‘ A” ' ' " .» -‘ .“- g '1‘ d‘) I. ”a! . 9‘ 5 . d 4‘ (:L; ‘1‘; ‘ i - i I. 33 .3 i; r Qiqn.’ - ; ' r- 03’ 31% 'I‘fi'r may I ‘ iI ‘3- ;za. .,~ _ a €33,333 , Ema tasty I L‘mn- 31-1,..an ’1 w ‘ V .- This is to certify that the thesis entitled A $71.de of BH‘MR‘] Misfit/(Q, Bad M7 50lmie15wle, PENSI13 Mai \SVI airmail/Jo.) [Sadat]? presented by Til-Z ~0d Hui has been accepted towards fulfillment of the requirements for M ‘ s I degree in MECIINJHAL/ L’ /”J[ ““7 /;é/Z’4 6 W19?— l') cat/51:";év fix Cc . 4441 (”Q2 W’M‘n /’ 27M) ‘* / DatJV/Q/g /9;L“7 /<,\//(/ 42476}% 513/,” [€WW%/W 0-7539 MS U is an Affirmative Action/Equal Opportunity Institution PV4E31.} RETURNING MATERIALS: Place in book drop to ngxARIEs remove this checkout from w your Y‘ECOY‘d. FINES will be charged if book is returned after the date stamped below. Dc W? cm Wt RIDOM USE m I+ V’TWI‘I‘I" 7'- ,‘J A STUDY OF BINARY MIXTURE BOILING: BOILING SITE DENSITY AND SUBCOOLING BOILING By Tze 6n Hui A THESIS Submitted to Michigan State University in partial fulfillment of the requirements MAbTER OF SCIENCE DEPARTMENT OF MECHANICAL ENGINEERING 1983 ABSTRACT A STUDY OF BINARY MIXTURE BOILING: BOILING SITE DENSITY AND SUBCOOLING BOILING By Tze On Hui Boiling site densities have been measured for ethanol-water and ethanol-benzene mixtures at 1.01 bar. Site densities were obtained photographically for a vertically oriented heated test surface. The effects of composition, heat flux. and subcooling on the boiling site density were studied. For ethanol-water mixtures the boiling site density increased about two orders of magnitude from pure water (rela- tively large bubbles) to the azeotrope composition (relatively small bubbles). This dramatic increase was noted to be caused by‘the nature of activation of the boiling surface; inception of individual boiling sites at low ethanol compositions and inception of boiling of the whole surface upon the activation of the first boiling site at medium and high ethanol composi- tions. For ethanol-benzene mixtures the boiling site density formed an unexpected maximum to the left of the azeotrope point while forming a minimum to the right. This phenomenon was postulated to be caused by condensation or evaporation of the more vola— tile component during the waiting period of the bubble growth ii cycle. Activation of the first boiling site caused rapid activation of the entire boiling surface at all compositions. The effect of subcooling (O to 20°C) on the boiling site density was observed to behave in three ways: (1) monotomically decreasing, (2) displaying a maximum, or (3) displaying a minimum. 'The boiling site density was found to increase with increasing heat flux as expected from previous single component studies. Pool boiling curves were obtained for subcoolings ranging from O to Zo‘b for heat fluxes up to 100 kW/mt. The heat transfer coefficient, based on (Twall—Tbulk), was found to decrease with increasing subcoolings. The decrease in the heat transfer coefficient in the mixtures for a given level of subcooling was less than that for the single components and azeotropic mixtures. LIST OF TABLES......................................... LIST OF FIGURES........................................ LIST OF SYMBOLS........................................ 1.0 INTRODUCTION ..................................... 2.0 REVIEW OF BOILING ................................ 2.1 2.1.1. 2.1020 2.2 2.2.1. 2.2.2. 2.3. 2.h. 2.5 TABLE OF CONTENTS Bubble grOWth rates OOOOOOOOOOOOOOOOOOOOOOOO van Stralen's derivation....OOOOOOOOOIOOOOO0 Thome's equation for bubble growth rate in binary mixtureSOOOOOOOOOOOOOOOOOOIOOOOOOOOI0 Bubble departure diameter and frequency..... Bubble departure diameter................... Bubble departure frequency......... Bubble nUCIeationooooooo00000000000000.0000. Temperature profile of the thermal boundary layer adjacent to a heated surface during nucleate pool boiling..... The influence of subcooling on pool boiling heat transrer..0.0...COCOCOOOOOCCOOOOOCOOOO EXPERIMENTAL DESIGN AND PROCEDURE................ Experimental design and procedures......... Heating surfaces........................... Electrical circuit for surface heater...... Description of experimental rig and overall setupO...I0.00.0.00...OOOOOOOOOOOOOOOOOOO Temperature measurement.................... Experimental procedure and calculation..... Determining the boiling site density....... Calculation for heat transfer coefficient.. vi vii 14 16 16 19 20 28 32 38 38 38 #0 43 46 #6 51 52 4.0 RESULTS AND DISCUSSION ........................... 55 4.1. Heat transfer coefficient vs. mixture compo- sition..................................... 57 4.1.1. Ethanol-water mixtures..................... 57 4.1.2. Ethanol-benzene mixtures................... 62 4.2. Heat transfer coefficient vs. subcooling... 67 4.3. Non-dimensional heat transfer coefficient vs. mixture composition.................... 67 4.3.1. Ethanol-water mixtures..................... 67 4.3.2. Ethanol-benzene mixtures................... 74 4.4. Boiling site density vs. mixture composition 74 4.4.1. Ethanol-watermixture....................... 74 4.4.2. Ethanol—benzene mixtures................... 82 4.5. Boiling site density vs. subcooling........ 89 4.6. Boiling site density vs. heat flux......... 96 4.7. Boiling Site density vs. wall temperature.. 100 4.8. (B.S.D.EXP)/(B.S.D.I) vs. mixture composi- tion.OOOIOOOOOOOOOOOOOOO0.0000000000000000 1014‘ 500 CONCLUSIONOOOO0.0.0.0...OOOOOOOOOOOOOOOOCOOO00....I 108 APPENDIX A Preparation of a mixture of known comPOSj-tionOOOOOOOOOOOOOOOOOOOOOOI0.00... 110 APPENDIX B Calculation for heat loss................. 113 APPENDIX C Experimental data. 0 O O O O O O O O O O O C O O I O O O O 0 O O O 117 LIST OF REFERENCES 0 O O 0 0 0 O O 0 O O O O O O O O O O 0 0 O O 0 O O I O O I C O O O O 0 135 LIST OF TABLES 2.1. The influence of subcooling on the heat transferred by one bubble.OODOOCOIDOOOOIOO'.O'OOOOIIOIIIOICIDOIIOOBI 2.2. Effect of subcooling on heat transfer coefficient.....35 3.1. Experimental conditions: mixture composition. heat fluxes. and subcooling.I.IO.IIOIOOIIQOOOUICIOOOOUUOOIIug vi 1.1 2.3 2.4 2.5 2.6 LIST OF FIGURES Phase equilibrium diagram for an ideal binary mixmre systemOOOOOOOOOOOOOI.OOIOOOOOOOOOOOOOOOO Phase equilibrium diagram for an azeotropic mixture syStemoooooooooooooooooooooooooooooooooo Pool boiling curves with boiling site densities (Site/cm ) for the water-MEK system at 1.0 bar by van Stralenocoo0900000000000000000000000.0000 Bubble growth model of Van Stralen for a spherical vapor bubble growing in a superheated binary systemOOO...'000.0...O0.0000000000000000000000IO Dependence of bubble departure and heat transfer coefficient on composition obtained by Tolubinskiy and OStrOVSkiy.OOOOOOOOOOOOOOOIOOOOOO0.0.09.0... Bubble departure diameter for nitrogen-argon miXtureS by ThomeOOOOOOOOOOOOOO00.00.000.000... Bubble departure frequency for nitrogen-argon mixtureSOOOOOOOOI0.0.0.0.000...00.000.00.000... Bubble departure diameter in nitrogen—argon mixtures vs. bubble inertia force term........ Variation in the advancing contact angle with composition for ethanol-water mixtures measured by Eddington and Kenning at 20°C against nitrogen gaSOOOOOOOOO0..00.000.000.00...OOOOOOOOOOOOOOO. Vapor trapping model of Singh et al............ Incipient and deactivation superheats for liquid nitrogen-argon Mixtures ooooooooooooooooooooooo Incipient and deactivation superheats for ethanol-water mixtures......................... Calculated vapor nucleus radius vs. mole fraCtion Of ethan01000000OOOOOOOOIOOOIOOOOOOOOO Amplitude of temperature fluctuations vs. heightabove surfaceOOOOOOOOO0.00000.0....00... vii 12 17 17 18 18 22 23 24 25 2.12 Average diameter, nucleation frequency, and growth rate for vapor bubbles as a function Of subCOOIingOIOOOOOOOOI.OOOIIOOOOOOOOOOOOOOO 2.13 Experimental boiling heat transfer data for a horizontal stainless steel cylinder immersed inwaterO00.000000000000000.0.0.0.0000... ' 2.14 Variation of surface-heat with bulk subcooling 2.15 Variation of active site with bulk subcooling 2.16 Variation of average bubble frequency with bulk subcooling.................................. 3.1 Test surface no. 1............................ 3.2 Boiling surface set-up........................ 3.3 Test surface no. 2............................ 3.4 Power supply circuit ......................... 3.5 Experimental boiling rig...................... 3.6 Experimental set-up........................... 4.0 Definition of a linear mixing law for the azeotropic ethanol-benzene system............. 4.1, 4.2, 4.3, 4.4 Heat transfer coefficient vs. percent ethanol for ethan01-Water mixmreSOOOOOOOOOIOOOOOOOIOO 31 35 36 36 36 39 41 42 44 45 1+7 56 58. 59. 60. 61 4.5. 4.6, 4.7, 4.8 Heat transfer coefficient vs. percent ethanol for ethanol-benzene mixtures................. 639 6n: 65! 66 4.9.4.10, 4.11, 4.12 Heat transfer coefficient vs. subcooling...... 68. 69. 70. 71 4.13, 4.14 H(exp)/H(I) vs. composition for ethanol- watermixtures ...... .0...‘.................. 72. viii 4.15, 4.16 H(exp)/H(I) vs. composition for ethanol- benzene mixtures........................ 75. 76 4.17, 4.18, 4.19, 4.20 Site density vs. percent ethanol for ethanOI-Water mixture.................. 77.78. 79. 80 4.21, 4.22, 4.23, 4.24a Site density vs. percent ethanol for ethanol-benzene mixture............... 83, 84, 85, 86 4.24b Phase diagram for ethanol-benzene system 88 4.25,4.26, 4.27, 4.28, 4.29, 4.30 Site density vs. subcooling........... 91. 92. 93. 94. 95. 96 4.31, 4.32, 4.33 Site density vs. heat flux.............. 97. 98. 99 4.34, 4.35. 4.36 Site density vs. wall temperature...... 101, 102, 103 4.38, 4.39, 4.40 (B.S.D. )/(B.S.D. ) vs. composition.... exp I 105, 106. 107 A-1 Values for fin efficiency...... ..... 116 ix NOMENCLATURE 1X2 azeotrope or azeotropic composition B‘S'D'exp experimental boiling site density (sites/cm2 ) B.S.D.I ideal boiling site density (sites/cmz) (3p liquid specific heat (kJ/kgl'C) I) liquid mass diffusivity (mZ/s) IDd bubble departure diameter f bubble departure frequency Fb buoyancy force Fd drag force Fi inertia force FE) excess pressure force on base area of bubble ti. surface tension force h. heat transfer coefficient (w/m2°C) hexp experimental heat transfer coefficient (w/mZ’C) hfg latent heat of evaporation hI ideal heat transfer coefficient (w/mZOC) Nsn Scriven number dPsat/dT slope of saturation curve q heat flux (w/mz) R vapor bubble radius A T wall superheat, TW - Tsat Tb bUlk temperature of liquid eff «d GREEK SYMBOLS effective wall superheat incipient superheat, Tsup - Tsat wall surface temperature saturation temperature wall temperature temperature measurements underneath heating surface binary mixture bubble growth time ideal binary mixture bubble growth time waiting period mass fraction of volatile component at bubble interface mole fraction of volatile component in liquid phase mass fraction of volatile component in bulk liquid mass fraction of volatile component in the vapor bubble mole fraction of volatile component in vapOr bubble liquid thermal diffusivity (mZ/s)v extrapolated superheated-layer thickness mass diffusion shell thickness rise in local saturation temperature liquid density (kg/ m3) vapor density (kg/m3) surface tension (N/m) average bubble growth time xi Chapter 1 Introduction Boiling is a physical process of great practical significance and has been the subject of intensive research for many years. Many of these research projects were motivated by the need for nuclear power vapor generator design and' safety and the sharp rise in energy cost. Most of the research efforts have been directed on the boiling characteristics of single component liquids. But mixture boiling research is important in the design of two-phase heat exchange equipment in the chemical and petrochemical process- ing industries, the refrigeration industry, the air separation industry, and the liquid natural gas industry as examples. The boiling of binary and multicomponent liquid mixtures is quite different from Single component boiling. The thermodynamics of vapor—liquid phase equilibria of mixtures allow the vapor and liquid phase to be of differing compositions. Thus, the boiling of a liquid mixture is distinct from single component boiling in that the driving force for heat transfer is in turn linked to mass transfer. The evaporation rate can be severely retarded in the mixture because the rate of mass diffusion is usually much slower than that of heat diffusion in the liquid phase. A working knowledge of the elementary principles of vapor-liquid phase equilibria is required for an under- standing of mixture boiling. Phase equilibrium diagrams are used to describe the relationship between temperature, pressure, and the compositions in the two phases at satura- tion. Figure 1.1 shows the phase equilibrium diagram for an ideal binary system at constant pressure. Saturation tempera- ture is plotted on the vertical axis. Mole fractions of the more volatile component in the liquid and vapor phases are plotted on the horizontal axis. The more volatile component is that with the lower boiling point at the pressure of interest. The dew point line denotes the variation in equilibrium vapor mole fraction with saturation temperature. The bubble point line depicts the functional dependency of the liquid mole fraction on the saturation temperature. It is evident that ’§>.