Transition Boiling Heat Transfer And The Film Transition Regime

1.2.3.4.5.6.7.8.9.101112immersion heatercompensating tankplate Ateflon flat gasketsbourdon pressure gaugeheat transfer elementpurge valveback pressure Regulatorsafety valveloading portdrainage tubecooling water13. condenser14. boiling vessei15. test fluid16. plate B17. air withdrawal18. stainless steel mount19. level sight glass20. steam chamber21. level sight glass22. electrical heater23. threaded rods24. 4 electrical leads25. wooden baseFig. 2 The present reconstruction of the classical "Berensonexperiment"condition. Notice that this means that if Klimenko is correct,Nu;*/ z(A7), and q is directly proportional to AT, except asthe temperature dependence of physical properties influencesthe relationship. This contradicts the conventional wisdom asexpressed in equation (3) and, in fact, we find the physicalmechanisms upon which equation (3) is based to be more convincing. Nevertheless, we shall subsequently see that the functional dependence of Klimenko's equation provides more accurate means for extrapolating film boiling data than doesequation (3).Present Aims. The objective of the present study is tomeasure boiling curves in a Berenson-type apparatus, with anemphasis on the transitional boiling region. We seek to do thiswith a lowered thermal resistance so as to gain improved access to the transition region, and to do so with a controlled setof surface finishes. We shall then seek to provide a workabledescription of film transition boiling and to locate its onset.ExperimentApparatus. The present experiment is shown schematically in Fig. 2 and described in full detail by Ramilison (1985). Itconsists of an upper vessel containing a boiled liquid, which isheated through a copper plate by condensing water in a highpressure chamber below. The plate is 6.35 cm in diameter andmade of 99.99 percent copper, 1.524 cm thick. It is flush withthe glass sidewalls of the upper chamber, and over 3 \d indiameter (for each of the boiled fluids) to guarantee a goodapproximation to an infinite flat plate geometry. The apparatus was well insulated during the tests.The plate is supported by a 2.5-mm-thick stainless steelbridge that almost thermally isolates it from the lowerchamber. The thermal resistance of the copper plate is748 / Vol. 109, AUGUST 19870.000252 m2- C/W (exclusive of the condensing film). This isl/6th of the value in Berensbn's experiment. It is equippedwith four thermocouples at different locations on the topwhich verified the unidimensionality of heat flow and gave thebasis for specifying the temperature at the bottom of the plate.(The bottom temperature was needed subsequently to predictthe condensation resistance.)Three surfaces were prepared for use in each of the fourboiled liquids: reagent grade acetone, Freon-113, «-pentane,and benzene. The surfaces were prepared in the followingways:1 A rough surface was obtained by wrapping a #80 emerycloth around a l-in.-dia shaft and using five strokes in onedirection, five strokes at right angles to that direction, etc.,until the surface was judged reproducible.2 A mirror-polished surface was prepared by passingthrough a series of increasingly fine emery papers, and doingthe final polish with 0.05/i alumina until the surface served asan optically flawless mirror.3 A Teflon-coated surface was made by commerciallycoating a previously mirror-polished heater (on the top only)with a 1 mil layer of polytetrafluorethylene. The coating wasinspected to verify that it was completely smooth and free ofany flaws.Procedure. The heat flux in the tests was obtained ineither or both of two ways. Before each test, the apparatuswas operated with no boiled liquid in the upper chamber. Thisestablished the heat loss of the insulated container as a function of the temperature of the condensing water. The heattransfer was then determined by subtracting the heat loss fromthe electrical supply to the water chamber. The heat flow wasalso computed by condensing the boiled vapor to atemperature as close to saturation as possible, and weighing it.The latter method could only be used accurately at relativehigher heat fluxes where it was used to verify the energy-inputminus-loss method discussed above.The transition-film boiling heat fluxes discussed here wereall obtained by the energy-input-minus-loss method. Theprobable error in the resulting q was found by Ramilison torange downward from a maximum value of 3.8 percent.The present film and transition-film boiling data were allreached from the