CRITICAL HEAT FLUX AND SUBCOOLED NUCLEATE BOILING IN TRANSIENT REGION BETWEEN A TWO-DIMENSIONAL WATER JET AND A HEATED SURFACE
Yoshiki MIYASAKA, Shigeaki INADA AND YOSHIHIKO OWASE Department of Mechanical Engineering, GunmaUniversity, Kiryu 376
The present paper is concerned with a high subcooling water jet boiling system at the stagnation point. The purpose of the investigation is to obtain a high heat flux and to reveal the high heat flux mechanism. Most of the discussion in this paper is based on experimental results and con- cerns the effect of subcooling, jet velocity, and stagnation pressure on critical heat flux and nucleate boiling in the transient region. The entire range of the boiling curve is divided into three heat transfer regions which maybe hypothesized to exist in nucleate boiling.
curves in subcooled pool boiling is discussed. Introduction In the previous study6\ the effect of forced con- Whenthe boiling phenomenonis used effectively in vection heat transfer on nucleate boiling was con- a technological application, it is convenient and im- sidered from the standpoint of superposition of the portant to removeenormousquantities of heat per heat flux. unit time and area from a heated surface and to ac- The present study was made within the same sub- complish this heat transfer at a relatively low surface cooling and the jet velocity ranges as in the previous temperature without burn-out of the boiling surface. paper. The important parameters of this study are Recently, a study of the effect of jet velocity on critical subcooling, the jet velocity, the stagnation pressure heat flux has been made by Monde and Katto7). and contamination of the boiling surface. Generally, Their experimentwascarried out with a systemcovered when the boiling surface is contaminated in some with a flowing film of saturated water at atmospheric degree, the coefficient of heat transfer increases pressure being maintained by a small circular jet of remarkably in the transient boiling region. In this water held at the center of the heated surface. study, it is considered that the boiling surface is not The present paper is concerned with a high sub- completely contaminated, but is moderately contami- cooling water jet boiling system at the stagnation nated. point. The purpose of the present investigation is Most of the discussion in this paper is based on the to obtain a high heat flux and to reveal the boiling experimental results and concernsthe effect of these mechanism. In this study, a heat flux of up to 4X parameters on critical heat flux and nucleate boiling. 107 kcal/m2-hr could be obtained in steady-state The boiling curve at high subcooling was not separated condition over the entire range of superheat 10- clearly into nucleate, transition and film boiling re- 800°C, by using a heated surface with a small diameter gimes. Heat flux was increased gradually over the of 1.5 to 2.0mm. Use of such a small diameter was entire range as superheat rose. necessary because it was very difficult experimentally The entire range is divided into three heat transfer to remain a high heat flux above 107 kcal/m2-hr in regions which may be hypothesized to exist in nu- steady-state condition by using a heated surface with cleate boiling. diameter above 2.0 mm.However, a heated surface 1. Experimental Apparatus and Procedure of 10 mmdia. was used for subcooled pool boiling. The effect of heated surface diameter on the boiling Figure 1 shows the experimental apparatus for the impinging jet, where high heat flux nucleate boiling Received May 4, 1979. Correspondence concerning this article should be addressed to Y. Miyasaka. Y. Owase is now with Kobe Steel Co., Ltd., of subcooled water was generated on a heat transfer Osaka 541. surface which was fixed on the copper heat conductor
