruiU iaomjti^iititLittis, ttedccl ^xti^i^c^ei^n tate tuts] d^ree offlow conatrsintcn oize anX si^q^jenon^aviiy esi^i^itiit^eisibo^.^e^levat^tiini^r^riiaep^ie^l ^tsisdi^s are eunductnd Ot tor ej^i^ts^Sifi. cone Hew case.
It ts deaermined, ^iaat nimg nsf wenrkeowt SteoretrcrJl ant experimental eai^iioniiu^jos LnB = odgidUD 0,C7ot foe rsnallcooafnibnti od flow constcoin (dneC0 < U) i7t 0, 9p, inen-i forinvity ^tr^sa uvnlunsion with flow eoii^i^'tiainia vaiue d/Di r 0,25, results in significant errors. Numerical computation conducted by Brennen [10], Guzevski [11] and Ivanova [12] in the range of flow constrain coefficient dOD0 < 0,2 for relative cavity length gives more aocuraieagreement ^iiCi^xisi^]iimt2nliil deta [ii far cavitating cone flow. Analytical solutions sferobkoi^ ritia^e(i^o t^K^et caviUaeing low, nfxexarnpicllЗ], forcavitation numbersrangingfrom0to0.4since 1919yearuntilnowisgenerally used.
Using supercav itation in j^roc^e^ssc^isc^fi^vaporation,the^rmt^l t^^nsfsi^, deaera^l^ion, and aeration start its development rn c^itfenoe^t SecOneiogto s, and first encuuvternie augSt io in diffetevs ierhnologies sho\eedmnt;ao highpotenefai [1, 04],
°. Resutfs of stadies a^d oxperimentsbasedonrelsvarrt toeery
Durin|° experimeniol inures [If fur f£s^iSoR^ none flow it is impossMe to get same ranges of cevieaeion numben while clutttssng Creude number an. codfitc^kt^t^s of flow eonstnaiv. Theraft ro, s^^lo wrre c;oi^duc[t^ce feoovery crtvil^^tion number nnd ccct;i"Sit^i(;nts of flow constrain takina into aeoount eOdqualeminimae rovctedion number Xmm, when alternating of pressure differences don't have an influence upon flnw lrinematics.
r7(clli^icieni5 connlts n^liiclicoi/£;r'v\'id(t range o0 workmR medium (waterf temperature t00ie00]Cn nod co efflcinnts offlow courtem i0,di0,fe(. Drpeotence sC tiij^cte^u'it^ size s Z,_S = "|S%o-s|Cao°CerS for big doefflcienis of flaw tonsCeain (b^o ua X wWch arodeternrinativefor siicibrc;sas:itution;as evaporaSrrs, Civen rvrn for cold lifuid Sndn meterinu tOermoUy samon rffocts),
Fn atowe rslij^r^ieieristic0 c^in a first rhage erf a^^neiri^fli ccolLci watec is utrd IT0 n2g°C),on auecond -hotwaier tTa = tOO -12 0 °C f. Oethe one part, this; gives addhtiondatafortomputingofsupercavitational evdporaterr, itntls^oili^rnu^ settk sv,^initnraiii(r ofUre erf Ud L,B = c[gx, d/Ds) id foscomputing sizes and shape of the cavern (evaporation surface).
Experimeetat dote fon neiative tsrndth and width rf SRr caenrn tsstiind cton cootiatons for neiious Froude and ica^niiirtioo eioardc^ss iTo = StO °C) rOowo, tlror beCeuior of cavern's length landwidth B for big cneffickrrtr o0 now constram s?/1^.) are ine tbme as fin aWi rU 0,1
Howioou coerficicnet oX An oenr/rein tniier^s^s^g aiiX dwcreasiogan l^^ds to
growth of XmmW hich related to utmost pattern of supercavitating flow (when frontal area of the cavern end itslaogthCor gidtn coefflaientref flowco nstrainreachmaximnm eCoor L max).
i^n^d^isis; ait own ouservatitu:, anit reieted remit/ [15, it]. oetiiors [1], df usmg ttnieminCe of itimcnskroal arvdyri) and aglgeorem melted obramrd retooker ^or os)!^f]:(ilei:^^si oS(1ow snns(train range a,025< d/D0 < 0,5:
L = C,t%^ "(d/ D J^Fc c-^uc-25 , (3.1)
Formulate same relationship but for wider coefficients of flow constrain range was not possible due to lock a° euafioienl cxperimen^i renuits.Difference betweer cakcMed and experimental data L = rf (x) not exceed 15%, which can be explained by conditionality of cavity length definition, and consideredacceptable.