film boiling side. First, we established thefilm boiling heat flux by going to the peak nucleate boilingheat flux, increasing the heat flux slightly, and then stabilizingthe system at the highest-heat-flux film-boiling condition.Then we varied the power to pass through decreasing AT. Thisprocess continued until the system abruptly reverted tonucleate boiling.The heater surface temperature Tw was measured by a thermocouple less than 1 mm below the surface of the copperblock. This gave temperatures within about a tenth of a degreeCelsius of the surface temperature at film-transition boilingconditions. The temperature difference AT was obtained asthe difference between T„ and Tsat for the boiled liquid.The temperature difference, (Tcmdstm - Tmt) (recall equation (2)), was controlled by regulating the pressure in the lowerchamber. This was done by adjusting both the regulating valveand the electric heat supply to the chamber, a process that involved a good deal of technique as described by Ramilison.Contact Angles. The interpretation of the results of thiswork required a knowledge of the advancing and retreatingcontact angles, (3a and /3r, for the various surfaces and liquidsused. Measurements of @r were obtained with the tilting platemethod, using the actual heaters as the tilting plates and making the observations at Tsat. Since the tilting plate normally involves wetting the surface, we had to modify it to obtain P„.The heaters had to be set at a given angle, immersed, the shapeof the miniscus noted, the heater withdrawn and completelydried out, the angle reset, and the plate re-immersed, until theTransactions of the AS MEDownloaded From: / on 12/02/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Table 1Hear, flux(W/n.2 )10-3Complete boiling heat transfer data from the present testsATDCHear Flux(W/m2 )10 .5136 .3130. 1112.771.24953.4mirror257. 7172.4216.6291 .9310.097.452.4127.117 .826.9115.298.390.483.674.8118.670.767. 1217 .4154.272.447 .7240.5327.0350.7366.219.814.6107.299.386.982. 173.968.960.852.2116.9393 .3399.726.941.4141 .1291.0379. 1370.5304.5218.431. 224 .937.922 . 136.6109 .8PointNo .Heat 4205. 131 . 5120.4110.4102.494.288.981 .825.528.7polished121 .513.210. 2100.40. 01 .557 .117 .7n-pentane,22.25.teflon-coated19 .113.254.5334. 1351.3167.0107 .7288.260.334.9251.201 .32 .0112.499.393.285.980.776.4122.1119.1237.235.207 195.4123.6100.395.089 . 884 . 2122.080.431 . 834.7117.8teflon-coated34.5111.6101 .195.291 .183.7114.3120.3107 .880.6torFreon-113,23.321.121 .315.115.1157.192.21 .rough217.4101.2141 .772.138.6178.9221.5169 .924.822 .0polished123.19.107 .5100.188.6139.21 .19.121.7114.2104.495.685.676.768.361.354.9liquid surface intersected it without being perceptibly bent ineither direction. The observations of both contact angles werejudged accurate within 5 percent.Results and Discussion135.171.Freon-113,216.174 .15.016. 323. 4.616.3Table 2 Contact angle values and temperatures at the onset of thetransition-film boiling regionLiquidSurfaceC o n t a c t AngleA " saResults. The complete heat transfer data and contactFinish 5 T- T cangle measurements from the present tests are given in TablessaacetoneTeflon190.00.961 and 2, respectively. Each set of data in Table 1 is ordered inMirror200.2142.80.59131 .40 . 55chronological sequence. The heat transfer data were plotted inFreonTeflon161 . 00.82two ways by Ramilison (1985): as full boiling curves, and asMirror177 . 5144 .90.67Rough132 .00 . 58expanded plots in the transition film boiling range. Since thecomplete data are given in Table 1, we include the completenormalTeflon148. 30 . 84Mirror164.1138.80.80curves only for acetone and Freon-113 (Figs. 3 and 4) and theRough128.80.64expanded curves only for M-pentane and benzene (Figs. 4 andbenzeneTeflon249 .0189.40 . 566).Typical "accessibility lines" are drawn in Figs. 3 and 4. Thefact that they are not all the same reflects the fact that each isbased on a different condensing heat transfer coefficient, in- highly polished surfaces consistently gave peak heat fluxesferred from the measured heat flux.that lay between 81 and 87 percent of the prediction. Theteflon-coated surfaces gave values that exceeded the predictionNucleate Boiling and Burnout. The nucleate boiling by 4 to 10 percent. Berenson found that a rough oxidized surregime exhibits the well-known sensitivity of heat flux on sur- face could give values almost 20 percent above the prediction.face finish, although it is interesting to note that the curves forWhile surface roughness clearly exerts only a