§ for the more volatile component and §4.§' for the less volatile component. This is expected intuitively since the more volatile component is above its normal boiling point while the reverse is true for the less volatile component. Figure 1.2 illustrates a temperature-composition phase diagram for a binary mixture system forming an azeotrope at E, . At the azeotrope, the compositions of the liquid and az vapor phase are identical. To the left side of the azeotrope, IV) Q, and to the right yé g. The slope of the bubble point line changes from negative to positive as the azeotrope is passed from left to right. However, the product (I-X)(dT/dx) is always positive as a consequence. The P=constant of L. 3 4.0 E de 0 ' of" 2' t ””e ,2 Tsat ________ 6 —————————— l 656/ l l 'o/,, I I t ”he : I I l I l | I l | L J t 0 ii 9i Vapor/ Liquid Mole Fraction Figure 1.1 Phase equilibrium diagram for an ideal binary mixture system 11 ll 0 L 3 .. _P_=cnns_ta11_L CO L- Q a. E .— Tsat ”—- l I I : I l I l I l ' I I l I 3' l o I ' 3' I ' 8| I ' gI l l I L l l 0 - .. xi yI VAPOR/LIQUID MOLE FRACTION Figure 1.2 Phase equilibrium for an azeotropic mixture system azeotrope behaves like a single component liquid since the compositions in both phases are the same. The boiling heat transfer coefficient of binary mixtures can be drastically smaller than that predicted by using an ideal linear mixing law on single component boiling heat transfer coefficients. Thus, the fundamental mechanisms causing this variation need to be studied and ultimately, a method is needed to predict the boiling heat transfer coefficient for binary mixtures. Anobjective of the present experimental program is to determine the effects of composition and subcooling on the boiling site density. Boiling site density is defined as the number of active boiling sites per unit area. The boiling heat transfer coefficient also will be measured in order to ascertain the dependence of the heat transfer coefficient on the boiling Site density. The boiling site density is an important parameter because it affects the rate of total vapor generation and thermal boundary layer removal. Consequently, it plays a significant role in the overall enhancement of the heat transfer rate in nucleate pool boiling compared to single phase natural convection. No analytical information is available at the present time to predict the site density as a function of composition and the degree of subcooling. The only previous experimental work on site density in binary liquid mixtures as a function of composition was performed by Van Stralen (1). However, his results seem impractical since his study was performed on a very thin wire (0.2 mm in diameter) which is much smaller than the diameter of the bubbles themselves. His tests covered a number of aqueous systems. Figure 1.3 depicts the results for water, methyl ethyl ketone (MEK), and a mixture of u.1% wt. MEK. At a constant heat flux of 0.3 mw/mz, for instance, the number of boiling sites per cm2 in pure water is 30 and in MEK over 200, but for the 4.1% mixture only one site per unit area is active. Thus, the variation in the boiling site density at constant heat flux shows a marked minimum. Several parameters are important in any model for predicting the site density: the boiling incipience criteria, the dynamic contact angle, and-the thickness and the tempera- ture profile of the thermal boundary layer. These parameters will be elaborated in Chapter 2. The experimental program involves performing boiling heat transfer experiments in which composition, heat flux, and the degree of bulk subcooling are varied. Two binary mixture systems were chosen for the study: ethanol-water and ethanol-benzene. In the aqueous binary mixtures of ethanol and water, the dynamic contact angle and surface tension vary substantially as the composition changes. Therefore, a large variation in the boiling site density with composition is expected for this mixture system. On the other hand, the variation of boiling site density for ethanol and benzene mixtures is expected to be smaller since the surface tension does not change as much for this non- aOueous binary system. Also, the contact angle is thought “5“ 3‘. ‘_&‘~ 13 7' aaxv 15. f l l : 1A , l l I l 12 i l l l a to { I MW 3% 1 as [ 0X11; 1‘2'0 05 90 I I I 1 ad A , o /" '...'100% m»’ _; //1 2a: 450 1’ #090 o "30'. 1o 20 30 40 so ATEC] Figure 1.3 Pool boiling curves with boiling site densities (sites/cm ) for the water- MEK system at 1.0 bar by Van Stralen (1) to be fairly constant. For each experimental condition. photographs of the boiling surface are taken at a shutter speed of 1000 HZ. The boiling site density is obtained from the photographs. The heat transfer coefficient is obtained by calculating the wall temperature of the boiling test surface and the heat flux through a prescribed area. Chapter 2 is a state-of-the-art review on the areas of importance in the present study. Chapter 3 describes the experimental design and procedure. Experimental results and a discussion of these results will be presented in Chapter h. Chapter 5 presents the conclusions of the study. Chapter 2 Review of boiling It has been well established from experimental studies that the boiling heat transfer coefficient of binary mixtures is much lower than that predicted by using an ideal linear mixing law on their single component values. In the follow- ing sections, fundamental phenomenological topics such as bubble growth rate, bubble departure diameter, bubble departure frequency, bubble incipience, and boiling site density are presented in the context to explain the lower heat transfer coefficient for binary mixtures. A section will be devoted to discussing the effects of subcooling on the boiling heat ransfer process and its effect on the different parameters will be examined. 2.1 Bubble growth rates The bubble growth rate of a single component liquid is limited by the rate of heat transfer to the bubble interface to provide for the latent heat of evaporation. In binary mixtures, however, the growth rate depends upon the rate of mass diffusion of the more volatile component as well as upon the diffusion of heat. During the growth of the bubble, IIIIIIIIII-___________ I ...‘~ 10 the more volatile component is evaporated preferentially since its mole fraction in the vapor phase,'y, is greater than its mole fraction in the liquid phase,'§ (Figure 2.1). Due to this preferential evaporation, the volatile component is depleted near the bubble interface and must be replenished by mass diffusion through the depleted layer. Consequently, the bubble growth rate is slowed down. The local saturation temperature rises also, due to the higher composition of the less volatile component. Thus the effective driving force for heat conduction to the evaporating interface,ZlT eff' is lowered. 2.1.1 Van Stralen's derivation of bubble growth rate equation for binary mixture In the next two sections, derivations for bubble growth rates for binary mixtures will be presented. The first derivation will be the pioneer work of Van Stralen (2) who extended the theory for spherically symmetric bubble growth in a uniformly superheated liquid for single component liquids to include binary mixtures. Next, Thome’s model (3) is presented. Thome's model extends Van Stralen‘s model by considering a further rise in the local saturation tempera- ture due to the evaporation of neighboring sites and a previously departed bubble. Van Stralen starts his derivation by using a mass balance equation at the bubble interface. The rate of 11 preferential evaporation of the more volatile component is equated to its rate of mass diffusion through the interface, va—me/dt = PL D( Bx/ Ar)r=R (2.1) The mass fraction of the more volatile component drops from a value of xb to x across a spherical diffusion shell of thickness Sm (see Figure 2.1). Assuming the mass concentra- tion gradient across the diffusion shell to be linear, one gets (Bx/3r)r=R = Xb - x (2.2) 3m Substitution of equation 2.2 into equation 2.1 gives = - — 2' dR/dt (PL/PV>(xb x/y x)(D/%m) < 3) To approximate the value of Sm, Van Stralen uses a model for one-dimensional transient mass diffusion through a spherical shell, i.e. 2.u Sm = (n Dt/3)1/3 ( ) The bubble growth rate is then given as dR/dt = (PV/PLbe-x/y-x) D (2.5) 1/2 (“Di/3) 2 34‘ y 'Sr-4 l 3: ' I xb m l ”i :8 44 E 11 : +7 Diffusion }-— Sm she" I Thermal boundary l layer l Bubbie l Inter ace 41 i" g .4 l E I % Afe i. " ' AT 1. . g. i : Aférr ‘ T x } W I A: satl b radius, r [al [bl Figure 2.1 Bubble growth model of Van Stralen (2) for a spherical vapor bubble growing in a superheated binary mixture. (a) tem erature and comgosition profiles; (b)process illus rated on phase iagram. 13 Van Stralen next examines the bubble growth rate in light of the Plesset and Zwick (4) bubble growth equation based on a heat balance: 1 2 (12/7‘ )1/2 (3ch AT( oi of bubble departure - d, 0 19a ¢$ and heat transfer coef- $34Lhn ‘ amxmuuc ‘ ficient on composition ; (q = 116 kw/n‘) obtained , 4_; by Tolubinskiy and 120 ”an "0 Ostrovskiy (5) i Md cl’g m0 7?; ‘13! mm d" m m' 20 a l a; as :01”: c 5L1 6'5 f,llF_s_ec ' '4— m f‘ . . - W‘Mi—m a (3‘ I gymzo deg C, q wt/mz deg i\ i .. 0.7 can . . 0 . . ° 0 , 20 w 0 “5;”, Wm, Methanol Dd 0.6 (mm) 0.5 0.4 OI3 ' 0.2 - 0.1 - 0 J Figure 2.3 Bubble departure diameter at q = 2.1 kW/m‘ for nitrogen-argon mixtures by Thome (6) l o 0.2 014~0.6 0.3 1.0 an 120 18 Figure 2.4 Bubble departure frequency at q = 2-1 kW/ mzfor nitrogen-argon mixture by Thome (6) l 1 I I 1 l T J I 1003 o f (VS) 0 l 1 1 1 1 a L 1 o 0.2 0.4 ~05 0.8 an 0 $1191 3: Site 6 Ddhnm) 1 05- 01— . 03‘ 02 0.1L: 1 1 1 1 1 I J;— 0 05 lo 15 20 25 30 35 L0 - 1 [o‘niLn-1ith 2]/3 3 . 1.0 Figure 2.5 Bubble departure diameter in nitrogen-argon mixtures vs. bubble inertia force term, Thome and Davey (7). Site #1 is an artificial site of 52/4m dia. and site #6 is a naturally occuring site. 19 Using this model, Thome (8) noted that aneffect of the slower bubble growth rate in binary mixtures is to decrease the inertia and drag force terms. If the drag force is considered insignificant in comparision to the inertia force, and applying the usual bubble growth law of R g at“ (2.16c) where a and n are empirical constants, then the bubble depar- ture diameter, Dd’ is found to be proportional to the inertia term as D rN/[aun(4n-1)tun-2] 1/3 d (2.16d) Using the experimental values of a and n obtained for the nitrogen-argon system (9), Thome was able to demonstrate that the reduced inertia force term does correlate the smaller bubble departure diameters in the binary mixtures (Figure 2.5). 