VOL. 13 NO. 1 1980 29 the top of the conical copper block and used to con- duct heat to the boiling surface. The base of the conical copper block was finished to 25 mmdia. and a carbon plate of thickness 2 mmwas placed on it in order to obtain radiant energy efficiently. The ceram- ic fiber heat insulator KAOWOOLwas packed tightly around the copper cylinder and conical cop- per block to reduce heat losses. This heat insulator possessed the function of the receiver of melting cop- per as well. Copper-constantan thermocouples of 0.1 mmdia. were used to measure temperature. The thermo- couples were calibrated over a wide temperature range of 100 to 900°C. Two constantan wires of 0.1 mm dia. were attached to the surface of the 1.5 mm-dia. copper cylinder by spot welding, one located 1.0 mm, Fig. 1 Experimental apparatus for impinging jet the other 2.0mm below the boiling surface. A copper wire of0.1 mmdia. was placed in a 0.5 mm-dia. hole drilled into the conical copper block and was stuffed with copper chips. The temperature indicated by these thermocouples was used as the average temperature in a cross section of the copper cylinder and heat flux was measured by calculations based on Fourier's equation for steady- state heat flow. Temperature of the boiling surface was measured by extrapolating the temperatures con- sidering the thickness of 0.05 mmof platinum foil. All the thermoelectric forces were recorded on a gal- vanograph through an attenuator and a changing- over switch. Fig. 2 Main part of apparatus for impinging jet The platinum foil attached on the copper cylinder was formed into a circular fin. The edge of the plati- by the diffusion-bonding method. This surface was numcircular fin was soldered to the brass plate to made of a 0.05mm thickness platinum foil. Dif- bridge the gap, leaving about 5 mmbetween copper fusion-bonding was achieved by keeping the tempera- cylinder and brass plate. Epoxy resin was used to ture of the contact face between platinum and copper prevent leakage of water at the outer edge of the brass at about 600°C for twenty-four hours in an electric plate. furnace filled with argon gas. The heat flux measured with the boiling surface The radiant energy of a molybdenumheater, being covered with Teflon rod showed that the heat losses heated by alternating current, was transferred to the through the platinum fin and the side of the copper end of the copper heat conductor. The a. c. power cylinder were negligible comparedto the rate of heat input was controlled with a 10-KVA adjustable transfer through the boiling surface. transformer. The furnace was filled with hydrogen Figure 3 shows the experimental apparatus for sub- gas in order to prevent the molybdenumheater from cooled pool boiling. Figure 4 shows the detailed oxidation. main part of the apparatus. The furnace used for A two-dimensional water jet was impinged upward subcooled pool boiling was identical to that shown in vertically on the heat transfer surface being standed Fig. 1. A 2.0mm-dia. copper cylinder, 5mm long, upside down in order to prevent the heater from adhe- was set facing upward and the platinum boiling sion of melting copper. surface was attached to it by the diffusion-bonding The test water was pumpedup to a height of about method. Furthermore, two boiling surfaces (3 mm 15 mand poured into the storage tank. The tempera- dia., 10 mmdia.) were used to investigate the effect of ture of the waterjet measured at the outlet of the noz- diameter on the boiling curves. Three 0.1 mm-dia. zle was kept constant at about 15°C. Figure 2 shows constantan wires were attached to the side of the cop- the details of the main part of the apparatus. A 1.5 per cylinder by spot welding. The copper wire of mm-dia. copper cylinder, 3 mmlong, was attached to 0.1 mmdia. was attached in muchthe same way as