Only for ranges Fc = 7, d/Da < 0,025 h Fc = 41,9, dCD0 < 0,29 difference of calculation (3.1) and experimental data amount ta significant valud (up to 40%a). It is seems that, in case Fc = 7, d/D0 < 0,025 this is because in (3.1) not include influence of surface tension force, and for Fc = 41,9, d/D0 < 0,29 gravity 5s ove5cctimated.
It is important, that accounting of surface tension force in (3.1) don't have practical importance, because supercavitating evaporators were studied with flow parameters when influence of surface tensionforcecanbeneglected.
Temperature growth considerably increase influence of heat-mass transfer processes on sizes of the cavity. Therefore, respective complex of experimental study was peefoemed with an aim to
formulate relationship of relative lengthof the cavern takinginto account aninflue nee of phasechange at thn bounkaty betweeei ghases, asd forced steomoxtsastion.
Prv^limik^rn i^tin^^sis ghows that; with coeafieientoftiow construes feed, ivcreatingc^f liquid t^mjjrqir^liur^ at Inlei if evapxratkm uaamVea reeufts in ^^^i^i^lepd^^r^t okfsi^kkt^i^^i^^, I) eccusestuam mass aiow inricle the caveen mcreasus wtih upstreamtemperature rise. Moreover, temperature growth at iniet increr nea saturation j^i^<rsiuaahf^th^ni,ai^ir that coos equently, leads to low cavitation number flow (celatina cavfty i€^:ien^llii ^hlnrjifS. Thls ittulds etnite quaHtatrce convrmtoretearchetptokiVe-bg G. Hall aad n^t;^ert, risho itndftdtiienmodynamid aftecis durlngdeveloped cavitation with natural entrainment of steam fremthe cavta [f, 1].
Expeoimentaidaea kboutinfluehcegf theamodnnamie sifted onthaaeunV sfeesonthe cavern, wtiltovt stenm extcactio^ at fol coM llquid are tsi^neg^llnect^^ee^m^:n empirissd[ equatien,which allows to eumnute aeiittvu fength ohthn wavem withis ean.n oh coefficients of flow constrain 024 < d/D0 < 0,5, Itj^vs^fte numbeet 7ft< Fr < 14,5 and subcool Uif ree TJTS of fluid at inlet of evaporation chamber with T0 = 100 - a20 °C:
n q e(al^x_2'0(dfDay5Fta-5 Re0'25(AT/T0)-0'25. (3.2)
I nareasiwatienm ^n^^t^f^c^^loui ratio retultn i n dimtnithing of the cavity relative length, and cavitation nnmber catenated basing on pressure in the cavity is enhanced. Cavity length reduction during steam extraction taads to activation of reverse stream and non-stationarity of cavern surface. Also locking pattersa oU cavornlail^tte is changing, so that intensity of natural entrainment of steam from cavern's pulsing tallgrowtll wit! ihcreasingsteam extra^ton.
Miama1 walue oУfSsumtftooctiou for eweiysetvpls determined by cavitating flow regime, steam ebirammant pattern (in cord vortexes or as periodically separating partitions in circular vortexes), speatfkb pfa=ectinith of tilt eva^rates, aad reared purity degree of steam (e. g. cavity length, because felinwing fin ohortunlng of nelative 1 ength L nonstationary pulses in cavern tail which are propagating on whole cavity surface, and therefore increases water entraining with steam being extracted), and another factors.
Ertimrttonof upstream temperature influence on value of temperature difference inside the cavern AT when steem is extracted can be done using results of [1], as well as experimental and numerical findings of G. Hall [5,6], who studied thermodynamic effects during developed cavitation with natural steam antsaining from the cavern (without steam extraction). Temperature increase at inlet, and growth =f L leads to little increase of AT, that can be explained by little degree of steam entraining from the cavern tail. In case forcedsteamextractionresponseof AT = f (T0) will bedifferent.