2.2.2 Bubble departure frequency The bubble departure frequency,f, is defined as f = 1/(tg + tW) ' (2.17a) The bubble growth time, tg’ is determined by the bubble growth rate and the bubble departure diameter, which in turn is governed by forces acting on the bubble. Thome showed that the ratio of the bubble growth time in a binary mixture to that in an ideal mixture is 2/5 t = (N ) (2.17b) Since Nsn S 1, a shorter bubble growth time is predicted for binary mixtures. During the departure of a bubble from a heated surface, the surrounding thermal boundary layer is stripped and must be reformed in order that the vapor embryo in the cavity can begin to grow again. This time interval is called the waiting time, tw. Several physical parameters that can affect the waiting time are the bubble nucleation superheat required, the thermal diffusivity of the liquid mixture, and the wall superheat. Experimental data of Thome (9) and Tolubinskiy and Ostrovskiy (5) showed that the combined effect of bubble departure diameter and frequency is to yield a lower vapori— zation rate and thus can partially explain the lower heat transfer rate for binary mixtures. 2.3 Bubble nucleation In this section, the nucleation criteria for a vapor embryo trapped in a cavity on a heated wall will be discussed. Observations show that bubbles growing on a heated surface originate as minute vapor nuclei trapped in pits and cracks 21 on the surface. The nucleation criteria are important for two reasons. First, it is important to know the superheat temperature required for boiling to initiate. It is also important for predicting the number of boiling sites per unit area on the boiling surface. The incipient superheat required for thermal and mechanical equilibrium for a vapor nucleus of radius r trapped in the micro—structure of a heated surface is given as AT. = T - T = ZCTI/(r dp inc sup sat ) (2'18) sat * dT Shock (10) has evaluated AXTinc for the binary system of ethanol-water based on equation 2.18. Comparing the calcu— lated values with those obtained experimentally, he concluded that the wetting characteristics can be a principal parameter controlling ZlTinC. The dynamic contact angle for water is about 700 but drops off toward 00 as the mole fraction of ethanol is increased (Figure 2.6). Using the model of Singh- et al (11) shown in Figure 2.7, the effect of a small contact angle, 6), is to decrease the size, i.e. the radius , of the vapor nucleus trapped and hence the nucleation superheat is increased. Recently, experiments (12) were performed with the binary systems of nitrogen-argon and ethanol—water and the results supported Shock's claim concerning the importance of the wetting characteristic on boiling incipience. Both IOO’ Oaruu I 59““! "col Ethanol, % mass Figure 2.6 Variation in the advancing contact angle with composition for ethanol-water mixtures measured by Eddington and Kenning at 20°C against nitrogen gas. Reference 26 ADVANCING lIQUID / \ l__ V coniCAL CAVITY CYLINDRICAL CAVITY Figure 2.7 Vapor trapping model of Singh et al. (11) for (a) a conical cavity (b) a cylindrical cavity. 23 experiments were carried out to determine the effect of compo- sition on boiling incipience and boiling site deactivation. In the experiments with liquid nitrogen-argon mixtures, no change was observed in the incipient superheat as a function of composition. Furthermore, the deactivation superheat coin- cided in value with the incipient superheat. In choosing the nitrogen-argon system, it was known a priori that no large variation inCT', dpsat/dT’ or contact angle occurred. Therefore no significant variation in the incipient super- heat was expected. The solid line in Figure 2.8 depicted theoretical value from equation 2.18 for ZlTinC based on values of CY', dpsat/dT' and a vapor radius value of 1.0 /(m. The deviation of the experimental value from the theoretical value might be due to a smaller contact angle for nitrogen. A large variation in ZlTinC was obtained for the ethanol- water binary system. This was expected since large variations in the values for CV and contact angle exist for this system. The results are shown in Figure 2.9. A maximum value of hhoc was found for the mixture at a mole fraction of about 0.5. Again, the solid line gives the value of ASTinc calculated by using equation 2.18 and a vapor nucleus radius of r. A large discrepancy is noted. By substituting their experimental values of ZkTinc into equation 2.18, Thome et al (12) obtained the calculated values of the vapor nucleus radii (Figure 2.10). The large decrease in the radius can be explained by the rapidly decreasing value of the contact angle as the mole fraction ATinc (°C) A Tdeact (°C) 211 0 l J J i 1 l 1 l l 0 0 2 0.4 0 6 0 8 1.0 y XNZ (a) (b7 Figure 2.8 Liquid nitrogen-argon mixtures. (a) Incipient superheats; (b) Deactivation superheats. 1.0 25 m T I I 1 I I I I l Sro I - | d 8 ° I 40 40 b 0 ° : q T I I u l 1 - 3o 3, 1' _ :3 I r ‘L O I. - q ' I: “a I n 1' . — 7'; I r 3 I ‘ ' V l i . u. AZ ' 0 1 1 A 1 4 1 4 1 1 0 0 0 2 0 4 0.6 0 8 1 0 N (a) Xeth 20 I. I I I l r I I 1| A _ ' o . i - cl). ' . , x I 7;; 10 " . . . :8. ‘ 8 I .P 1i g .3 <1 AZ 0 1 1 1 1 1 1 1 1 1 0 0.2 0.4 0.6 0.8 1.0 (b') "" xeth Figure 2.9 Ethanol—water mixtures (a) Incipient superheats; (b) Deactivation superheats. 26 5 - .— .4 - E 3 3- - 2 - _ 1 _ _ . tr-v""’firg'fl. 0 1 1 J I 1 1 L J 0 0.2 0.4 0.6 0.8 1.0 «I Xeth Figure 2.10 Calculated vapor nucleus radius vs. mole fraction ethanol. 27 of ethanol in the mixture is increased. Equation 2.18 was derived for the case of a vapor nucleus surrounded by superheat liquid of constant temperature. For a vapor nucleus growing on a heated surface, it is surrounded by a thermal boundary layer with a temperature gradient. Recognizing the significance of the temperature gradient in the thermal boundary layer when the height of the vapor nucleus is comparable to the thickness of the thermal layer led several investigations (13,14,15,16) to develop more detailed correc- tions for ZSTinc. The analysis of Hsu (14) can be divided into two parts. First, it is important to know the temperature profile within the thermal boundary layer. Secondly, a new criterion for nucleation must be defined. Hsu approximates the problem of the thermal boundary layer as one of one-dimensional transient conduction of heat into a slab. The thickness of the slab is a parameter called 8 . Beyond the slab, the turbulent agitation is so strong that the temperature is essentially at the bulk temperature, Tb' At steady state, the temperature profile within % is linear. To establish the criterion for the initiation of bubble growth, Hsu argues that it is necessary for the thermal layer surrounding the bubble nucleus to be at a temperature equal to or greater than the temperature of the bubble nucleus in order to give an inward flow of heat through the bubble interface to provide the latent heat of vaporization. But the temperature of the vapor bubble is 28 defined previously as Tsup and given by equation 2.18 as ATinc = Tsup - Tsat = 2 G/(r dpsat) (2'18) dT The temperature of the thermal layer at the top of the bubble must be equal to or greater than Tsup' The results of Hsu's analysis can be summarized as follows: 1. Given a wall temperature, there are an upper limit and a lower limit for the vapor nucleus radii for nucleation to occur. Equation 2.18, on the other hand, has a lower limit only. 2. For a given vapor nucleus of radius r, Hsu's value for'13T; Inc is higher than that given by equation 2.18. 3. Hsu's analysis points to the importance of the thermal boundary layer in understanding incipience. It is important to know the temperature profile as well as its thickness. 2.4 Temperature profile of the thermal boundary layer adjacent to a heated surface during nucleate pool boiling The thickness of the superheated boundary layer adjacent to the heating surface and the temperature profile within it have long been recognized as significant parameters in nucleate boiling. It is this highly superheated region which is responsible for the origin and growth of a vapor 29 bubble. To a large degree, the thickness of this region and its temperature distribution control the growth rate of a vapor bubble as well as its departure size. In addition, these parameters play a significant role in determining the size range of active cavities on a given surface. Several experiments were carried out to measure the temperature profiles within the thermal boundary layer (17, 18, 19). Marcus and Dropkin (17) used thermocouple junctions with a diameter of less than .002 in. (.0051 cm) in their experiments with water. Their results showed that the temperature profile is linear very near the heating surface. The linear region of the temperature profile exhibited simi- larity with respect to the "extrapolated superheat-layer thickness", S , regardless of the heat flux.applied. That is, for all of their data, the temperature profile from the wall to about 0.57 S is given as _' 9 O ‘< y $0057 (2019) For the region above 0.573 , the temperature profile is expressed in the form of T -n b = 00/3 > (2°20) where n and C are functions of the heat flux applied. The 30 "extrapolated superheat-layer thickness", 8 , is defined as the height of the intersection between the tangent to the temperature profile at the surface and the constant liquid bulk temperature line. Figure 2.11 is an example of their result. The value of 81 , which is a measure of the super-heated region adjacent to the surface, appears to be primarily a function of the heat transfer coefficient. The experimental results of Marcus and Dropkin were satisfactorily correlated in the form 2 = and A (2.21) 1 where Ci and d are functions of the liquid and the surface used. It should be noted that the instantaneous temperature at any point in the superheated boundary layer is a widely and rapidly fluctuating variable. The amplitude of these fluctuations varies with the height above the boiling surface. It reaches a maximum value a small distance from the surface and decreases to a very small value as it approaches the surface. Thus the surface appears to act as a smoothing agent inhibiting the agitation in the liquid. Similar results were obtained for water, Freon-113, and methyl alcohol in the experiments performed by lippert and Dougall (18). Niebe and Judd (19) carried these experiments one step further by considering the effect of subcooling on the thermal boundary layer. Their result showed that the wall TL 177 140 100 62 AT- deg F AT: 35 112 150 ' 1 1 1 I I 1 I 1 1 1 1 7 18 2 -1 q . 15,140 Btu/hr-ft _ 6 h . 1,010 Btu/hr-ttz-deg F’ _ ‘ .:r,. 226.20 deg F _ 14 a 12 - IO — a - /—TMAX'TMIN __ 6 . A "j I g — I 4 ‘. -—I I .— 2;— 3k _ — | —-1 o— .1 ’11111111‘1111 0.00 002 0,04 0.06 Y - inches (T. - R’mx ' 1 TL) (7; — T1)_l 912:? deg F Run. in. X 10' T ’ sec 80 0.022 0.85 909 117 0.019 0.80 1100 157 0.016 0.64 1430 195 0.013 0 43 2000 . 0 20 ‘0 atmb°f 31 Figure 2.11 Amplitude of tem- perature fluctuations versus height above surface: high heat flux. Curve also shows average temperature profile and definition of extrapolated superheated layer thickness. Ran ‘ (TC-.TL) .1. 037 Table 2.1 The influence of 028 subcooling on the heat (31% transferred by one bubble. Figure 2.12 Average diamgter dm, nucleation frequency f and growth rate 0;? for vapor bubbles at p= 1 bar as a function of the subcooling. 32 temperature ksrelatively insensitive to the degree of sub- cooling, Tsat 'Tb' At a heat flux of 20,000 BTU/Hr—ft2 (63.08 kW/mz), the wall superheat dropped from approximately 20°F to 10'F (11.10C to 5.600) while the subcooling was increased to 50oF (27.80C). When the heat flux was increased to 100,000 BTU/Hr-ft2 (315.40 kW/mz), the wall superheat remained relatively constant at 400F (22.20C) while the subcooling was increased from GOP to 90°F (0 to 50°C). One might then conclude that the wall superheat is relatively insensitive to subcooling in the well established boiling region. The effect of less subcooling is to decrease the thickness of the extrapolated superheated-layer thickness,% . Thus, similar boiling conditions can be brought about by inde- pendent changes in heat flux or subcooling. 