30 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN in Fig. 1. In the case of the 10mmdia. boiling sur- face, further, three constantan wires of 0.1 mmdia. isolated in a glass tube were fixed by spot welding in 0.5 mm-dia. holes drilled into the center of the copper cylinder with separation distance 1.0 mmbelow the heated surface. The test liquid, about ten liters of water, was placed into the boiling vessel so that the water level was about 250 mmabove the heated surface. The liquid tem- perature was measuredby time-interpolation of the temperatures at the beginning and end of the run. The maxmumvariation of liquid temperature from start to end of run was found to be about 10°C. The heated surface used in this work was cleaned with a 5/0 emery paper and acetone before each ex- perimental run. The power input to the molybdenum heater was increased very slowly. After a steady- Fig. 3 Experimental apparatus for subcooled state condition was reached, as indicated by tempera- pool boiling ture measurement, experimental data were taken. Each experimental run required about eight hours. 2. Boiling Curve 2. 1 Subcooled pool boiling curve Heat flux vs. superheat data measuredin subcool- ing 85°C at atmospheric pressure are plotted in Fig. 5. At a heat flux of about 106kcal/m2-hr, violent nucleate boiling on the heated surface was observed. The vapor generated at the active sites on the heated Fig. 4 Main part of apparatus for subcooled pool surface was in the form of discrete bubbles of 0.1 mm boiling dia., and was condensed immediately. As the tempera- ture of the heated surface was raised, heat flux increas- ed. Though the data showed scatter in some degree, these data appeared as an extension of the ordinary high heat flux saturated pool boiling curve at atmos- pheric pressure. The boiling curve equation is ex- pressed by ?pool=68Jrs3a°t (i) where qvool is in kcal/m2-hr and z/rsat in °C. As the heat flux and the superheat reached about 7 x 106 kcal/ m2-hr and 50°C, the population density of active nucleation sites on the heat transfer surface very much increased. Departing discrete bubbles, about 0.2 mmor 0.3 mmin diameter, condensed immediately in subcooled water. Fromthis region, the slope of the boiling curve begins to change. As the superheat was raised, the heat flux increased still further. At a superheat of about 100°C, coalescence of discrete bubbles begin appearing in local surface areas. The Fig. 5 Subcooled pool boiling curve frequency of coalesced bubble emission was about 10 per second and explosive boiling sounds were heard the first transition region agreed approximately with correspondingly to the frequency. The first transi- the burn-out heat flux generally reported in the litera- tion region based on the first change of slope of the ture for water boiling on wires. The boiling-curve curve in Fig. 5 is hypothesized to exist in nucleate equation in this region is expressed by boiling. A heat flux #DNB.sub.pooi at the beginning of ^ub=85.pooi.Poo=5.93 x l05 irs°a6t5 (2)
VOL 13 NO. 1 198Q 31 experimental equation of the boiling curve in this re- gion is expressed by #sub=85.pool.Poo-y.OOX lU 41 sat ^Jj where tfs*u*b=85.pooi.Poo is in kcal/m2-hr and JTsat in °C. The effect of heated surface diameter on the boiling curve is shown in Fig. 5. In the case of the 10mm- dia. surface, the boiling curve has a tendency to reach stable film boiling at the end of the first transient region; in the case of 3mmdia., at the end of the second transition region. The previously described platinum foil attached to the copper heat conductor becomes fin-like. The effect offin thickness on the boiling curve is also shown in Fig. 5, to compare the heat losses through the fin with the rate of heat transfer through the boiling sur- face. It can be considered that there is no effect of fin thickness and water purity on the boiling curve. 2. 