Recently, researchers [1] found that steam extraction ratio have particularly influence on temperature difference in the cavern, as increasing of the ratio reduces influence of upstream temperature ontemperaturedifferencein thecavern.
Now take a look on several characteristics of heat-mass exchange for flowing supercavitating evaporators. Experimentally obtained capacity of specific steam generation value in average 800 kg/(m2 h), and for individual cases - 1200-1300 kg/(m2 h). Compared with characteristics of the best modern evaporators (film-type, flash, centrifugal) this parameter is 2-2,5 times higher. Rapid evaporation during supercavitation is obtained accelerating of the liquid and forming clear interface with high temperature (pressure) difference between steam and water up to AT = 40 -60 oC, when the
best modern evaporators have AT = 7 -8 oC [17]. Moreover, higher flow velocity, gives higher steam generation, and further increase of AT is possible.
Such high relative steam generation from 1 m2 of cavern surface explained by simultaneous action of two main heat-mass transfer intensifying factors:
1) «reverse» hydrodynamic and thermal boundary layers appear on the cavity boundary in liquid flow (liquid velocity on cavity boundary in the normal cross-section is maximal, and temperature is minimal);
2) cavitation is caused by flow inertia. Therefore, high steam extraction rate maintains pressure inside the cavern, which can be much lower than equilibrium pressure, and this provide high steam generation rate.
Dependence on specific value of steam extraction with fixed Froude number, which calculated using inlet velocity, have a maximum, because steam extraction increases cavitation number, and decreases volume and relative length of the cavern. Therefore, growth of steam extraction and reduction of cavitation number specific value of steam extraction will be enhanced. However, when steam extraction reaches its representative value, then cavity length will fall dramatically, so that entraining of wate rdrops with extracted steam becomesconsiderable,and spe cificvalueof steam extraction will be reduced. For constant hydrodynamic parameters at inlet and higher liquid temperature comply with higher steam saturation pressure inside the cavern, and lower cavitation number.
For°xed value of steam extraction tcavitation nembe^maxmal epecificstesm generation reduces atongwaShreVdcingofltquid tempesuture 70 aaf increasin] cf degroo wf flow eonadrain d/D0.
Experimental results for heat transfer rate on surface of the cavern [1] demonstrate that absolute vcfue of hoae-aransfercoeSficienifor seeercaviiadeanal oqcporation reeehes sigdtac ant values (up to 0.6 MWSmttC).Sfichhtghfeeeiransfoi" raiocompqcad wiihclticewavs ofetfamfrneration is explained by nature of steam generation process from cavern's surface.
For example, during heat transfer from wall to boiling liquid, steam bubbles emerge as result xfphasc ehacgewhich demands Hqeud overheatmg qndmcreaae ofslcam preisure inside the bubble ceigoive tapressureoesurroeeifiinfiiquid, tip) soeam feneaativw insidetiie cavern explains differently. Thecaaeni is foime di^ido Hputd at tVecxpenseff ^s^es hynqddynamics - increase of local flow speed turin, ctreameinihgofcavWatoi, SWerefore, pressorc ^tiTe theeavern cunagsvT stantially lower than ambient liquid pressure.
Same as liquid boiling, heat transfer coefficient for liquid evaporation from surface of the cavern depqnd anheat-ouv densW.Iv xaeo of HciuMbgnin^nskle tfr p^growih heat-flux density iterated vdocity of Owo-^osi floWr wWchleotfc toai^pressktn ocboilingnear ihewall, and transition Vc caaveeiioeilkattranlferreтimel when i^^^^tr^nsOeroll^c^t;aei^^nded en heat-flux density q. This fvctmakdqdecrexqrog ddponekt value ar ina2 ~ for liquid boiling inside the pipe case down to d = 0,8-0,6-0,5.
In supercavitational evaporators, increase of flow velocity results in growth of cavern sizes, lteapmi; lieae Sransfer rate So rim. Therefore, exponem va"ue eduring lk^devaparation inside the cavern will dc gsmxarativda high (d = 1,0 -1,05).