2.5 The influence of subcooling on pool boiling heat transfer It was stated earlier that given a fixed heat flux, the wall superheat, Tw - T remains essentially unchanged while sat’ subcooling may be changed by a large factor (by as much as 100 F or 150¢F). Engelberg—Forster and Greif (20) have proposed an explanation for the apparent insensitivity of the heat transfer rate to subcooling based upon a "vapor— liquid exchange" mechanism. They postulated that the primary mechanism of nucleate boiling heat transfer is the stripping or displacement of the superheat thermal boundary layer by 33 the departing vapor bubble. This process may be visualized as a kind of pumping action in which a layer of hot liquid is displaced and replaced by cold liquid from the bulk. When a bubble grows to a maximum size of Rm , it causes ax the exchange of a liquid volume proportional to (Rmax)3' The rate of heat energy transferred per boiling site is then given as q ~Cp PLIRmaX>3(TW - TbI/m (2.22) where'I_is the average time between each growth cycle. The insensitivity of heat flux to subcooling can be explained by combining the effects of subcooling on each of the parameters in equation 2.22. Tolubinskiy and Konstanchuk (21) and Ellion (22) performed experiments with water to study the effects of subcooling on Rmax and ”C, . Ellion's experimental data are shown in Table 2.1 and those of Tolubinskiy and Konstanchuk are shown in Figure 2.12. Both data sets point to the fact that Rmax decreases while 1/%; increases as sub- cooling is increased. Column 5 of Table 2.1 shows that the product Riax’(Tw - Tb) decreases as subcooling increases, despite the fact that higher subcooling increases the total temperature difference between the heating surface and the bulk liquid. Column 7 depicts the heat transfer rate per boiling site. By comparing column 7 with column 2, it is seen that while subcooling was changed by more than 400 percent, the product appearing in equation 2.22 changed only by about 15%, an insignificant variation in view of experimental accuracy. 34 The analysis of Engelberg-Forster and Greif (20) has some drawbacks. The volume of the hot liquid displaced is more accurately described as being proportional to (KRmaX)ZE;, where 0 is the thickness of the thermal boundary layer. K is a factor multiplying R max to give the area of influence in the liquid by the bubble. K, intuitively, will depend upon factors such as the viscosity of the liquid, the bubble growth rate, the velocity at the moment of departure, and the boiling site density on the heating surface. They failed also to consider that the boiling site density might be affected by the change in subcooling. Fand and Deswani (23) performed a detailed study on the effect of subcooling on the wall temperature of a heating surface. Their results are shown in Figure 2.13. Figure 2.13 is a plot of the surface temperature, TS, as a function of the bulk temperature of the liquid, Tb. At a given heat flux, TS possesses a maximum, which occurs at progressively higher degrees of subcooling with increasing heat flux. Table 2.2 gives the calculated values for the heat transfer coefficient as a function of subcooling (note that TS=TW). ~The heat transfer coefficient, h, is defined as n = q/(Tw -Tb) (2.22a) Sultan and Judd's (24) experimental results on the effect of subcooling on the wall temperature, boiling site densiti, and average bubble frequency are shown in Figures 2.14, 2.15, and 2.16. Figures 2.14 and 2.15 suggest a 35 I I I l I l; L I I I TIL] I I VI mm 2401- f 5 - - V! a fi . - . 23- ._ a - Figure 2.13 Experimental gum Yum-ZWMF‘ boiling heat transfer data s 'w'finm‘“ for a horizontal stainless :ZZSL . I“ 226740qu . . .- Yw-ZZJ'quF steel cylinder (Dia. = 2m» « 0.4555 in.) immersed in 215- q water. 0 139213111111 1 J l l J l J 1 1 j l J 2101 l 1 1 m 90 MO 1}“ I t? 200 220 230 5‘" Table 2.2 Effect of subcooling on heat transfer coefficient (Calculated from figure 3 of Fand and Keswani (22) ) 1 2 3 4 5 (PTU/ Hr-ftz) T T T - T 2 q - - w (F2_ b (F) sat .a (a) h (asu/ Hr-ft -? 51960 226.7 212 0 3535 51960 228.5 204 8 2112 51960 230.9(max) 190 22 1270 51960 230.9 142 70 584 51963 223.6 136 76 561 511a. 226.7 132 80 548 c"‘60 224.2(min) 129 53 545 36 ’° " nan-tun m man" In: con ‘ I! " .4 __ A—A-fl‘AK e /A/ A A\A o." «I b .5 : O O g .0 kHlfi—‘O\ \O\ . I U \D\ D §uu «nub 5 O 1?" an um!) I A % 333.1 ‘I'JI o J 1 . J 1 1 A ° ’ 0 II no a so a a g g. a: :uocoouuo 17.4.1 ,2, u , I 7 Y Y T H In ‘ o: - q .o \- .0 p ‘ Q; \ § u- . .3, . 2 : 30 b ‘ C \ M 3 a O 0\0 1 t \ S N . O E ‘ '- U g-ICfi urn}. ‘ O 3. 0"“ Ind/1:) o b A $033.1 {Ii/J) s \ o 1 ° ' '° I u u so :9 oo . m 1!.-L11'c1 to I Y mom mu nan-u lawn: ‘1 / D -2-'“-0 11~JI O %.Ic¢.o 11.1}. A .9. A . 333.1 (II/J! 1 9 :o no so suocoouu 13-1 111:1 - 30 Figure 2.14 Variation of surface-heat with bulk subcooling. Figure 2.15 variation of active site with bulk subcooling. Figure 2.16 Variation of average bubble frequency with bulk subcooling. 37 direct dependence of site density upon the wall temperature. Contrary to the results of Tolubinskiy and Konstanchuk (21) and Ellion (22), Sultan and Judd's data showed a maximum in the average bubble frequency when plotted against subcooling. Chapter 3 Experimental Design and Procedures 3.1 Experimental Design All experiments were performed at the Boiling Heat Transfer Laboratory at Michigan State University. This section describes the experimental design and set up. 3.1.1 Heating surfaces Two different heating test surfaceSmade of brass were used in performing the boiling experiments for the two binary systems. At the beginning of each trial, the test surface was prepared by rubbing the heating test section with a fine emery paper (silicon carbide 320) and then finished with a crocus cloth. It should be noted also that a circle with a diameter of 19.1 cm is inscribed on the test section. In the counting of the site density, only bubbles inside this circle are considered. Surface no. 1 (see Figure 3.1) was used for mixtures of ethanol and water. The outer section of the test surface was made very thin (O.b mm) to minimize the conduction heat loss in the radial sirection. Therefore, ‘V‘> the major portion of thermal energy is tran U) fe-red through 38 39 bi —_-_]jj]::j:] flange \\\\\ :::::: Three thermocouples thin fin ““H :~electrical heater attached to this surface boiling surface \\ \ \ / inscripted K / circle 1 I 1 I '5 ’ 2 2 2 5’ f ,/ I ./ I / (3) Figure 3.1 Test surface no. 1; (A) SIDE VIEW, (B) TOP VI EW no the midsection since the boiling heat transfer rate on the inner section is much higher than the heat transfer rate by natural convection on the outer section. An adhesive with high temperature resistance and low thermal conductivity was used to attach a circular ring to the bottom of the thin section of the test surface. The ring is in turn screwed to a cylindrical shell (see Figure 3.2). When surface no. 1 was used for ethanol—benzene mixtures, it was discovered that the mixtures chemically attack the adhesive used, thus creating a leakage problem. For the mixtures of ethanol-benzene, surface no. 2 (Figure 3.3) was used instead. The surface is screwed directly to the cylin- drical shell. The bottom of the test surface. as shown in Figure 3.2, is fastened to anelectrical heater by means of a screw. A high thermal conductivity grease is used to lower the thermal contact resistance between the bottom of the test surface and the heater. The heater was specially designed and built with a nichrome heating filament. Its resistance is about 1.U ohms. The maximum current used in the experiments is about 12 amperes. 3.1.2 Electrical circuit for surface heater To measure the total heat flux passing through the test surface, it is necessary to know the current and voltage across the heater filament. Section 3.2.3 presents a more hl Figure 3.2 Boiling surface set-up (legend; l-test surface, 2-test surface base, 3-circular ring attached to the test surface using low conductivity adhesive, 4-thermocoup1e wire, 5-power lead for electric heater, 6-electric heater, 7-cylindrical shell, 8-o-r1n83) u2 1 flange three . . thermocouple thin fin holec R‘\ Electrical heater attached to this surface \ \2 .\I L ‘. \. inscripted circle (E) Figure 3.3 Test surface no. 2: (A) side view, (B) top view #3 detailed description on the conversion of the power of the heater into heat flux for the heating surface. Figure 3.4 is a schematic diagram of the circuitry for the surface heater. Two voltage measurements are made by a digital multime- 'ter. The first measurement gives the voltage across the heater itself. A shunt with a known resistance of 1 m 1 1% is used to indirectly measure the current passing through the heater. By measuring the voltage across the shunt, one can obtain a value for the current by dividing the voltage by the known resistance of 1 ml?” The power is then given as: Power = (Voltage across heater) X (current) (3.1) 3.1.3 Description of experimental rig and overall set up A schematic diagram of t.e boiling rig is shown in Figure 3.5. The vessel is a 1/4 inch (6.h mm) thick stainless steel cylinder cross (U inches in internal diameter) with flanged ends. To maintain the desired temperature and pres- sure inside the vessel, a proportional temperature controller connected to an immersion heater and a condenser using water as coolant are used. The test surface is mounted vertically, facing a sight glass window. For all of the test trials, it is desired to maintain the pressure inside the vessel at 1b.? p.s.i.a. (1.01 bar). In cases where subcooling is maintained in the bulk liquid5 POWER SUPPLY HEATER SHUNT DMM Figure 3.4 Power supply circuit RS H n KFITJ FJ lL :25: l 10::; l I g I I I i W— s . 9 “/1 2\ l 4 5 % 5==J L :15— I | .4 -fiL-d}. 1 l —Jh- Ht—nndL—n Figure 3.5 Nucleate pool boiling rig (l-stainless steel vessel, Z-teet surface, 3-electric heater, h-bulk liquid thermocouple, S-temperature controller thermocouple, 6- immersion heater, 7-sight glass windows, 8-liquid fill line, 9-condenser, lO-valve to vacuum pump/atmosphere, ll-pressure gauge, 12-aafety relief valve. as nitrogen gas is fed into the vessel at the valve located at position 10 of Figure 3.5. A system of pressure regulators is used so that the pressure is maintained at 14.7 * .3 p.s.i.a. (1.01 * 0.02 bar). Figure 3.6 shows the overall set up for the experiments. 3.1.h Temperature measurement Copper-constantan thermocouples and digital temperature indicators are used for temperature measurements. The estimated maximum error for each measurements is 1 0.200. Two thermocouples (at positions 4 and 5 in Figure 3.5) are used to measure the bulk temperature of the liquid. One of these measurements is interfaced with the temperature controller and the other with a digital temperature indicator. Three thermocouples are embedded at three different locations of the heating surface and their temperatures are read from another digital temperature indicator. The two digital temperature indicators are calibrated to agree with each other. The temperatures of the test section are used to extrapolate the wall temperature (see section 3.2.3) of the heating surface. 3.2 Experimental procedure and calculations The purpose of this study is to investigate the effect of heat flux, composition, and degree of subcooling on the LL? (L. ff— Figure 3f5' Experimental set-up (legend; 1-boiling surface, 2-viewing window, 3-camera, u-lighting) h8 boiling site density and the boiling heat transfer coefficient of binary mixtures. Also, qualitatively at least, a funda- mental relationship between the boiling site density and the boiling heat transfer coefficient is being sought. Two binary mixture systems were chosen : ethanol-water and ethanol—benzene. As mentioned in Chapter 1, it is known a priori that a large variation in the dynamic contact angle existed for the ethanol—water binary system. This variation is thought to be less significant for the ethanol-benzene system. Therefore, it is hoped that the experimental results of site density from the mixtures will help us to understand the importance of the dynamic contact angle on the site density. Table 3.1 lists the compositions, heat fluxes, and subcoolings used in the experiments. Appendix A gives a summary of the procedure used to prepare a mixture of the desired composition. The following is an outline of the steps used in the experiment.) 