1、N ?3- j?Po _NASA CONTRACTORREPORTOIe_ZNASA CR-2270COPYEXTENDED HYDRODYNAMIC THEORYOF THE PEAK AND MINIMUMPOOL BOILING HEAT FLUXESby John H. Lienhard and Vijay K. DhirPrepared byUNIVERSITY OF KENTUCKYLexington, Ky. 40506Jor Lewis Research CenterNATIONAL AERONAUTICSAND SPACEADMINISTRATION* WASHINGTON,
2、D_ C. JULY 1973Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1. Report No. 2. Government Accession No. 3. Recipients Catalog No.NASA CR-22704. Title and SubtitleEXTENDED HYDRODYNAMIC THEORY OF THE PEAK ANDMINIMUM POOL BOILING HEAT FLUXES7. Author(s
3、)John H. Lienhard and Vijay K. Dhir/9. Performing Organization Nam_ and AddressUniversity of KentuckyLexington, Kentucky 4050612. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, D.C. 205465. Report DateJuly 19736. Performing Organization Code8. Performing O
4、rganization Report No.None10. Work Unit No.11. Contract or Grant No,NGL 18-001-03513. Type of Report end Period CoveredContractor Report14. Sponsoring Agency Code15. Supplementary NotesProject Manager, Thomas H.Center, Cleveland, OhioCochran, Chemical Propulsion Division, NASA Lewis Research16. Abst
5、ractThe hydrodynamic theory of the extreme pool boiling heat fluxes is expanded to embrace avariety of problems that have not previously been analyzed. These problems include theprediction of the peak heat flux on a variety of finite heaters, the influence of viscosity onthe Taylor and Helmoltz inst
6、ability mechanisms with application to film boiling and to thepeak heat flux in viscous liquids, the formalization of the analogy between high-current-density electrolysis and boiling, and the description of boiling in the low-gravity limit. Thepredictions are verified with a large number of new dat
7、a.17. Key Words (Suggested by Author(s)Peak heat fluxMinimum heat fluxHydrodynamic theory18. Distribution StatementUnclassified - unlimited19. Security Classif. (of this report) 20. Security Classif. (of this page)Unclassified Unclassified21. No. of Pages194* Forsale bytheNationalTechnicalInformatio
8、nService,Springfield,Virginia2215122. Price*$3.00Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CONTENTSPageC HA PT ERIo INTRODUCTION . 1Hydrodynamic Theory . 1Other Results 2II. PEAK AND MINIMUM HEAT FLUXES FOR1NVISCID LIQUIDS ON INFINITE FLAT PLAT
9、ES 4The Original Hydrodynamic Theory . 4,Modifications off the Theory . 10The Problem off the Finite Flat Plate 11Experimental Determination of qmax . 12Discussion of Expergmental Results 18Conclusions 24Ill. THE PEAK AND MINIMUM POOL BOILINGHEAT FLUXES ON FINITE HEATERS 27Sane rat Considerations .
10、27The Horizontal Cylinder, An Illustrative Example . . 27The Evaluation of d and Ai/A h 30JComparison of the Present ModiFied Theory withData for“ Cylinders . 35Comparison of Theory with Data For“ Spheres 35Comparison of Theory with Data for HorizontalRibbons Oriented Vertically . 42Conclusions 48IV
11、. A VISCOUS THEORY OF TAYLOR STABILITYWITH APPLICATION TO FILM BOILING 53Introduction 53Hydrodynamic Analysis . 53Experimental Determination off Vapor BlanketThickness_ Wavelength, and Growth Rate 64Vapor“ Blanket Thickness Correlation 72Comparison of Wavelength Predictions withExperiment 78Comparis
12、on of Wave Growth Predictions withExperiment 82iiiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Bubble Release Frequency . 91Effect of High Volume Fluxes on theDominant Wavelength . 97On Predicting the Minimum Heat Flux . 101Conclusions 103Vo THE P
13、EAK NEAT FLUX IN VISCOUS LIQUIDS 104The Maximum Stable Vapor Velocity in a Jet 104Peak Heat Flux Prediction . 109Comparison of Theory . 110Conclusions 117VI, HYDRODYNAMIC THEORY OF ELECTROLYSIS Introduction 118The Transitions in Electrolysis 121Experiments . 124Discussion off Results . 131Conclusion
14、s 137VII. BOILING ON SMALL WIRES 138Intr-oduction . 138Experiment . 140The Inception of Boiling 156Mixed-Mode Boiling 159Film Boiling 166Conclusions 168VIII. CONCLUSIONS 171APPENDIX A NOMENCLATURE 174REFERENCES 181iVProvided by IHSNot for ResaleNo reproduction or networking permitted without license
15、 from IHS-,-,-SUMMARYThis PepoPtdescPibes the last thPee yeaPs woPk of a five-year-NASA-suppoeted study of the interacting effects of gPavity and geo-metry on the peak minimum and pool boiling heat fituxes. The woekhas geneeaty sought to ctar-ify this tnteraction by seeking an under-standing off the
16、 hydr-odynamic mechanisms which dictate it. Acoordingly,this repoet emphasizes that portion of the last three year“s woek whichhas extended the hydr-odynamic theoey.The work in this aeea, embeacing two doctor-a disseetations, two-masters thes_s, two special undergeaduate peojects_ and a vaeiety offo
17、ther“ studies, eepr“esents a major“ extension off the theor“y as a whole.The major“ elements of the eepor“t include:1.) An extension of the hydr“odynamic theory of the peak heatfitux flop Flat plates off both finite and infinite size, suppoeted by agreat d#at of new data.2.) A gener“at theory of“ th