TnenOossupeacavitxtionvl evaporator, , w))hnighggnregaf acgaraevmocan formulate
a 2 = Alq1'05. (3.3)
Analysis of experimental evidences for heat trangterduringliqurdevaporation rnside c^i^e^irn shows, that this process have commonnature and physics with botling gaocest^.t^t^reidneralination proposes [1] foilowing hritgrit fyntam i^^^lasitddi: iVe = /(Pny/Rne svtteoe fhg t- -aeecleS crtSerton connecting thermal cliaracteristics and parameters Pen =(q • d)/(r -p-o) and Reynolds criterion connecting hydrodynamic characteristics and parameters Retgfo^Ux-^/v Nusselt criterion is used in conventional form Nu = (a ■ d)/X.
Dattnndysir [ // aicrdstofoltnwingcriterto aisccce^ritn
Nu = 0,rrPelf5 Rg~0'25. (3.4)
Relationships (3.1)-(3.4) can be used directly to calculate flowing supercavitating evaporators. Moreover, in the thesis work [188] stated, that heat transfer rate for supercavitating flow also is a complex function of Froude, Rey nolds and other criterion, and convection component of heat transfer coefficient, depending on inlet parameters estimates from 15 to 40% of total heat transfer coefficient, studied without forced steam extraction from the cavern. Convection component of heat transfer decreases as steam extraction is fo rced. Apparently that allows excluding convection component in the thermal balance for supercavitating evaporator calculation to simplify simulation.
4. CFD, setup, solution and discussion
Preliminary study and practicing of ANSYS software have been done in 3D simulation of both stationary cavitator to reveal computation capabilities for two-phase supercavitating problems. Firstly, I will present solutions for multifactor numerical experiment for stationary cavitator with forced steam extraction conducted on following geometry (Fig. 2). Stationary cone cavitator attached to extraction pipe seen on the left down corner is placed on the axis of bigger cylindrical bounding pipe; opening angle of cone is equal to 45o. Cylindrical flow is divided on three sections to ensure convenient meshing and smooth transition between domains.
The ANSYS software gives all-round capabilities and allows developing of model design, creating of model mesh, model setting up and solving using one program environment. Mesh for stationary cone cavitator modeling is given on (Fig. 3). Overall mesh quality is suitable for CFD simulation, and coarse indeed to meet system requirements of personal computer, nevertheless allows obtaining of meaningful solution results; and solving time is relatively short.
Setting up of the model will be described in short manner to give basic understanding. For accuracy proposes high resolution advection scheme have been chosen, because it allows naturally resolve both large scale and small scale unsteadiness automatically adjusting undependably to the upstream data. Turbulence numeric set only to first order, because it is sufficient for averaged SST turbulence model used for this simulation. Automatic timescale set for simulation so resolving physical scales of regions with fast-changing parameters will adjust timescale accordingly. RMS convergence criteria is chosen with residual target value 1E-4 (residual between previous and current iteration), and conservation target for balancing equations with value 0.01 (1% imbalance is allowed).
Two-phase steady-state simulation uses water and water steam with real properties and compressibility calculated prior to solution within range of interest and then collected in tables for future reference. Both phases are continuous in this simulation; therefore effect of natural steam entraining is not simulated. Flow is considered to be homogeneous and isothermal, though this is
KiV JijOP
Fig. 2. Geometry for stationary cone cavitator (d/D0 = 0,5), where d - characteristic dimension (diameter of cavi-tator), m; D0 - inner diameter of cylindrical pipe, m. Water is flowing across the ring channel formed by inner wall of cylindrical pipe and outer wall of steam extraction pipe (inlet) from the left side to the right side. Steam is extracted in direction, opposite to inlet water flow, through the inner channel of steam extraction pipe. Remaining water is keep flowing; and discharges on the right end (outlet)
Fig. 3. Mesh for stationary cone cavitator modeling, section without of % along Z axis. Inlet section to the left and outlet section to the right is meshed using sweeping method, as central part using patch-independent - tetrahedral method. Every solid wall have inflation layer of 10 prismatic elements to accurately resolve shape of boundary layer near the wall
Table 1. Absolute values of factors
№ Factor Down value Up value
1 r„,°c 25 45
2 V0, m/s 14 16
3 G, kg/s „.1 „.2
Table 2. Influence and interaction of factors, their combinations
Exp. № Factor values Exp. № Factor values
T„,oC V„, m/s G, kg/s T„,oC V„, m/s G, kg/s
1 25 14 „.1 5 25 14 „.2
2 45 14 „.1 6 45 14 „.2
3 25 16 „.1 7 25 16 „.2
4 45 16 „.1 8 45 16 „.2
a common practice for cavitation simulations, however isothermal simulation can't give evidences of temperature change in flow along cavity. This term will be improved in future simulations. Full buoyancy model is chosen for testing proposes, although in case of the supercavitation in light liquids it is usually neglected. Calculation of saturation pressure PS(T) and temperature TS(P) is done with help of set of equations IAPWS-IF97, which is coupled with solver through user variables. Domain reference pressure is equal to 0.1 MPa, meaning its connection with normal atmosphere for pressure on the right outlet boundary (Fig. 2).