3.2.1 Experimental procedure (1) The prepared mixture is fed into the vessel gradually (to minimize air bubble formation) until the level of the liquid is about in cm above the heating surface. (2) The temperature controller for the bulk liquid is set to the saturation temperature corresponding to 14.7 p.s.i.a. (1.01 bar). The sytem is closed to the 49 Table 3.1 Experimental conditions; mixture composition, ~heat fluxes, and subcooling. (A) Mixture composition: Mole fraction of ethanol Ethanol-water Ethanol-benzene 0% 0%: 15.00% 15.00% 28.67% 30.00% 49.04% 45.00% 60.00% 65.00% 70.00% 80.00% 80.00% 100.00% 89.40% (B) Heat fluxes tested, (kW/mf) 97.39 74.62 55-48 38.54 24.41 13.74 (C) Degree of subcooling,°C 0 C 5 lO 15 20 C300 0 (3) (4) (5) (6) (7) ‘..J 50 atmosphere, but the excess pressure caused by the degassing process is released periodically.- The experiment is ready to start when the saturation condition is reached. At this point , the liquid has been degassed. ‘ The power to the surface heater is turned on and increased gradually to give a heat flux of about 150 kh/ m2 in the inner section of the heating surface. This ensures that boiling is taking place and that all the possible boiling sites are activated. Boiling continuesfor approximately 5 minutes to achieve steady state condition. The power to the surface heater is then lowered to the desired level. A period of time is allowed for the system to reach a steady state condition. The temperatures (Tb, T1, T2, T3) are then recorded and photographs of the boiling surface taken. Step 5 is repeated for the five other heat fluxes. (See Table 3.1 for a list of heat fluxes tested) The bulk temperature setting on the temperature controller is then lowered to the degree of subcooling desired. The system is allowed to reach the desired bulk temperature. At this point, the pressure is lower than 1.01 bar. Nitrogen gas is then fed into the system to make up for the pressure difference. Steps 4,5, and 6 are repeated for each subcooling condition. (See Table 3.1 for the different degrees 51 of subcooling tested. (9) At the end of each experiment a sample of the mixture is taken from the vessel and its density measured at e420°C to ensure that its composition remained the same. The heating surface is cleaned with crocus cloth to eliminate surface aging as a factor in the experiment. 3.2.2 Determining the boiling site density Three photographs are obtained for each set of experi- ! mental conditions, i.e.. mixture composition, heat flux, and degree of subcooling. For each active boiling site on the heating surface, the boiling cycle can be divided into the bubble growth time and the waiting time. During the waiting time. the thermal layer above the surface is being heated by transient heat conduction until it reaches a tem— perature high enough to reactivate the boiling site as defined by the nucleation criteria. Since the vapor nucleus is too small to be seen in the photograph, a counting of the 0‘ oiling site density from any single photograph would under- estimate the actual number of active sites. Therefore, a scheme is used to reduce this error in the counting procedure. During the counting of each photograph, a piece of paper is placed directly underneath the photograph. The counting is done by punching a tiny hole in the center of the bubble. Thus the location of the boiling site is also recorded on 52 the piece of paper. This procedure is repeated for the two other photographs and in this manner the boiling sites of the three photographs are superimposed on the paper. The boiling site density is then obtained by counting the holes on the paper, which gives a better estimate of the actual boiling site density. 3.2.3 Calculation for heat transfer coefficient The heat transfer coefficient is defined as: = _rp h q/(TW -b) (Note that several previous experimental studies have used TSat instead of Tb in the definition of h) In the next two sections. calculation procedures for determining the heat flux through the boiling surface area, q, and the wall temperature will be discussed. Heat flux through the boiling surfgce area As mentioned earlier in Section 3.1.1, the heating surface has a total diameter of 2 inches (5.08 cm). The total area of this surface can be thoughtof as being two separate regions: a boiling heat transfer region and a natural con- vective heat transfer region. For our calculations, all the heat energy generated by the surface heater is assumed to pass through the heating surface . In order to obtain the heat flux through the boiling area (inner region with a diameter of 2,5h cm), heat loss by natural convection in the 53 outer region must be subtracted from the total heat transfer rate. It should be noted that the distinction of the two heat transfer mechanisms on the two regions is justified by experimental observations made on the heating surface. The heat loss to the outer region is calculated by assuming it to be a case of heat transfer by conduction through a circumferential fin of rectangular profile. The heat which is conducted through the circumferential fin is removed by natural convection to the bulk liquid. For detailed discus- sion of this calculation, see Appendix B. I Heat losses through the fin ranged from 8% to about 65% depending upon the experimental conditions. i.e., this heat loss is more significant at low heat flux and high subcooling. The actual heat flux through the boiling test section is then adjusted appropriately in the calculation for the heat trans- fer coefficient. Cther designs incorporating an insulating material rather than the metallic fin could have been used to reduce heat losses but bubbles formed at the joint would have adversely affected the boiling site density measurements. Wall temLe ra tu re Three thermocoupleSwere placed at different distances underneath the heating surface. The heat energy generated by the electric heater is conducted to the test surface through a circular base located at its bottom (seeFigures 3.1 and 3.3). Inside the cylindrical shell ( .it is assumed that the energy loss by natural convection to 54 air is insignificant. Thus the temperature profile along the length of the circular base is assumed to be linear and the wall temperature can be extrapolated by measurement of T T2, and T3. However, two problems were encountered: (1) 1. the temperature profile in the region between T2 and T3 is not quite linear due to the shape effect of the electric heater bolt hole, and (2) occasionally, a loose contact exists between the junction of the thermocouple and the point of temperature measurement in the cylindrical rod. The first problemi53eliminated by using only T1 and T2 in extrapolating the wall temperature, Tw. The temperature pro- file of T1, T2, and T3 is checked qualitatively to ensure that the junctions are in good contact with the wall of the drilled holes in the circular base. Chapter 4 Pesults and Discussion Experimental results are presented and discussed hi this chapter. Seventeen experimental runs were performed: 10 experiments for ethanol-water mixtures and 7 experiments for ethanol-benzene mixtures. Experiments for two compositions of ethanol-water mixtures (at 70% and 80% mole fraction ethanol) were repeated and the results were consistent with each other. A tabulated form of all experimental data is presented in Appendix C. In the following sections. different aspects of the results are organized by presenting them in graphical form. Specifically, the effects of compositions, subcooling, heat flux, and wall temperature on boiling site density are examined. Presented also are plots of the heat transfer coefficient as a function of composition and the heat transfer coefficient as a function of subcooling. Finally, ratios of (hexp/hI) and (experimental boiling site density/ ideal boiling site density) at constant heat flux are plotted against mixture composition. The ideal quantities are defined by an ideal linear mixing law. An example showing D the value of hoxpand hI for ethanol-benzene mixtures is shown in Figure 4.0. Note that hI is the ideal heat transfer ' '1 coefficient calculated by using an id,al linear m 55 Heat Transfer Coefficient 56 hexp .45 1.00 Liquid Mole Fraction Figure 4.0 Definition of a linear mixing law for the azeotropic ethanol-benzene system S7 < ”.5,“ i.e. for 0 \ x xaz =I‘V ~ -~ hI .i hexp ~ ~’ + xaz x h (4.1) xaz x - xaz § exp N = O az X <’v < and xaZ \ x \ 1 N H N ‘ = - + - hI x xaz hexp ~ 1 x hexp N 'v (4.2) X=1 ~ X=X _ N 1 - az 1 xaz az 4.1 Heat transfer coefficient vs. mixture composition 4.1.1 Ethanol—water mixtures Figures 4.1, 4.2, 4.3, and 4.4 are graphs of the experimental heat transfer coefficient plotted against mix- ture composition for the ethanol-water system. For each heat flux used, five different levels of subcooling were maintained in the bulk liquid. The negative deviation of the actual heat transfer coefficient from that calculated by a linear ‘Je mix n law is conclusive for high heat fluxes and low subcool- 0Q ings. The minimum point for most of the curves occurs in the Vicinity of about 30% mole fraction of ethanol. For the mixture composition of 30m ethanol at a heat flux of CO L) p~: \ 3 N O *‘3 3" (D (D :24 fU (D ‘1 He :3 (D :5 r}- m H < D) H C (D I_J I U) \ A) \O E? \c .. \ 33 3 0° $0 \J'I l—b J3. ‘58 (‘Figure 4.1 HERT TRRNS COEFF V8 PERCENT ETHRNOL ETHRNOL RND NRTER MIXTURE HEFIT FLUX IS 97.39 KN/M" O c? 2';- r ° X 0 + c? A i; _ " 0 A1 c’ I ‘3 534 I - 90 I '4: I E8 «5 ‘é. ,4 - I 7 I 2 So I O (.3 «a | _ H0 P | Ll. ” I 800 I O. \ >5 . o _ Em \\ X /I u. X I °° I 02:0}\ 0 0 + O Eféj \\‘-~,._.r”’// X + ////I b E ‘ x + a ‘ | L£gl\ ¥‘___’/ A 0 0| (TfixT“‘-8Z:::-8""”"'3 a) 0 I b I a I C? I Cb.00 2b.oo Jr.oo 5b.oo eb.00 100.00 COMPOSITION: PERCENT ETHRNOL o °c SUBCOOLING s °c SUBCOOLING 10°C SUBCOOLING 15°C SUBCOOLING 201C SUBCOOLING Ku/m'c 6.00 1 HERT TRRNSFER COEFFICIENT 9.00 7.00 8.00 J k l V o/ 4.00 5.00 ‘1 2-00 A 1.00 3 00 //n o x CD\ ‘\ A____/‘ 59 Figure 4.2 HEFIT TRFINS COEFF VS PERCENT ETHRNOL ETHHNOL 0N0 NRTER MIXTURE HEHT FLUX 18 74.52 mm1 0\0___"/0 I I o I I I I I 20.00 4117.00 €0.00 80.00 COMPOSITION: PERCENT ETHHNOL 100.00 0 °c SUBCOOLING s °c SUBCOOLING 10 '0 suscooLmo 15 'c suacoounc 20 'c suacoouno 20 KH/M C 00 HERT TRHNSFE§ COEFFICIENT .40 .60 S .80 4 3.20 4. l .40 .60 1 .00 l l l ’\ .‘\\“~. 60 Figure 4.3 HERT TRRNS COEFF VS PERCENT ETHRNOL ETHRNOL 0N0 NPTER MIXTURE HERT FLUX IS 38.54 KN/M‘ Al /x/ // ’,/’ | I t I I I I I I I I I I I l I X I I l \\\\w X\X _ \"’ 0 X + ”" (9/0 + .00 60.00 80.00 PERCENT ETHRNOL 20.00 40.00 COMPOSITION: 100.00 0 “c SUBCOOLING 5 'c SUBCOOLING 10 'c SUBCOOLING 15°C SUBCOOLING 20’0 SUBCOOLING 3.20 .60 2 .‘O l KIA/r12 ’c 2.00 2 l .60 l l .20 l 0.80 HEHT TRRNSFER COEFFICIENT e40 l 0 61 Figure 4.4 HEFIT TRRNS COEFF VS PERCENT ETHRNOL ETHRNOL HNO NFITER MILXTURE HERT FLUX IS 13-74 KN/M o 0 °c SUBCOOLING x s ‘c SUBCOOLING + 10% SUBCOOLING . 15 °c SUBCOOLING o 20°C SUBCOOLING o+——-x————————.——————————.