2 Impinging water jet boiling curve Whenthe jet velocity was kept constant and super- heat was raised, a boiling curve such as shown in Fig. 6 was obtained. It can be considered that the jet boiling curves show a similar tendency to pool boiling through the whole boiling region. In the left-hand region of Eq. (1), the boiling curves separate corre- spondingly to the jet velocity and approach Eq. (1). In the region where violent nucleate boiling can be seen on the heated surface, all the boiling curves appear on a linear extension of the boiling curve of ordinary saturated pool boiling, though the data showed scatter in some degree. For comparison, Fig. 6 also includes the correlation equations of Katto and Kunihiro4) for a similar system with an impinging jet of saturated water of velocity u0, 2.0 to 2.7 m/sec and by Nishikawa- Yamagata9) for nucleate boiling heat transfer in pool Fig. 7 Effect of subcooling on critical heat flux boiling. The heat flux, gDNB.sub.fOrced, which begin where #s*Ub=85.Pooi.Poo is in kcal/m2-hr and z/Tsat in °C. to depart from the pool boiling curve indicated by The slope of the boiling curve begins to change Eq. (1), rose as the jet velocity increased. As the superheat rises, the boiling curve can be again from the end of the first transition region, and classified into the following two regions in the same the second transition region starts. Heat flux in this region does not increase so muchas the superheat is manner as pool boiling, namely the first and the second further raised. At a superheat of about 300°C, transition region which may be_ hypothesized to exist intermittent boiling sound ceased. As superheat in- in nucleate boiling. creased, the entire boiling surface became covered 3. Critical Heat Flux with a thick, rather stable film of vapor though this boiling phenomenon seemed to be film boiling at a 3. 1 Critical heat flux in subcooled pool boiling glance. As the superheat was raised above 500°C, Critical heat flux will be discussed in the present boiling surface was heated to redness and a numberof paper as being the heat flux #DNB.sub.Pooi at the begin- vapor bubbles of 0.1 to 0.3 mmdia. leapt from the ning of the first transition region. Critical heat flux boiling surface and escaped. A number of needle #dnb.sub.pool measured in subcooled pool boiling at pillars, considered to be strips of heated fluid, were atmospheric pressure is plotted in Fig. 7 against sub- seen to be rising through gaps in the bubbles. It is cooling JTsuh ranging from 30°C to 85°C. It was considered that this behavior of the vapor bubbles found that critical heat flux increased approximately may be observed because the film thickness of the proportionally to AT\$. vapor covering the entire surface is very thin. The For comparison, Fig. 7 also includes the data of
32 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Gunther and Kreith^, the analytical results of Zuber10) and Kutateladze5). The relationship between critical heat flux and subcooling in this study is given by the dimensionless equation.
#DNB.sub.pool"(7DNB.sub=0.pool
This equation is similar to the analytical equation of Kutateladze; in it #DNB.sub=o.Pooi was determined from the Kutateladze criterion for saturated pool boiling critical heat flux.
(/DNB.sub=0.pool-U.1O ±j pv\ 2- \J) L Pv J 3. 2 Critical heat flux injet boiling The ratio of the (#DNB.SUb.forced-#dnb.sub.pOoi) to ^dnb.sub.pool is plotted in Fig. 8 versus thejet veloc- ity u0 ranging from 1.5 m/sec to 15.3 m/sec. The relationship between critical heat flux in jet boiling and the jet velocity in the present study is expressed by #DNB.sub.forced.P,=^DNB.sub.pool,p/l+0.8oZV ) (6)
Where #DNB.sub.forced.Ps> #DNB.sub.pool.Ps are ln KCal/ Fig. 9 Coefficient of experimental equation in the first transition region m2*hr and u0 in m/sec. Wemade correction for the dynamic pressure of the data of Ishigai and Mizuno2), and qfub.Vooi.ps represents the heat flux of subcooled Mondeand Katto8) at a stagnation point and for com- pool boiling at the system pressure P8. Here, it is parison plotted the data in Fig. 8. Ishigai and necessary to estimate £?ub.Pooi.2v Mizuno's data were obtained in an impinging region If the boiling curves obtained in subcooled pool on the direct heating stainless plate (10 mmX8mm) boiling at the system pressure above atmospheric with alternating current within a range of u0 up to pressure moveparallel with the boiling curve shown 10 m/sec, ATsnh=15°C, jet nozzle diameter d of 10 to by Eq. (2), qfnh.VOoi.ps at the system pressure in ques- 17mm.The data of Mondeand Katto were ob- tion is defined by the following equation: tained on a steadily heated copper block boiling sur- #sub.pool.Ps-^4 *(7sub=85.pool.Poo face (ll.6 mmdia.) covered with a radially flowing film of water within a range of u0 up to 12m/sec, using Eq. (2), JTsnh of 10 to 30°C and jet nozzle diameter d of *?ub.pooi.P.