18、e peak heat fflux on Finite bodies offvar“ious configur“ations. The theory is applied to a var“tety off paeticular“configur“ations and suppor“ted_ in these cases, by much new data.3.) Viscous theor“ies of the Hetmhottz and Taylor“ stabilitypr“obtems. These theories are born out in gPeat detail with
19、new datafor film boiling and for“ the peak heat flux, in viscous liquids. Aviscous theoPy of the peak heat flux is developed and vePified exper“i-mentally.4.) A hydr“odynamic theory, flurry vePiffied with new data, For“high cur“r_nt-density etectrotysis.5.) An examination of the deter-toration of th
20、e conventionalboiling curve, that takes place when size or gravtty ar“e reduced tothe point at which inertia ceases to be of tmportance. The resutt isa new phenomenon for“ which a new set of analyses ape developed andcorroborated with much or-tginat data.Provided by IHSNot for ResaleNo reproduction
21、or networking permitted without license from IHS-,-,-I. INTRODUCTIONDuring the past five years, the NASA Lewis Research Center hassupported an ongoing study of the hydrodynamically dictated peak andminimum pool boiling heat fluxes at this laboratory. The results of thiseffort have ranged broadly ove
22、r many related areas and they are reportedin 28 project-related publications 1 to 28 1 .The general functional objective of the study was to learn howgravity influenced the peak and minimum pool boiling heat fluxes tn vat -_ious configurations. The primary contribution of the work has been tobroaden
23、 the hydrodynamic mechanisms of these heat fluxes, as proposedby Zuber 29 and Kutatetadze 30, into a general body of theory whichcan describe a large variety of situations These mechanisms are thecombined result of gravity, inertia, and capillary forcesThe initial stages of this program were summari
24、zed in the NASAContractor Report 7 of the first two years activity (Sept. 1967 toSept. 1969). The first extension of the grant (Sept. 1969 to Dec. 1970)was reported by a brief letter“ listing the publications of that period.Therefore, this final report will detail the work of the first and second(Ja
25、n. 1971 to May 1972) extension periods as they relate to the hydrody-namic theory. Those efforts of the project which do not bear directlyon the hydrodynamic theory wilt only be summarized briefly at the endof this chapter.Hydrodynamic TheoryThe present report presents the following extensions of th
26、e hydro-dynamic theory of the peak and minimum pool boiling heat fluxes, which ,have been made since the last contractor“ report 7 was presented:Chapter l describes the hydrodynamic theory of the peak and min-imum pool boiling heat fluxes on infinite flat plates. The theory, asoriginally formulated
27、by Zuber, ts altered in the light of recent experi-mental evidence and tested against new data. Chapter III is devoted tothe adaptation of the theory to a variety of finite heaters. Many newexperimental data are offered in verification of the resulting predictions.The variable of viscosity is introd
28、uced in the IVth Chapter. Herethe Taylor and Helmholtz stability theories, which underlie the hydro-1Numbers in square brackets denote entries in the REFERENCES section,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-dynamic pr,ocesses, ape for,mulat
29、ed with consider,ation of the Pole of suchvar,iables as liquid depth, vapor density, and finally liquid viscosity. Ex-perimental data ape pr,ovided to ver,ify the theor,y. In Chapter“ V, theser,esults ar,e used as the basis for pr,edicting the peak heat flux in viscousliquids. Or,iginal q data ape g
30、iven in ver,ification of the pr,ediction.maxChapter VI deals with the application of the hydrodynamic stabilityconcept to high current-density electr,olysis pr,ocesses. Experiments andtheoretical considerations show that the peak electr,olysis gas flux doesnot correspond with the Hetmhottz-unstabte
31、gas r,emoval flux, as is thecage in boiling. Rather it occurs at the Moissis-Berenson point of firsthy(_rodynamic transition. A region of film electrolysis is also identified.An impor,tant limitation on the hydr,odynamic theor,y is its failure insituations where sup,face tension completely overbalan
32、ces iner,tiat for,cesThis occurs when heater,s ape ver,y small or“ gravity appr,oaches zer,oChapter“ Vii treats the boiling pr,ocess on ver,y small wir,es in an attemptto learn how the tr“ansition to low-gravity behavior“ occurs. The peakand minimum heat fluxes ape found to vanish completely They ap
33、e r,e-placed by a heat flux vs. temperatur“e curve that r,ises monotonicallythrough a mixed natural convection and film boiling r,egimeThe objective of learning the Pole of gr,avity has been satisfied inthat every theor,eticat result given in Chapter-s II thr,ough Vii incor,per,atesgr,avtty explicit