~—— 00-00 .00 20.00 40.00 60.00 80.00 100 .00 COI‘IPOS I TION: PERCENT ETHRNOL 62 reduction from the predicted value. The deviations from the predicted values become smaller for lower heat fluxes and higher degrees of subcooling. This can be explained by the fact that at these conditions, natural convection becomes more significant in the heat transfer process and the heat transfer coefficient is less affected by the preferential evaporation of the more volatile component (i.e. ethanol). This is illustrated by Figure 4.4 where for subcoolings of 5, 10, 15, and 2000, the heat transfer coefficient can be accurately predicted by using a linear mixing law. 4.1.2 Ethanol-benzene mixtures Some results for heat transfer coefficient as a function of mixture composition for ethanol-benzene mixtures are shown in Figures 4.5, 4.6, 4.7, and 4.8. The negative deviation from the ideal values is again obvious. Two minima are observed for this system: one at each side of the azeotropic mixture composition (45% mole fraction of ethanol). The azeotropic mixture thus seemsto behave like a pure liquid. As in the case of the ethanol-water system, the deviation is more significant at high heat flux and low subcooling. The deviation from the ideal values, however, is smaller for this system than the ethanol-water system. For the minimum point at the composition of about 80%, at a heat flux of 97.39 kI‘I/m2 and 0°C subcooling, a 27% reduction from the ideal value is obtained for the experimental heat transfer coef— .o° ' 4. 1102.911 0. 2. 8.00 7.20 . 4-80 2 4-00 \x l 3.20 HERT TRRNSFER COEFFICIENT ./+ \, I I "I” Figure 4.5 HERT TRRNS COEFF VS PERCENT ETHRNOL ETHHNOL 9ND BENZENE MIXTURE HERT FLUX IS 97.39 Kw/M‘ up Ou-n-nnnaun—o—o—fl. > / I [G 1.60 0 .0 7 6 I I I 0 V50.00 40.00 60.00 80.00 COMPOSITION: PERCENT ETHRNOL 100.00 0 °C SUBCOOLING 5 ‘C SUBCOOLING 10 °C SUBCOOLING 15°C SUBCOOLING 20”C SUBCOOLING HERT TRRNSFER COEFFICIENT 2.00 ml 1.60 l .20 I l A 64- Figure‘4J5 HERT TRRNS COEFF VS PERCENT ETHRNOL ETHRNOL HND BENZENE MIXTURE HEAT FLUX IS 38.54 KIT/I1z \. ( A5 I I I I\9 /; \9 9 / 1 'l V .00 COMPOSITION: 40.00 60.00 80.00 PERCENT ETHRNOL 20.00 100.00 0 °c SUBCOOLING s ‘C SUBCOOLING 10'C SUBCOOLING 15°C SUBCOOLING 20°C SUBCOOLING KIT/11‘ °C HERT TRRNSFER COEFFICIENT 7-20 l 7"/' M 4-00 3.20 .40 2 /:/:///’ .80 1 60 1 5(/. (3 Figure 4.7 HERT TRRNS COEFF VS PERCENT ETHRNOL RND BENZENE pIXTURE HERT FLUX IS 74.62 KN/M .00 20.00 COMPOSITION I T r 40 60.00 80.00 .00 100.00 : PERCENT ETHRNOL ETHRNOL 0 °C SUBCOOLING 5 °c SUBCOOLING 10°C SUBCOOLING 15°C SUBCOOLING 20°C SUBCOOLING 20 .00 l /o 1 0.80 l u 1 HEFIT TRHNSFER COEFFICIENT 0 0.60 *4 e 66 Figure 4.8 HERT TRRNS COEFF VS PERCENT ETHRNOL ETHANOL AND BENZENE MIXTURE HEAT FLUX IS 13.74°KN/M‘ I Cp.20 .00 60.00 80.00 PERCENT ETHRNOL 20.00 40.00 COMPOSITION: 100.00 0 °C SUBCOOLING 5 °C SUBCOOLING 10 ’C SUBCOOLING 15 °C SUBCOOLING 20°C SUBCOOLING 67 4.2 Heat transfer coefficient vs. subcooling *IJ ’Je gures 4.9, 4.10, 4.11, and 4.12 show the effect of subcooling on the heat transfer coefficient. Note that each figure is for one particular composition. The heat transfer coefficient is seen to decrease as the subcooling increases. This is due to the fact that TW drops atéfilBSSextent than Tb, i.e. Tw is relatively insensitive to changes in subcooling. Also evident is the fact that the decreasing value of h is more significant at higher fluxes. This suggests that TW is relatively insensitiveto subcooling in the well established boiling region. On the other hand, since natural convection is the more dominant mode of heat transfer at lower heat fluxes, h is relatively insensitiveto subcooling. It should be pointed out also that the results here show a similar trend to those obtained bT Sterman, Vilamos, and Abramov (25). J 4.3 Non-dimensional heat transfer coefficient, hexo/hT’ vs. mixture composition 4.3.1 Ethanol-water mixtures The value of the non-dimensional heat transfer coeffi— 4---J-, the exten. c a. fh I’D CiGhC, defined h-re as h /h , indicate eJCp I .— negative deviation of the experimental value of h from that (I) predicted Ev an ideal linear mixing law. In A TI res 4.13 '_\ ,71 I r) .5 (L J I\ and 4.14 (at constant heat fluxes of 92.”? k?/ ~2 L...‘ Slam—115.42 _. 3'3. -afi— —. __ —-- , KN/M2°C 4 00 A4180 5:60 I I //°// /// HERT TRRNSFER COEFFICIENT Figure 4.9 HERT TRRNS COEFF VS SUBCOOLING ETHRNOL PND NPTER MIXTURE COMPOSITION- 60.00 PERCENT ETHRNOL l 3.20 l .40 \\‘ >\\ .00 8.00 12. 00 16.00 20 SUBCOOLING: DEGREES CELSIUS V1 1e 1 0.60 Cp.00 GD+XO+ .00 97.39 74.62 65.48 36.54 24.41 13.74 KIT/nz KH/n‘ KN/n‘ KN/n‘ KH/n‘ KH/n“ l 4.00 3.00 ‘ l 2.00 l HERT TRRNSFER COEFFICIENT n l 1.00 159 Figure 4.10 HERT TRRNS COEFF VS SUBCOOLING ETHRNOL 6ND BENZENE MIXTURE COMPOSITION- 100.00 PERCENT ETHRNOL Cp.00 .00 4100 8100 10.00 10.00 SUBCOOLING: DEGREES CELSIUS 20 0.4-X04 .00 97 74 55 36 24 13 .39 .62 .48 .54 .41 .74 KIT/nz Ku/n‘ Ku/n‘ KN/n‘ KN/n’ Ku/n‘ u 3.20 .40 l RHNSFER COEFFICIENT .60 I—v-41 HERT O .00 (90 Figure 4.11 HERT TRRNS COEFF VS SUBCOOLING ETHRNOL HND BENZENE MIXTURE COMPOSITION- 80.00 PERCENT ETHRNOL .00 1000 8000 10.00 10.00 SUBCOOLING: DEGREES CELSIUS O G>+X0+ .00 S7. 74. 55. 38. 24. KH/n‘ KH/n‘ KH/n‘ KH/n‘ Ku/n‘ KN/n‘ I 29 KN/M C 4.00 3 20 .40 2 .60 1 HERT TRRNSFER COEFFICIENT 0.60 l Cp.00 71 Figure 4.12 HERT TRRNS COEFF VS SUBCOOLING ETHRNOL RND BENZENE MIXTURE COMPOSITION— 0.00 PERCENT ETHRNOL - + 97.39 KIT/nL ‘ e 74.62 KH/n‘ x 55.48 XII/nL ' + 38.54 KN/n‘ 4 24.41 KH/n‘ 0 13.74 KN/n‘ X\\\\\\\\\\ \\\\\\\\\\\ \\\\\\\\\\, -I \x\: o\\: ‘L 0 A D;\\\ \+. \1- \0~ 0 10.00 20.00 00 4100 8100 12.00 SUBCOOLING: DEGREES CELSIUS 72 Figure 4.13 HIEXPJ/HIIJ VS. COMPOSITION ETHANOL ANO HATER MIXTURE HEAT FLUX 16 97.39 KN/M‘ G>+XO 1 0-60 0.40 J HIEXPJ/HII) 0.20 1 ~00 0 A . - 0 0 + ‘ x z I A ’ + .— X X 0 X 0 .00 20.00 40.00 60.00 80.00 COMPOSITION: PERCENT ETHRNOL 130.00 0 °C SUBCOOLING 5 °C SUBCOOLING 10°C SUBCOOLING 15 °C SUBCOOLING 20°C SUBCOOLING 73 Figure 4. 14 HIEXPJ/HII) VS. COMPOSITION ETHANOL ANO NRTER MIXTURE HEAT FLUX IS 74.62 KN/M‘ 8 4. - e 0 °c SUBCOOLING x 5 °C SUBCOOLING + 10°C SUBCOOLING 3, A 15°C SUBCOOLING m - o 20 °C SUBCOOLING O N 0‘ P 4"- I I g I '1' a #— 2 + I 0 A ' ° 0 3 I F: 0 ° 0" A I '- A + I o x I o + 9 A e I (D O c?" x + : ' ... 2 I .... x I ‘33? I 0.. >< I u’ I 3:0 I t I _ ° I I I g I . I c0.00 40.0 80. 00 80. 00 100.00 0.00 COMPZO 0=SITION PERCENT ETHFINOL 74 kW/mz), the minimum values of hexp/hI occur in the neighbor- hood of 30% ethanol composition: the values being about 0.5 in both cases. For the composition region between 0% to 60%, the values of hexp/hI incresed when subcooling is increased. Again, natural convection begins to be more significant at higher subcooling and the degradation in the boiling heat transfer process becomes less dominant. This trend is not as obvious for the data at the compositionsof 70% and 80%. 4.3.2 Ethanol—benzene mixtures Some values of hexp/hl for the ethanol—benzene mixtures are shown in Figures 4.15 and 4.16. As pointed out earlier, two mimima are obtained: one on each side of the azeotrope. The mimima of hexp/hI are in general less profound for this system compared to the ethanol-water system. In the region from 45% to 100% ethanol, hexp/hl increases as subcooling is increased. However, heXp/hI has its maximum values at 0 O subcooling in the region from 0% to 45% ethanol. This is .2 ..2 true at both heat fluxes: 97.39 kw/m and 74.52 kI/m . No plausible explanation is available at the present time. 0 0 Boiling site density vs. mixture composition 4.4.1 Ethanol-water mixture Figures “-17. “-18. 4.19. and 4.20 are experimental 40 HIEXPg/HIIJ 0.20 1 cp.00 75; Figure 4.15 HIEXPI/HIII VS. COMPOSITION ETHRNOL HND BENZENE MIXTURE HEAT FLUX IS 97.39 KN/M‘ ,ma +0 0 use mm-J“m_l-ul___nm_______*_ x+e0 -— —-.-. n. ...- —-. I .00 20.00 40.00 60T00 80.00 COMPOSITION: PERCENT ETHRNOL 1 00.00 0 °C SUBCOOLING 5 ’C SUBCOOLING 107C SUBCOOLING 15 ‘C SUBCOOLING 20°C SUBCOOLING 76 Figure 4.16 HIEXPJ/HII] VS. COMPOSITION ETHRNOL 6ND BENZENE MIXTURE HERT FLUX IS 74.62 KN/Mz 0.4-X0 )> (u 0.60 HIEXPl/HIII 0:40 0.20 ex+P Ge 4 .X O O( :0-.........__.__.........._......__...___._.._.._..___..._..____._ __ T cp.00 60. 00 80. 00 100.00 00 COMPZOSIOITION'0 PERCENT ETHRNOL 0 °C SUBCOOLING 5 °C SUBCOOLING 10 °C SUBCOOLING 15 °C SUBCOOLING 20'C SUBCOOLING Figure h.17 SITE DENSITY VS PERCENT ETHRNOL ETHRNOL HND NRTER MIXTURE HERT FLUX 15 97.39 Kw/M‘ 0 x s c SUBCOOLING + 10°C SUBCOOLING A 15°C SUBCOOLING o 20°C SUBCOOLING COMPOSITION: PERCENT ETHRNOL Al I I I I I _ I. I I 0 .. A I I _ I I o I A I _ I I I I I I I I A I o I //// I .00 20.00 40.00 60.00 T00.00 100.00 78 Figure 4.18 SITE DENSITY VS PERCENT ETHRNOL ETHHNOL RND NRTER MIXTURE HERT FLUX 18 74.52 Kw/M‘ 400.00 I 350.00 I 300.00 250.00 4 200.00 1 150.00 100.00 1 TE DENSITY.SITES/CM SI 0.00 l S I i S dyoo .00 - 20.00 40.00 60.00 00.00 COMPOSITION: PERCENT ETHRNOL 1 00.00 s °c SUBCOOLING 10 E SUBCOOLING 15 E SUBCOOLING 20 E SUBCOOLING 79 Figure 4.19 SITE DENSITY VS PERCENT ETHFINOL ETHHNOL RND NRTER MIXTURE HERT FLUX IS 38.54 KN/Mz 4 > —N +___.___ G_.—..—— 0.4-X6 Cp.00 I .00 ' 20.00 40 COMPOSITION: .00- 00.00 80.00 PERCENT ETHRNOL I 00.00 0 °C SUBCOOLING 5 °C SUBCOOLING 10°C SUBCOOLING 15°C SUBCOOLING 20°C SUBCOOLING 160.00 140.00 120.00 I 100.00 80 Figure “.20 SITE DENSITY VS PERCENT ETHRNOL ETHRNOL RND NRTER MIXTURE HERT FLUX IS 24.41 KN/M” 0 °C SUBCOOLING 5 °C SUBCOOLING 10°C SUBCOOLING 15°C SUBCOOLING 20°C SUBCOOLING GD+X0 x——————# X .00 20.0 COMPOSI - 1 i- v 0 80.0 100.00 40.00 0 ,00.00 TION: PERCENT ETHRNOL 81 results for the boiling site density as a function of composi- tion at different heat fluxes. Based on the results of Thome. Shakir, and Mercier (12) on the incipient superheats for ethanol—water system (Figure 2.9), a minimum value for the boiling site density is expected in the Vicinity of 50% mole fraction of ethanol. The results of the deactivation super- heats showed a smaller variation as a function of composition. For the experiments performed in the present study, the deacti— vation superheat would be more reliable in predicting the boiling site density since all possible sites were activated by using a very high heat flux at the beginning of each trial. For each of the heat fluxes studied, the boiling site density is relatively small in the composition region from 0% to about 60% mole fraction of ethanol. Beyond this point the boiling site density increases very rapidly, until an increase of two orders of magnitude is reached at the azeotrope. A vapor spreading phenomenon is observed to be responsible for this huge increase in the boiling site density. For mixtures with a relatively large percentage of ethanol, the following observation was noted. When the heat flux through the heating surface is increased gradually to about 200 kW m2, the wall temperature can be about 30 to b5°C above the saturation temperature before boiling takes place. A single site would be activated first and it is surmized that its vapor in turn "seeds" neighboring si causing them to be activated also. A "chain reaction 82 phenomenon" thus occurs. causing the entire heating surface to be activated and hence,a high boiling site density to result. This aqueous system shows a large negative deviation of the boiling site density from that predicted by an ideal linear mixing law. It is noted, however, that the bubble departure diameter of water is about 3 to 4 times that of the azeotropic mixture. It should be pointed out also that some site density results were not obtainable because the sites were too crowded'uabe counted. This usually occurs at high heat flux and low subcooling. 4.4.2 Ethanol-benzene mixtures Figures 4.21, 4.22, 4.23, and 4.24a are results for the site density as a function of composition for ethanol-benzene mixtures. The variation here is much smaller than_that found in the ethanol-water system. The results demonstrate a maximum to the left of the azeotrope but a minimum to the right. It is noted that the vapor spreading phenomenon occur— red over the entire composition range from pure benzene to pure ethanol while activating the boiling surface. The following offers a plausible explanation for the observed site density variation. After a bubble departed ‘ ' : '1 ‘44. ° ' from the heating surface, a vapor nucleus is left behind in " ° 4 4' - , 43% + w‘ "'1 1 OH ‘0‘." M 1" the micr -s.ructu:e. at b e same -1 e, liaii "-0 -.e bulk rushes in to take up the space that the departed ' L 83 Figure 4.21 SITE DENSITY VS PERCENT ETHRNOL ETHRNOL HND BENZENE MIXTURE HERT FLUX IS 97.39 KN/M1 x s °c SUBCOOLING + 10°C SUBCOOLING A 15°C SUBCOOLING o 20°C SUBCOOLING ;>< Z I I I I I I I A 0 / i I | l | | l I l I l I l l Cp.00 fii .00 20.00 40.00 50.00 80.00 COMPOSITION: PERCENT ETHRNOL 100.00 40.00 84 Figure 4.22 SITE DENSITY V8 PERCENT ETHRNOL ETHRNOL HND BENZENE MIXTURE HERT FLUX I8 74.52 Kw/M‘ J> x-+———nm—-u——-m A + X + (D GD+X ’rv O 20.00 40. COMPOSITION: I l | l l A I I I l 0 l l I i I I | 0 P 0 50.00 50.00 ERCENT ETHHNOL l 00.00 5 60 SUBCOOLING 10°C SUBCOOLING 15°C SUBCOOLING 20°C SUBCOOLING 160.00 140.00 120.00 100.00 I 85 Figure 4.23 SITE DENSITY VS PERCENT ETHRNUL ETHRNUL RND BENZENE MIXTURE HERT FLUX I8 55.48 KN/M’ o 0 °C SUBCOOLING x 5 °C SUBCOOLING + 10°C SUBCOOLING A 15°C SUBCOOLING o 20°C SUBCOOLING 52/ P c30.00 .00 20.00 40. 