=^à"5.93X 105-ATVá" (9) 2.0mm. It may be considered that the ratio of the where A is the proportionality factor. WDNB.sub.forced #DNB.sub.pool) tO #DNB.sub.pool IS not A is calculated by the following procedure. Since affected by either subcooling or jet nozzle diameter. the critical heat flux <7DNB.sub.Pooi.p, obtained by Eq. System pressure was calculated from the Bernoulli (4) and Eq. (5) appears on the boiling curve shown by equation Eq. (1) within a range ofw0 up to 20 m/sec, the super- P.=Po.+Pi ' ull2 (7) heat z/Tsat against #DNB.sub.Pooi.ps is calculated from Eq. (1) by substituting #DNB.sub.Pooi.pf for the left- where PMis atmospheric pressure. hand side ofEq. (1). After all the A is decided from Eq. (9) since AT^t against #DNB.sub.Pooi.ps calculated 4. Estimation of the Heat Flux in the Transition Region by such a procedure must also satisfy Eq. (9). Even without such a tedious calculation, A is cal- 4. 1 First transition region in nucleate boiling culated by the following equation of a convenient The heat flux g?Ub.forced.ps of jet boiling in the first approximation within a range ofu0 up to 20 m/sec : transition region is expressed by the following equa- ^4=#DNB.sub.pool.Ps/#DNB.sub=85.Pool.Poo V^j tion on the basis of the heat flux #?Ub=85.Pooi.Poo of the subcooled pool boiling: The coefficient of Eq. (8) is plotted in Fig. 9 against the superheat. It is seen that Eq. (8) has a coefficient <7sub.forced.Pt=#sub.pool.P,(l~f~0""6 uo' ) (8) of about 0.66, though the data show scatter in some where #*ub.forCed.ps is in kcal/m2-hr and u0 in m/sec, degree.
/OL. 13 NO. 1 1980 33 where Ps is in kgf/cm2, qvool in kcal/m2-hr and Jrsat in°C. In the case of fluid temperature 7>=15OC, the limitation of ^DNB.sub.Pooi.p, calculated by Eq. (4), Eq. (5) and Eq. (13) is shown in Fig. ll by the broken line. In the case of fluid temperature 77=15°C and jet velocity above 20m/sec, the limitation of #dnb.sub.forced.ps calculated by Eqs. (4)-(7) and Eq.
Fig. 10 Coefficient of experimental equation in (13) is shown in Fig. ll by the thin broken line. the second transition region The heat flux above the limitation of#dnb.sub.forced.ps will be calculated in the same way as in the previous section except that Eq. (13) is used instead of Eq. (1). However, the proportionality factor A is not calculated from Eq. (10), but is decided from Eq. (9) by substi- tuting ^dnb.sub.forced.ps for the left-hand side of Eq. (13) and Eq. (9). In the left-hand region of Eq. (13), the heat flux is obtained approximately as the sum of the forced con- vection heat flux and the nucleate pool boiling heat flux. In accordance with the idea mentioned above, heat flux vs. superheat are expressed by the heavy solid line in Fig. 1 1 forjet velocity u0 of20, 60 and 100 m/sec. Conclusion 1) Nucleate boiling curve in this system appears as a linear extension of ordinary high heat flux pool boiling and the heat flux extends to 3 X 107 kcal/m2 -hr. Fig. ll Effect of impinging jet velocity on boiling 2) The boiling curve can be obtained in steady- heat transfer when uo> 15.3 m/sec state condition over the entire range of Jrsat, 10 to 4. 