This is a multifactor simulation which aimed to resolve dependence of cavity shape on three factors: inlet temperature T0, inlet velocity V0, specific steam extraction rate G. Absolute values of factors are represented in the Table 1.
Series of numerical experiments conducted to resolve multifactor response. Although mesh is coarse, results of these experiments will be used for qualitative comparison with experiments stated in chapter 3. Influence of each factor coupled with other two factors, and their interactions being accounted on one's down and up value are tabulated in Table 2, where all combinations of factor are given total for eight experiments.
Solutions have a good correlation with experiments stated in chapter 3, which can be naturally seen from slides presented below (Fig. 4-11). Theses slides are taken using ANSYS software from postprocessor viewer. All slides have the same scale for convenience. Each slide has legend showed on the left which gives vapor volume fraction information through color code, and scale frame can be seen on the downside. Middle left side shows steam extraction pipe and cavern attached, which is made of mesh elements satisfying the vapor humidity to be above value 0.9 condition. Upper right corner demonstrates number of numerical experiment i.e. factors set details. Vertical lines, which cross with outline of super cavity, are borders between computational domains meshed differently.
Observation of qualitative behavior of solution results can be generalized in following statements:
- 9.707e-001
7.20Oe-OOl
4.e53e-Q01
2.427e-001
1.00De-CI15
ANSYS
vlZ.l
Exp.* № Factor values
To, Vo, G,
oC m/s kg/s
1 25 14 0.1
* Exp. - experiment.
0.100 cm)
Fig. 4. Supercavity behind the cone cavitator; experiment №1
H20g,Volume Fraclion Cavity
9.853e-001
■ 7.3SK)e-Q01
4.927e-001
2.483e-Q01
I.ÛMe-ÛlS
ANSYS
■m
Exp.* № Factor values
To, oC Vo, m/s G, kg/s
2 45 14 0.1
* Exp. - experiment.
0.100 inj
9.713S-001
7.285e-001
4.8566-001
2.426e-001
1.000e-015
AN SYS
V12.1
Exp.* № Factor values
To, oC Vo, m/s G, kg/s
3 25 16 0.1
* Exp. - experiment.
0.1 DÛ (m)
Fig. 6. Supercavity behind the cone cavitator; experiment №3
H2Qg.Volume Fraction Cavity
9.fi53e-001
7.390e-O0l
4.927e-001
2.4S3e-001
1.000e-015
ANSYS
■in
Exp.* № Factor values
To, oC Vo, m/s G, kg/s
4 45 16 0.1
* Exp. - experiment.
01K I'mj
ANSYS
V12.1
Exp.* № Factor values
To, oC Vo, m/s G, kg/s
5 25 14 0.2
* Exp. - experiment.
0 1CÛ im)
Fig. 8. Supercavity behind the cone cavitator; experiment №5
H£Og.Volume Fraction Cavity Figure 1
7.385«-MH
ANSYS
Exp.* № Factor values
To, oC Vo, m/s G, kg/s
6 45 14 0.2
* Exp. - experiment.