50.00 80.00 100.00 COMPOSITION: ERCENT ETHRNOL 86 Figure 4.24a SITE DENSITY VS PERCENT ETHRNOL ETHRNOL RND BENZENE MIXTURE HERT FLUX IS 24.41 XII/Mz D D. o g- — o 0 C SUBCOOLING x 5 ’C su0C00LIN0 + 10°C SUBCOOLING A 15°C SUBCOOLING o 20°C SUBCOOLING EE- 0 I I‘ _ )I‘ .’ A V 40. 100.00 .00 ' 20.00 COMPOSITION: 87 bubble left behind. The composition of the vapor nucleus is likely to have a lower concentration of the more volatile component than the vapor composition corresponding to the bulk liquid due to the preferential evaporation of the more volatile component. Therefore, the vapor nucleus will not be in chemical equilibrium with the bulk liquid. N F! . o 0 -or 0 $ Xb 4 Xaz (see Figure 4.24b for a phase equili— brium diagram for the ethanol—benzene system) Suppose that the bulk liquid is of composition?b with a its corresponding vapor composition equal to'y . The vapor a nucleus has a vapor composition that is of a value somewhere between?ba and'ya. Therefore the composition of the vapor nucleus hassalower mole fraction of ethanol than the vapor compositionfya, corresponding to the bulk liquid composition, N x% . It is postulated that in order for the vapor nucleus ”a to attain a vapor composition of’ya, ethanol is preferentially evaporated at the vapor and liquid interface. Thus the radius of this vapor nucleus is increased and the incipient superheat required is lowered. This would lead to a higher boiling site density. It is also postulated that the maximum in the boiling site density is strongly influenced 'I _|_ ° N N 0y the maXimum value of y — x‘. (J N For x $ x. $ 1 For this composition range, the vapor composition of the vapor nucleu 0) has a higher composi 88 |°Cl Figure 4.24b Phase equilibrium diagram for ethanol-benzene system. 89 vapor composition corresponding to the bulk liquid. Therefore. it is postulated that the ethanol component in the vapor nucleus is preferentially condensed so that the vapor nucleus will be in chemical equilibrium with the bulk liquid. Thus the radius of the nucleus is decreased and a higher incipient superheat is required for the nucleus to begin to grow . The resulting effect is a lower boiling site density. Again. the minimum value of the boiling site density is in the vicinity of the maximum value of ry -‘§l. Finally. this non-aqueous mixture system is shown also to have a very nonlinear varia- tion in the boiling site density with composition. 4.5 Boiling site density vs. subcooling It is seen from Figures 4.25, 4.26, 4.27, 4.28, 4.29, and 4.30 that the site density as a function of subcooling can behave in three different ways (1) monotonically decreasing with subcooling, (2) displaying a maximum, or (3) displaying a minimum value. As discussed in Chapter 2, the wall tempera- ture is a relatively weak function of subcooling and the data from the present study further supports this idea, i.e. Tw drops at a slower rate than that of the decrease in the temperature of the bulk liquid. But at the same time, the heat transfer coefficient is smaller for a higher degree of subcooling used. Since the thickness of the thermal boundary layer is related to the heat transfer coefficient in the form % = and (2‘21) SITE DENSITY V8 SUBCOOLING COM 90 Figure 4.2 ETHHNOL 9ND NRTER MIXTURE P05ITION- 89.40 PERCENT ETHRNUL .00 SUBC ‘5.00 '10.0 15.0 20.0 00L ING: DEGREES CELSIUS G>+XO+ 97 74 38 as £2 5& 54 2M J4 w 41 4M KH/H KH/H KH/H KH/H KH/H KH/H r e r v r .00 I 49.00 58.00 84 40.00 00 a D\\\\\“v-a 91 Figure 4.26 SITE DENSITY VS SUBCOOLING ETHHNDL 0ND NRTER MIXTURE COMPOSITIDN- 60.00 PERCENT ETHQNDL X A $-M._._ - \.. 0\ cP-UU .00 3100 8400 3 12.00 It.00 SUBCOOLING: DEGREES CELSIUS 20. G 'D X D G XII/ML KIT/MI MIT/MI KII/M1 . Mw/Mz MIT/M1 15.00 14.00 I 12.00 I 10.00 1 8.00 1 .DO I 6 1 SITE DENSITY.SITES/CM 4.00 2.00 00‘ ‘ t 92 Figure 4.27 SITE DENSITY VS SUBCOOLING ETHRNOL 0ND NRTER MIXTURE COMPOSITIDN— 28.67 PERCENT ETHRNDL v /+\ / \ / 4 //’-‘I- \ ,-’ 0 1’ 1],, \\\ 4 \f \\ I, a / / X ,———--— + \ -r’ / \ . o 7\ ‘ x l x + \ \ K A \ .00 4103 5100 = 15.00 V'IE.00 SUBCOOLING: DEGREES CELSIUS D+X0+ 1 KH/H ‘L KH/H KN/Mz Z KH/H Z KH/H Kw/MZ 320-00 I 280.00 1 240.00 1 200.00 160.00 1 120.00 1 SITY.SITES/CM 93 Figure 4.28 SITE DENSITY VS SUBCOOLING ETHRNOL RND BENZENE MIXTURE COMPOSITIDN- 100-00 PERCENT ETHQNDL C m 9 4400 8400 I 1b.00 V 10.0 20 SUBCOOLING: DEGREES CELSIUS D+X0+ .00 97. 55. 38. 24. 13. 74 . MIT/MI KH/M‘ KH/M‘ KN/ML KH/HL KH/M‘ 160.00 140.00 1 120.00 1 100.00 1 a ./ V’M A """-‘—'~—§._ A 94 Figure 4.29 SITE DENSITY VS SUBCDDLING ETHRNDL 9ND BENZENE MIXTURE COMPOSITIDN— 80.00 PERCENT ETHRNDL ~——-—x .__—_.x___._——-——-')( ’K—K“ + +h” _ ...__‘ __~ A 4m\ .00 v T 4200 8100 c IE.00 15.00 20 SUBCOOLING: DEGREES CELSIUS G>+X0+ .00 I KN/M L KH/M ‘- KH/H Kw/M‘ t . KH/H . _ KN/M‘ 2. DENSITY.STTES/CM 40.00 50 00 80 00 100.00‘ 120 00 140 00 150.00 SI‘TE 00 20 C000 95 Figure 4.30 SITE DENSITY VS SUBCOOLING ETHeNOL 0ND BENZENE MIXTURE CDMPDSITIDN- 15.00 PERCENT ETHQNDL _. _ 4‘ \ .1 ¢~er o l\ . \ ) X < \x 111 / / 9—-—£>.—___J+. _. \é\ \ . fT I CC 20- 4. 3’0 5 SUBCOOLING' DEGREES2 CELSI IS 0 51 D (J L . KN/M xw/Mz Xw/M‘ Rw/M‘ KN/M‘ KW/M‘ 96 where d is a negative number, the thickness of the thermal boundary layer is expected to increase when a higher degree of subcooling is used. Also, the bubble departure diameter decreases with subcooling as observed here qualitatively and quantitatively in Figure 2.12. Thus. as subcooling increases. there is a possibility of packing boiling sites closer together. Thus three general trends can be caused by an increases in the subcooling: (1) a decrease in the wall temperature, (2) an increase in the thickness of the thermal boundary layer adjacent to the heating surface, and (3) Dd is smaller as subcooling is increased. It can be assumed that a decrease in wall temperature would cause a lower boiling site density to occur. On the other hand, an increase in the thickness of the thermal boundary layer may increase the boiling site density. an idea suggested by Hsu's analysis in Chapter 2. Thus. these three phenomena should be considered in the analysis of the boiling density as a function of subcooling. 4.6 Boiling site density vs. heat flux As expected, the boiling site density increases as the heat flux is increased as shown in Figures 4.31, 4.32, and 4.33. Note that the slope of the curves gets steeper as the heat flux is increased. An energy balance can be written in the form energy = (Boiling site density) (average energy A t' ( rea)( ime) removed per bubble) (Average frequency of bubble cycle) (4.1) 320.00 280.00 1 240.00 3. /CM 150.00 200.00 1 J J 120.00 80.00 1 SITE DENSITY.SITES 40-00 97 Figure 4.31 SITE DENSITY VS HEHT FLUX ETHRNDL RND NRTER MIXTURE COMPOSITIDN— 80.00 PERCENT ETHRNDL - x 5 °C SUBCOOLING 10°C SUBCOOLING 15°C SUBCOOLING o 20°C SUBCOOLING + 9 0+ Cp.00 .00 #TF 1 I 1 20.00 40.001_ 60.00 80.00 100.00 HERT FLUX: KN/M 280 00 320.00 240.00 00.00 W L. 98 Figure 4.32 SITE DENSITY VS HERT FLUX ETHQNOL 0ND BENZENE MIXTURE COMPOSITIDN- 100.00 PERCENT ETHQNOL 0 - - — e 0 C SUBCOOLING x 5 °C SUBCCCIING + 10°C SUBCOOLING ' 15‘0 5055001100 0 2C°C SUBCCCIING -I A r- 3 -I + I— + X 0 X _ + A. O X .1- 1’. A _ 5 O A 'f ‘r I V T T I .0 20 00 40.00 50 00 80.00 100.00 THEQT FLUX: RM/M‘ .00 99 Figure 4.33 SITE DENSITY VS HERT FLUX ETHRNOL RND BENZENE MIXTURE COMPUSITION— 45.00 PERCENT ETHRNOL 0 ‘0 SUBCOOLING 5 0C SUBCOOLING 10 t SUBCOOLING 15 t SUBCOOLING o 20 t SUBCOOLING D+X0 X+ GDOX- I * 0 I A O C0.00 = 20.00 40.00 L 50.00 50.00 100.00 HERT FLUX: KN/M 100 01‘ Heat flux = (Average energy removed per bUbble) Boiling site density X (1/fi;) (4.2) Since the experimental data point to the fact that the ratio of (heat flux/boiling site density) is decreasing as heat flux is increased, this shows that the product of (av. energy removed per bubble) X (1/h;) is therefore also decreasing as the heat flux is increased. Since it is well known that 7:decreases as heat flux is increased, this suggests that the average energy removed per bubble decreases at higher heat flux. 4.7 Boiling site density vs. wall temperature The boiling site density is plotted as a function of wall temperature in Figures 4.34, 4.35. and 4.36. The following observations are noted I (1) The deactivation superheats can be extrapolated from each curve. Note that the data seem to suggest a higher deactivation superheat for lower subcooling, pointing to the importance of the thickness of the thermal boundary layer suggested earlier. (2) Within the range of conditions tested, i.e. a heat flux up to about lOOkW/mz, the rate of increase in the boiling site density increase rapidly as the wall termperature is raised. 320.00 280.00 101 Figure 4.34 SITE DENSITY VS. NHLL TEMPERRTURE ETHFINOL RND NHTER MIXTURE CUMPOSITION- 80 .00 PERCENT ETHRNOL 0A 6 i )1 5 °C SUBCOOLING 10°C SUBCOOLING I 15°C suacoouuo 20°C SUBCOOLING . G) 1 1! 14.00 68.00 NRLL TEMPERRTURE . 1 a 72.00 1 QET’ i 1_ 075-00 80.00 84.00 8200 C I 91.33 102 Figure 4.35 SITE DENSITY VS. NHLL TEMPERHTURE ETHRNOL 0ND BENZENE MIXTURE COMPOSITIUN- 80.00 PERCENT ETHRNOL o 0 °C SUBCOOLING x 5 °C SUBCOOLING + 10 °C SUBCOOLING A 15 °C suacooLme o 20 ‘C SUBCOOLING ‘ “'~-____ ___._)( : ,4; / k 0.0 0 5'4 .00 55 .00 7‘2 .00 NHLL TEMPERFITURE . °C 103 Figure 4. 36 SITE DENSITY VS. NFILL TEMEPERRTURE ETHRNDL FIND BENZENE MIXTUR CDMPOSITION- 30. 00 PERCENT ETHFINOL D O o 0 3' o 0 C suacooune- x 5 "C SUBCOOLING 8 + 10°C SUBCOOLING g A 15°C SUBCOOLING N o 20'C su5C00L1N0' O 9 O ‘7‘- N —- D 9 O O- .. N A D o 4 9 0 Eco. _ UH \ x (D LL10 h—c H . <03— ‘ + _ >— 1.. H X ”8 Z ' e as . x a “1 2 F' ; H ([33 + A i D- 0 .1 ‘ 5 v + x O i 0 O 8 Ax o . 3 fl T ‘—T— c3 0 72.00 75 no idea 35.. 00 c 50.00 32.00 NRLL TEMPERRTURE.‘ 1 5 68.0 C 1011 I (3) Note that given the same wall temperature, the general trend is for the boiling -site density to be larger for higher subcooling. Again. this can be due to a thicker thermal boundary layer at higher subcooling. 4.8 (Experimental boiling site density)/(Ideal linear boiling site density) vs. mixture composition Figures 4.38, 4.39, and 4.40 show the variation of (B.S.D.eXp/B.S.D.I) versus the mixture composition 1 where (B'S'D'exp/B‘S'D'I) is the ratio of the experimental boiling site density to that predicted by an ideal linear mixing law. Note the inadequacy of trying to predict the boiling site density from the linear mixing law. This is especially true for the ethanol-water mixtures at the mole fractions of 15%, 28.67%, 49.04%, and 60.0% ethanol where the experimental boiling site densities for these mixtures are less than 10% of the predicted ideal values. For the ethanol-benzene mixture system, the value of B.S.Dexp/B.S.D. is greater that one to I the left of the azeotrope and is less than one to the right. For this system. it would also be very inadequate to try to predict the boiling site density based on a linear mixing law. .60 “-1 11' 00 80 I 0; /B.S.D.( $.60 0.40 .S.D.[EXP1 0.2 J 105 Figure 4.38 B.S.D.[EXPJ/B.S.D.(I] VS. ETHRNOL RND NHTER MIXTURE HERT FLUX IS 74.52 XII/ML COMPOSITI I + 10 c SUBCOOLING T A 15'C SUBCOOLING o 20°C suacooLINC + 0 ._.._...........--...-._-_.._. . —— ——.-—_ _—_—__—_._ ‘4P"“‘"‘-"?1 : 5 6 .00 20.00 40.00 50.00 50.00 COMPOSITION: PERCENT ETHRNOL 1 00.00 .60 "'1 .40 .20 ,..'1 .00 106 Figu r5439 B.S.D (EXPJ/B S D [I] VS- ETHFINOL FIND BENZENE MIXTURE HERT FLUX IS 97.39 KN/Mz COMPOSITI 0 - + 10 C SUBCOOLING A 15 °C SUBCOOLING e 20°C SUBCOOLING 1 B.S.D.(EXP)/B.S.D.(Il 0 0;.0 01.50 01.50 0.2 J cP-OU 00 2'0 .00 40 COMPOSITION: .00 50.00 50.00 PERCENT ETHHNOL 1 00.00 107 Figure 4.40 B.S.D.