2 Second transition region in nucleate boiling 800°C. In the same way as the first transition region, the 3) The entire range is divided into three heat heat flux #?u*.forced.p, of jet boiling in the second transfer regions which are hypothesized to exist in transition region is expressed by nucleate boiling. #sub.forced.P^^sub.pool.P,0 ~l~0#4Wo" ) (1 1) 4) The heat flux in impinging jet boiling is express- where #?u*.forced.ps is in kcal/m2-hr, u0 in m/sec and ed on the basis ofsubcooled pool boiling heat flux. ysub.pool.Ps-A #sub=85.pool.Poo \1^) Nomenclature Here A is calculated by Eq. (10). B = jet nozzle width [mm] The coefficient of Eq. (ll) is plotted in Fig. 10 Cpl = specific heat of liquid [kgm à" °C/kcal] D = heated surface diameter [mm] against the superheat. One would expect Eq. (ll) to d = jet nozzle diameter [mm] have a coefficient of 0.4. g = gravitational acceleration [m/sec2] L = latent heat [kcal/kgm] 5. Supplementary Note Ps = system pressure [kgf/cm2] It may not be useless to expand the above empirical jPco = atmospheric pressure [kgf/cm2] equations beyond the present experimental regions q = heat flux of boiling [kcal/m2 à"hr] <7dnb = critical heat flux [kcal/m2 - hr] in a similar way of thinking reported by Katsumata Tf = fluid temperature [°C] and Hirata3). It is well known that heat flux vs. jrsat = superheat [°C] superheat curve in nucleate pool boiling movesparallel ^sub = subcooling [°C] as the system pressure increases. In the present study, t = thickness of platinum foil [mm] the system pressure Ps is up to 2.2 kgf/cm2. The heat M0 = impinging jet velocity [m/sec] flux in nucleate pool boiling is expressed approxi- a = surface tension [kgf- m] pt = density of liquid [kgm/m3] mately by the following equation, considering the
34 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Ps - system pressure 3) Katsumata, I. and M. Hirata: Trans. JSME, 43-375, 4257 Poo = atmospheric pressure (1977). sub = subcooled boiling 4) Katto, Y. and M. Kimihiro: Bull. JSME, 16, 1357 (1973). sub=0 = saturated boiling 5) Kutateladze, S. S.: Jzv. Akad. Nauk. SSSR, 4, 529 (1951). sub=85 = subcooling 85°C 6) Miyasaka, Y. and S. Inada: /. Chem. Eng. Japan, 13, 22 (1980).
MECHANISM OF CHLORIDE ION TRANSPORT THROUGH DIAPHRAGM-TYPE LIQUID MEMBRANE
Takeshi KATAOKA, Tadaaki NISHIKI, Yoshio TAMURAand Koretsune UEYAMA Department of Chemical Engineering, University of Osaka Prefecture, Sakai 591
The permeation mechanism has been studied to obtain fundamental information for developing liquid membraneprocess. Chloride ion was concentrated across a diaphragm-type liquid mem- brane impregnated with Amberlite LA-II as a mobile carrier. This process is considered to con- stitute a kind of active transport process. The permeation rates of chloride ion are explained approximately by a permeation model in which hydrochloric acid reacts with the carrier at the interface of one side of the membraneand the complex formed by the reaction then diffuses through the membraneand further reacts with sodium hydroxide in the vicinity of the opposite interface.
Introduction examined and further investigations are needed. In this work, the concentration of chloride ion was Liquid membraneseparations have been recently studied to clarify the permeation mechanism, serving noted as a novel technique which can selectively as fundamental information on the liquid membrane separate and concentrate specific solutes and ions. process. The permeation rate of chloride ion was Liquid surfactant membranes have been used for measured through a diaphragm-type liquid membrane separation of hydrocarbon mixtures and for waste impregnated with Amberlite LA-II as a mobile carrier, water treatment, especially for recovery of heavy from an aqueous hydrochloric acid solution to a mixed metal ions. In basic research concerning their appli- aqueous solution of sodium chloride and sodium cations, Cussler et al.ltBi4>6) have studied separation hydroxide. The experimental results were compared and concentration of several ions by using a thin micro- with a transport model for concentrating chloride ion porous membranecontaining mobile carriers within across the membrane. its pores. However, the mechanism of permeation 1. Theory through such a membranehas not been sufficiently 1. 1 Model for concentration of chloride ion Received January 29, 1979. Correspondence concerning this article should be addressed to T. Nishiki. Y. Tamura is with Hitachi Shipbuid. & Eng. When chloride ions are concentrated across a Co., Ltd., Osaka 554. liquid membrane containing a mobile carrier, the
VOL 13 NO. 1 1980 35