34、ly, and ever,y experimental cor,r,etation incor,per,ates thevat,table of gravity in the nondimensionalization.Other“ ResultsA great deal of the wor,k done on the pr,oject has been essentiallyomitted from the pr,esent account since it would add unduly to the lengthof the r,epor,t. We shall ther-efor“
35、e describe the deleted material br,ieflybefor,e moving on to the hydr,odynamic theor,y:Condensation: The pr,acticat pr,oblem of r-efluxing boiled liquids withinthe centrifuge ted to theor,etical wor,k on condensation and natur,al convec-tion in var“iable gr,avity fields. A litst paper- on laminar“ c
36、ondensation10 showed how to r“ewr,ite Nusselts equation in a for.m that will applywhen gr,avity var,ies along the condenser, and which will handle a variabler,adius of cur,vatur“e as welt. The equation differ,s fr,om Nusselts equa-tion only in that it r,eplaces gr,avity with an “effective gravity“ w
37、hichtakes account of the ar,bitr,ar,ity variable gr-avity and r,adius.2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-A second paper on laminar condensation 23 showed how an ar-bitrary variation of wall suction could also be incorporated into this s
38、ortof analysis.Convection: A second problem that was motivated by the reflux con-densor design was that of predicting natural convection heat transfer ina variable gravity field. This led us to formulate a general integralmethod for predicting natural convection in a variable gravity field 22.The me
39、thod was applied to a variety of notating, and curved-surface,heaters. A series solution was developed for the full differential equ-ation to provide verification of the accuracy of the integral method.Fin design: A brief note was written to show how to design a “per-fectty effective“ fin 8. By boil
40、ing a coolant on a fairly short, iso-thermal fin, neap the peak heat flux, an extraordinarily high heat re-moval rate can be achieved. Design relations are given for such a fin.Electrolysis bubbles: An important task within the last grant fromNASA was that of exploring the analogy between gas format
41、ion and remo-val in electrolysis and boiling. The task was divided into two portions:a) a study of the analogy between electrolysis and boiling bubble growth,and b) the study of the analogy between the hydrodynamic stability mech-anisms in electrolysis and boiling which is treated in Chapter VI.The
42、bubble growth analogy is dealt with in references 11 and 17.In these studies, the equations for bubble growth are non-dimensionalizedin such a way as to make them identical for either electrolysis or boil-ing. Comparisons are then made between predictions of electrolysisbubble growth and measurement
43、s of vapor bubble growth.Computer coding: A very large number of data had to be cast intovarious schemes of non-dimensionalization. FoP convenience of handlingthe data, a computer code was developed. The complete data of theproject were put on cards and the equations for the physical propertiesof th
44、e boiled liquids were assembled in a subroutine. The routine makesit possible to call forth plots of any appropriate data in any desirablescheme of non-dimensionalization. This code is described fully in refer-ence 13.3Provided by IHS Not for ResaleNo reproduction or networking permitted without lic
45、ense from IHS-,-,-If. PEAK AND MINIMUM HEAT FLUXES FORINVISCID LIQUIDS ON INFINITE FLAT PLATESThe Original Hydrodynamic TheoryThe hydrodynamic theory of Zuber showed rationally in 1958 29why the older correlative equation of Kutateladze 30 fop the peak heatflux_ qmax F, on a horizontal flat plate:1/
46、2 1/4q = (TT/24) 0 dg(0f- pg) - (1)max F g hfg qmax Z2was correct . He formalized Kutateladzes suggestion that the peakoccurred when the vapor outflow from the plate became enough to obstructthe returning liquid flow: Figure 1 shows his physical idealization ofthe process.Fig. 1 Zubers vapor jet con
47、figuration for boiling from ahorizontal Mat plate heaterThe square array of jets is spaced on the “most susceptible“ or“most rapidly growing Taylor unstable wavelength, This is sometimes2Symbols not explained in context are ones in common use,explained in the NOMENCLATURE section.They ape4Provided b
48、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-called the “most dangerous“ wavelength; hence the symbol, Xd, is usedto identify it. The reason for this choice is that the vapor generated atthe plate is lighter than the liquid above it and the configuration isnherently Taylor-unstable.Zuber had access to no experimental data of a kind that would tellhim whether the interface would collapse into jets on the most susceptiblewavelength, the “critical“ (or shortest unstable) wavelength, k , o