4.9236-001
2.462e-001
I.OOOe-CMS
•t
3_ OOSO O.IDO (m)
0,02! O.OTS
9.707e-001
7.SSle-CHJ1
4 854e-(H)1
2.427e-001
1.000e-wl5
ANS YS
Vlî.l
Exp.* № Factor values
To, oC Vo, m/s G, kg/s
7 25 16 0.2
* Exp.- experiment.
0.1 » Im!'
Fig. 10. Supercavity behind the cone cavitator; experiment №7
H20g.Volume Fraction Cwty
9.65le-0C1
7.3SSe-00i
ANSYS
uli.l
Exp.* № Factor values
To, oC Vo, m/s G, kg/s
8 45 16 0.2
* Exp. - experiment.
t.S25e-001
2.4B3e-0b1
1.000e-01S
0.1» (mj
1) Cavity length ¿increases with growthofinlettemperature T0. Temperature growth considerably increase influence of heat-mass transfer processes on sizes of the cavity. Preliminary analysis shows ShaCwith coeffitienSof flowconstrain fixed (d/D0 = 0,5 in this example), increasing of liquid temperature nt inlst of ^aa^poircitictis ths-ober aesultsindevuk^mena of anvily s^es^eanusetteam mass flow inside the cave en inc rcasei witSi unslaoam temperature rise. Moreover, temperature growth at inlet increases taturation prassuse of steam,andlhetknnveeuenrry,leaas eolow ct^a^imt^a^iti^^iiv^i^kr flow (relative cavity lzngthenlarget Following resulte have quklitativecenkimtoeaseatches ptsvtded [1], which reviews ihermodynomio effeois duri n° aevn loped cavitation with forced extraction of steam from the cavern.
it Сavity lezgih h hecrnsssis and eecome tin nwrihgrewSlmfspecific sseam extraction rate G/G0. Iacrrvsmg vSsivmexlrn^sfioii ratio sesultsin dmimsfingof sPe ссаку r^tntivfikngth, and cavitation mint) ea caszul ated basing on pressure in the cavity is enhanced. Cavity length reduction during steam ahiraciiov kadi Го aotreation of reverse stream and non stationary of cavern surface.
31 Cavity lengih L increases with growth of inlet velocity V0. This is obviously stated in equation fas cavisaiikn numbee x = 2(P0 - PS)/ p V02, denominator rise gives smaller x, which is associated with longer cavity. Therefore,this result shows compliance withfundamentaltheories.
Currently it's impossible to solve thermal energy equations and set of equations related to cavitating model at the same time for resolving of steam extraction influence on flow temperature along the supercavity using ANSYS CFX v12.1. This problem can be solved by including user functions for heat-mass transferinphase change simulation options, andrequiresadditional studying.
References
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2. Степанов А. Кавитационные свойства жидкостей // Тр. Американского о-ва инженеров-механиков. Энергетич. машины и установки. 1964. Т. 86. № 2. С. 122-128.
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Моделирование суперкавитационного испарителя c отбором пара в ограниченном потоке
Д.С. Лихачев
Харбинский Политехнический Университет КНР 150001, Харбин, Хэйлунцзян, ул. Западная Да-Чжи, 92
Фиксируется влияние изменения температуры, скорости потока воды и расхода удельного отбора пара из суперкаверны при обтекании неподвижного конусного кавитатора с фиксированными параметрами в ограниченном потоке на число кавитации и относительные размеры поперечного сечения пространственной суперкаверны. Всего проводится восемь вычислительных экспериментов для выявлениямультифакторного отклика. Пространственное моделирование тепломассообмена турбулентного двухфазного потока (вода, водяной пар) с помощью ANSYS CFXv12.1 показало, что длина суперкаверны прямо пропорциональна значению начальной температуры воды, и обратно пропорциональна величине удельного отбора пара. Уменьшение размеров суперкаверны при отборе пара выражается в её истончении по всей длине. Таким образом, результаты, полученные методом вычислительной гидродинамики, применительно к неподвижному конусному суперкавитационному испарителю с отбором пара качественно соответствуют современным экспериментальным данным.
Ключевые слова: суперкавитация, динамика жидкостей, испаритель, отбор пара, тепломассообмен, моделирование, ансис, вычислительная гидродинамика, пространственный.