second-orderthe teflon-finished surfaces are only slightly steeper than those influence on burnout, it is an influence that is not yetfor the mirror-finish data.understood and which merits further study.The present burnout data and those of Berenson were compared with the hydrodynamic peak heat flux prediction ofStable Film Boiling. The stable film boiling data lie in aLienhard et al. (1973). The present rough surface data were range in which radiation heat transfer contributes virtuallyconsistently between 93 and 98 percent of the prediction. The nothing to the total q. In this range both our data and those ofTATAT113Journal of Heat UGUST 1987, Vol. 109/749Downloaded From: / on 12/02/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Klimenko'scorrelation400e o %35000o 300250 GSt cteflonmirrorrough25jacet one jo20I-o z, o15050100Wall superheat, ( T w - T s a t ) C100 - #Fig. 5 Film and film-transition regions for n-pentane boiling on tefloncoated, mirror-finished, and rough surfaces5030 W«e»** 50100150Wall superheat, ( T w - T s a t ) CFig. 3 Boiling curves for acetone boiling on teflon-coated, mirrorfinished, and "rough" surfaces250 sP 150§— HPCOaSI5050100Wall superheat, ( T w - T s a t ) Cdeal of data scatter based on film boiling in differentgeometries, with specific values for each liquid. The valuesused were: 0.0057 for Freon-113 and «-pentane; 0.0066 foracetone; and 0.0154 for benzene. The film boiling curve fit isshown graphically in Figs. 5 and 6.While the details of Klimenko's formulation are probablynot perfect, it nevertheless provides us with a very nearlyperfect basis for fitting the existing data. We therefore believethat his rationale merits further study.DD100A.Freon-1 13crx"25Fig. 6 Film and film-transition regions for benzene boiling on a tefloncoated surfaceD S"B200Klimenko's predictionoom,1m\\\1S H\150rWall superheat,100(Tw-Tsat) CFig. 4 Boiling curves for Freon-113 boiling on teflon-coated, mirrorfinished, and "rough" surfacesBerenson are almost perfectly represented - within a constant - by Klimenko's turbulent film boiling correlation (equation (15)) for J a 0 . 5 . This expression tells us that the onlytemperature dependence of the heat transfer coefficient arisesin the temperature dependence of the viscosity and thermaldiffusivity of the vapor.However, we had to replace Klimenko's empirical constantof 0.0086, which had originally been established with a good750/Vol. 109, AUGUST 1987Film-Transition Region. The data separated fairly abruptly from the film boiling extrapolation as the surfacetemperature was lowered below a certain point A, which differs in each configuration. This separation doubtlessrepresents the point at which the liquid-vapor interface beginsto make contact with the heater. We accordingly define qAand ATA at that point, where ATA (TA-T„).The filmtransition boiling region then lies to the immediate left ofpoint A. It is worth noting that qmia is less than qA, and alwayswithin 12 percent of it in our experiments.In the present work, point A was deemed to occur at thepoint at which the film boiling data first reached a value thatwas 1.05 times the Klimenko data fit.The data for acetone on a teflon-coated surface, and onlythese data, fail to pass into the transition-film boiling region atall. Both contact angles in this case (see Table 1) representalmost perfect wetting. Consequently the q-AT data in Fig. 3do not diverge from the film boiling curve; they leave it veryabruptly. This behavior signifies a direct jump to transitionfilm boiling.Transactions of the ASMEDownloaded From: / on 12/02/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

P—-range of(1-K)present dataand u n c e r t a i n t yBerenson's runsNo's 16 and 17for 40 fi 501020304050607080180A d v a n c i n g c o n t a c t a n g l e , /3 aFig. 7 Variation of the onset of transition boiling with the advancingcontact angletangentially, in the film-transition mode. The recognition ofthe role of the two contact angles makes it unnecessary topostulate this form of contact.)A Recent Corroborative Experiment. Chowdhury andWinterton (1985) gave boiling curves obtained by quenching avertically oriented finite cylinder in water and methanol. Theydid this for several values of contact angle as given by thesessile drop method. While these experiments cannot be compared quantitatively with ours, they very clearly show that TAdecreases strongly with increasing 13.A Model for the Film-Transition Boiling Heat FluxLimit of Liquid-Solid Contact. We envision filmtransition boiling as involving limited liquid-solid contact.Therefore, we must first consider the temperature at which thefirst contact can occur. It is well-understood (see, e.g., Yaoand Henry, 1978) that, based on the contact of two semiinfinite regionsT-* Willi—Tk,/ay2/2 Kkn.fiXff/ay -r/lkAh//ai * V'sat(6)The limiting value of the contact temperature should thenbe the absolute limiting homogeneous nucleation temperaturer h n , which has been shown by Lienhard (1982) to be well approximated by" Area ofcharacteristic \Kcel4Contact area ofradius rContact area foralternate oscillation - .(b) : top viewFig. 8 Model of contact of the liquid-vapor interface with the heaterduring film-transition boilingThe film-transition boiling curves in each case passed frompoint A to the left through a minimum and back up to a pointat which neighboring points could no longer be reached. It isimportant to note that, at the last attainable film-transitionboiling point, the "accessibility lines" were not tangent to thefilm-transition boiling curve. If the reason for our inability tomeasure further in this region had merely been a loss of accessibility, then they would have been tangent.What we therefore witness must be a collapse of the filmtransition process. It is our belief that this collapse occursbecause, as the extent of surface contact increases, we reach apoint at which the surface no longer dries out between contacts with the interface. When this occurs, the contact anglechanges from its relatively high advancing value /3 r . Thesystem must then leave film-transition boiling and find a newequilibrium in either nucleate transition or nucleate boilingwhere behavior is dictated by /3 r . (When Witte and Lienhardoriginally discussed the two possible modes of transition boiling, they suggested that the interface might contact the surfaceJournal of Heat TransferTh„ [0.923 0.011{TsJTcf]Tc(7)In Fig. 7 we indicate the fraction of the limiting liquidsuperheat at which the first liquid contact occurs. Bearing inmind that (TA - TsM)/(Tha - Tsat) cannot ever exceed (1-K)for the system, we note that as fia approaches zero - or perfectwetting - TA approaches the temperature required by perfecthomogeneous nucleation. (Notice that (1 -K) is given as a narrow range rather than as a single value, owing to the slighttemperature variation of the thermal properties.) At increasing values of /3 a , it becomes harder for the liquid to make contact, and easier to carry film boiling down to lowertemperatures.A Model for Correlating the Transition-Film Boiling HeatFlux. The liquid-vapor interface in film boiling takes theform of a cyclically collapsing, two-dimensional, square arrayof Taylor-unstable waves as shown in Fig. 8. The size of acharacteristic cell in this grid is \d 2 W 3a/g{pj — pg) whereXd is the most rapidly collapsing one-dimensional Taylor wavegiven by Bellman and Pennington (1955). The twodimensional wave exceeds Xrf by a factor of V2 (see Sernas,1969).The liquid-solid contact area can be represented as a fraction of the area of the cell, (r/\d)2, where r is the radius of thefrustrum of the cone of liquid that contacts the surface. Theduration of the contact tc will be a fraction of thecharacteristic period of the Taylor wave (see, e.g., Zuber)T l j/g3(pf--pg)]1/4(8)Next we wish to relate the heat flux added to the filmboiling heat flux by transient contact Aq to the local transientheat flux to the liquid resulting from liquid-solid contact. Aqis related to qtmnsknt b y t n e simple energy balance\d(T)(Aq) rHtc)qUmAentis given by the semi-infinite region expressionBut qtnkh(TSi 7tn(ahT)l/2it)kh(TvTs&i)(ahT)l/2K(9)(10)where we use equation (6) to eliminate T contact . If we put thisback into equation (9) we obtain an expression for Aq in termsof the unknowns tc and T.To eliminate tc and r we make two physical assumptions:AUGUST 1987, Vol. 109/751Downloaded From: / on 12/02/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

0.10I10.081 -1111BFreon-113e0 n-pentane1m *Freon-113}}On-pentaneAbenzeneOBerenson'sdata111I " 1K' 3.74x 1CT6(J a ) —v-'oteflon-coatedD Co-runs # 4 & # 1 0- t on filmboilingoao—l AA*,?Bi*mirrorMm boiling11IB0.02 --0.008-80 'Freon-113D 25bi acetonen-pentane0i9ace

Heat Transfer/Phase Change Laboratory, Mechanical Engineering Department, University of Houston, Houston, TX 77004 Transition Boiling Heat Transfer and the Film Transition Regime The "Berenson" flat-plate transition-boiling experiment has been re-created with a reduced thermal resistance in the heater, and an improved access to those portions