(EXPJ/B.S.D.(I] VS. COMPOSITI ETHRNOL HND BENZENE MIXTURE HERT FLUX IS 74.82 KN/ML 0 )0 + S.D.(I .50 0:50 /B. 0 0.40 .S.D.(EXPI B 0 0.2 J .00 1---... + 10°C SUBCOOLING A 15°C SUBCOOLING o 20 ”C SUBCOOLING 1 “0.00 20.00 40. COMPOSITION: To 1—.-——-—--s—-9- -——‘-o~—Io-——-o—-o-—o-v—— q—a—— .— 0 ERCENT ETHRNOL 0 50.00 50.00 100.00 108 Chapter 5 Conclusions The following conclusions are made on the effects of subcooling and composition on the boiling heat transfer coef- ficient and boiling site density for the binary systems tested: (1) (2) The boiling heat transfer coefficient decreases as the degree of subcooling in the bulk liquid increases. The ideal linear mixing law is found to be very inadequate in the prediction of the boiling site density of both the aqueous and non-aqmnms binary mixture systeistudied. (a) (b) For the ethanol-water mixture system. the boiling site density can increase by two orders of magnitude from pure water to mixtures close to the azeotrope. A vapor spreading mechanism is proposed as an explanation. The decrease in the actual boiling site density compared to the ideal value is suggested to be due to mass diffusion effects. The ethanol-benzene mixture results demonstrate a maximum in the boiling site density to the left of the azeotrope but a minimum to the right. This phenomenon is explained by postulating that during the waiting period of a bubble growth cycle, conden- sation or evaporation can take place at the surface (3) (4) 109 of the vapor nucleus so that the vapor nucleus can reach chemical equilibrium with the bulk liquid. Thus the size of the vapor nucleus can be changed and therefore changing the incipient superheat required. The boiling site density with heat flux and mixture com- position being held constant can (1) decrease monotoni- cally , (2) display a maximum value, or (3) display a minimum value when plotted as a function of subcooling. This suggests that the thickness of the thermal boundary layer is a significant parameter in determining the boil- ing site density. When the boiling site density is plotted as a function of the wall temperature, it was found that for a given wall temperature the boiling site density is generally greater at a higher degree of subcooling. 110 Appendix A Preparation of a mixture of known composition— a sample illustration To prepare an ethanol-benzene mixture of 15% mole fraction 9 ethanol (at 23 C). l. A) B O A) B C) A V B) O V V Mass of 1 mole of ethanol = 46.06952 gram 0 Density of ethanol at 23 C = 0.7903 gram/ml 0 Molar volume of ethanol at 23 C = a. 0 molar mass of ethanol/density of ethanol at 23 C = 46.06 ram = 58.29 ml 0.7903 gram7ml Mass of 1 mole of benzene = 78.11472 gram 0 Density of benzene at 23 C = 0.875 gram/ml c Molar volume of benzene at 23 C = molar mass of O benzene/density of benzene at 23 C = 8.114 2 ram = 89.24 ml 0.8753 gram7ml Volume of 15 moles of ethanol = 58.29 ml X 15 moles of ethanol = 874.35 ml mole of ethanol Volume of 85 moles of benzene = 82.24 ml X 85 moles of benzene = 7585.40 ml moles of benzene To prepare a mixture of a total volume of approximately 4400 ml (capacity of boiling vessel) Volume of ethanol = (874.35 ml X 4400 ml)/(874.35 ml + . 7585.40 ml) = 454.76 ml 111 Volume of benzene * (7585.40 X 4400 ml)/(874.35 ml + 7585.40 ml) = 3945.26 ml 112 Appendix B Calculation for heat loss The purpose of this section is to outline the method used in obtaining the experimental heat transfer coefficients. To start, we have an energy balance equation: (alsosae Figure 3.1) Power generated by = Total heat flux from inner section electrical heater of heating surface g. Total heat flux from outer section of heating surface (A-l) It is observed experimentally that the mode of heat transfer at the outer section is always by natural convection. Specifically, the outer section of the heating surface is modeled here as that of a case of heat transfer by natural convection through a circumferential fin of rectangular profile . Let us further assume that for a particular mixture, the heat transfer coefficient for natural convection does not change significantly for different conditions of heat flux and subcooling. This assumption is supported by the experimental data in the present study (Figures 4.9, 4.10, 4.11, 4.12). The heat transfer coefficient approaches an 113 asymptotic value as the degree of subcooling is increased and this value is relatively the same for different heat fluxes (represented by different curves)used. This suggests that the natural convection heat transfer coefficient is basically a function of the fluid properties only. Applying equation A-l to situations where natural convection is taking place on the entire heating surface , inner and outer sections: Power generated by = P’= ‘nfhn C Af(Tw-Tb) + h A(T-T) electrical heater - C W b n.c (A-la) where y\f fin efficiency hn c = natural convection heat transfer coefficient la 11 wall temperature at center of heating surface Tb = bulk temperature of liquid Af = surface area of circumferential fin A - surface area of inner section Incrder to obtain a value ofle. it is necessary to have a value for hn in equation A-1. Starting with an equation .0. to get an approximated value for hn c : h = P (A—2) (Af T Ac)(Tw'Tb) Another form of equation A-l can be rewritten as: P 11.0. - MfAf T ACHTW-Tb) (A 3) To summarize the steps that follows: 114 (1) Equation A-2 is used to get a starting value for hn c . (2) Using the value of hn.c. from equation A-2, a value onIf is obtained from Figure 2.11 of reference (27) and is reproduced here as Figure A-l. (3) The value of V\f is substituted into equation A-3 and a new value of hn.c.is obtained. (4) Iteration is used on equation A-3 until the value of hn.c. stabilizes. The method outlined above is applied to a heating condi- tion of lowest heat flux and highest degree of subcooling. Thus it is a situation where the whole surface is in the natural convection region. To obtain the boiling heat trans- fer coefficient when boiling is occurring in the inner section and natural convection in the outer region, we have, applying equation A-l: Power generated by = Total boiling heat flux from inner electrical heater section of heating surface Total heat flux by natural convection from outer section of heating surface (A-4) or P = thc(Tw-Tb) T Vlfhn.c.Af(Tw_Tb) (A‘5) where hb is the boiling heat transfer coefficient. Note that in order to solve for hb from equation A-5, we use values of Wtf and hn.c. obtained by equation A-3. 115 Lc=L+ Fin efficiency 1],, per cent r2c = r; + L... Am=t(r2:—rl) LCWZU#kAm)‘” Figure A-l Efficiencies of circumferential tins of rectangular profile 116 Appendix C Experimental data List of symbols used HFLUX BTEMP T2. 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oNocoH wNmooH ¢nno¢ Nae-m Hmmom momoh mwcow mmmom mhman nnmac Nnhom ammom Homom aamom thoN mhmon mnhum ¢mNo¢ cmmoé nmho¢ zHua ammowm camohm omooah omNo¢h oomomh oomomh owe-mm own-uh ammomh omnomh canomh com-mp anacmm bmwomh moaomh omnohh oomowh ooh-mu ammamh omoomh ammowh um¢omh 00¢.mh cmwomh ammonh oocomp cmaohh om¢omh meomh ochomh 3h omnomm com-mm umhomh ommowh cacoam acconw omno¢w mmHoNh ommo¢h ammowh ooh-mm momo¢m ammowm amno¢h oomoeh omwomh oonowm wono¢m com-Nb omnomh amcowh omhoom cowomm omfia¢w ammocs dcmohh ammomh omnoaw omaonm dohocm ¢h oouomm cowomm bomoah caeomb bc¢omh aom.om oomomm aomuflh ooao¢h bom.hh baaobw documm con-mm oomonfi doaowh comomh dam.om aaoowm 50¢omh bahomh dckohh oomomh adaoww dmwomm camonh oomomh comomh oomomh comodm ammomm Nh com. eawoh¢ Gomoh¢ uomoh¢ amwoh¢ bowoh¢ cowoh¢ acaonm ooaonm oaa.nm ocaonm ooa.mm ooaonm wowohm damohm domohm bomohm comohm cowohm momomm aomomm ocmowm bomon dam-mm bomomm fiahohm aohoho dohohm ao~ohm ocbohm aohahm QZMHm ouuu owm.m mhnoua amfioma oHHomN cam.hn cmn.m¢ ammow o#n.NH own-ma omnowm camohn bmnom¢ awm.m mhnoNH omnomfi canowm camchn umnom¢ owmom obnoma awn-mu oHHowN camohm ammom¢ oom.m ohnoma ammomfl GHH.mN cam.hn own-m: XDJmI .mn¢ n 02: 130 Hocmcpw Mo £030.95 36.: Rmm I Empwzm mzwwcmofifiocmcpm Nwmon¢¢ oomom ¢m¢o¢ umaomm ommomm dc¢omm aca.m¢ acmoo ¢nhoh¢¢ nw¢o¢ mam-h omwohm omhomm canodm coaom¢ chnoma mcmomhm Nwdooa wmmom omaomh ommomh dmo.mh acaom¢ ammoma Hhmodwnu ¢DMoNH manoca ooao¢h bomomh monomh cadow¢ cadomm noeommmn mmmomm m¢NoHH mmfiooh ammomh ochohh ooaowe cflwofim mhmowm¢w w¢nohn ¢oooNH ammomh omoamm now-cm aaaom¢ omn.m¢ mm¢onm¢ m¢mom #flmo¢ concem dohoeo am¢n¢m act-mm oomom mmn.m¢m omoom com-h mmm.Hh one-NF OQHoNN oo¢onm ohnoma abooomua HumoAH mNmoh caconh Boo-wk doao¢h ac¢.mm amnoma omhonmoa madam” mwmom omhomh ommowh baoohn 9o¢onm mauowm nmcommmm neaomm homom oomohh ooooflw dbeomh oo¢unm mamohn waoofimm ¢mhomn mwmoOH ocmomh cowonm oomoam ac¢onm omnomc dmwofiam mNhoN ¢nmo¢ ochomm canomm dag-mm dam-Mm owm.m Q¢Hodmw mm¢om Namom cowonh dam.¢p mcoo¢h mom-mm afinoma ammohm¢n mmmuNH Hmhom oo¢omh oaéohh a¢¢ooh gum-mm ammomfl thonmam ocmoom OHmoh ommohh omocam comomh aomomm aaaowm nhaow¢hm amnomm mN¢om annomh ammomm camoém ocmomm camohn «abommmn Nm¢oo¢ mmmom oo¢oam do¢o¢m on¢.mm oomomm omnom¢ h¢Howow mNoom mnmun ammonh omhonh oomonh cb¢onm ammom m¢m.¢mHH hhnoh nmmo¢ camomN canchh mamowh oo¢omm obnoma mhmom¢mfi mmmonu thom cacomh oomomfi aomomh eo¢onm bmnoma ncNomth mmwoflm Namom cmuomh omwonm aa¢oom ao¢omm oaa.ww mN¢oNHmn mhmoom Hmm-m anhoom ommomm comomm oa¢omm Damofim ammummm¢ ooNoN¢ cmHoF occoam dacomw oo¢omw oo¢onm omn.m¢ non-maca no¢o¢ hm¢om omooch ammomh ooaomh cam-mm ammom mmnommhd mmvum meon camohh can-NF oomohh oom.mm obnoNH mmmoonan mmnoma mmmon oo¢omh oomobm ammomh comowm amnoma Haho¢uo¢ mm¢omm ¢umo¢ ammomN om¢omw oomoam camomm anflcmm mmoo¢oam hfihomn nmoom umo.nm omao¢m Bum-mm wamomm odwohn mmflonmflm mhhon¢ thom omaomm ammomw ocmo¢w camowm umm.m¢ axm: hmzo ZHma 3h ¢k Nb m2m~m XDJmI coma n ovum .mn¢ n uz: L5; bmmonmc mnuowm¢ mmmahmw ¢¢mommnu ocnomdmu ocno¢a¢m nhhonh¢ mmmoonm namommua mnmonmmn amaommmm Homomhmw emmommc nmwomhh ¢¢ho¢mnn mmmouhom manonchm nmmomm¢n ammowmm mhmommaa accombhu hcoonmmm mmkohn¢n hmmonN¢ mdmonhm nmmon¢mu mmnoonmm nmaowmmn «cmomnmc dmwommmm aqu HOSMSHm Ho sowpowpm mace Rom u Empmzw wcmNCmnnaocmst mum.“ mu~.¢ o~a.efi mm~.~d mam.m~ www.mn mwm.~ ¢~m.¢ mmm.a~ msm.md omm.- mm¢.mn "mm.~ omo.m mom.- oa~.om «ma.m~ ¢mo.0¢ mmm.m Nam.m ~m~.nH oo¢.a~ mum.on m~¢.d¢ oom.n ~m~.m mm~.¢~ mmm.mm hmfl.~n cma¢n¢ puzc Nn¢o¢ modem ¢nNom anooa ¢NNoHd mncomu Hmnow ammoh macaw «naom ammom mmmooa mano¢ ownom a¢noh com-h mumom mmmom aooo¢ mmcom nmaom carom ¢¢Noh ammoh can.» nmuo¢ mmmoc Ndmom ncmom mmnom szc concao cmnomm ouuomh bmho¢h amfiuhh canomh oo¢omm coconh ao¢o¢h bmmomh ocmomh ammoom cad-oh oooomh oomomh omhowh oohoam ammomm cmNo¢h cowobh ammomh omhoom cmcomm owe-mm aoaohh bmcomh oewoow oomomw cmuonm oo¢o¢w 3h aomoom omwoafi oumonh ammohh 00¢oew oononw daoowm daoo¢h aocomh ammomh oomcqw ammo¢m adh.eh oom.mh oomomh ammonw cohonw omaomm ammo¢h domowh ammoaw onconm bmflomw aucohm com-sh omhocw ea¢omm aomo¢m om¢omm acco¢m ¢b éomoom oomomm oaoonh ace-ms domomh aa¢o«& oohomm oomcnh abvomh ooaomh acmcfim cah.mm aoeoah momomh camaph doooam aomoww como¢m aamo¢h cowowfi acmomh admonm obmanm bacomm aomohh ooaodm domon oo¢onw acmocm .oocomm up new. éomom¢ bomomt eaoom¢ bomo¢¢ aomomc oamgm¢ ooho¢m dofiocm Bchocm w¢ho¢m cchocm uofio¢m aamomm aomomm acmomm com-mm Gonomm ammomm aa¢o¢m ao¢o¢m bacoem Do¢o¢m co¢o¢m cacocm 60¢.mm cocomm oo¢umm 6a¢omm accomm cocomm azwhm 00mm cmmom ohn.NH omnomn cauowm camohn omn-m¢ ommoo ohnoma omnomfi ounomm camohn cmnome ommom ohnoNH www.mfi cauomm cfimohn amncm¢ ammom osnoNH omnomfl oaaomw camohm omnom¢ bmm.m ownoma ammoma canowm admohn amnom¢ KDAmI ¢ H 132 namoume mHmomH¢ mowowcm nm¢ohmna mmmowmQa h¢uoocmw mdmonc¢ HHmowmm mmmomawa mm¢onmhd mmmo¢m¢m hwhobmflm ncmoam¢ omm.dmm ¢mho¢mma nnmomanm meaonhnm Emmoamu¢ mmhowmw ¢¢momhmn hmm.HnaN m®momMHn mmhoama¢ amuowmmm HanomH¢H hoaommnw wamom¢wm mmhoflmm¢ «anowmhm namoh¢mw axu: Hocmfivm no 20392,“ 30.: Roofi I Empmzm mCmNCmQIHocmspm mom.~ NFH.¢ m¢m.m mmh.hfl ¢N¢.mm mmm.~n Nam.m ”mu.m pwm.HH «an.ma nm¢.mm www.mn mam.m ocn.m ¢mm.NH Hm~.a~ poa.on mnN.H¢ ~Na.» o¢m.~ www.ma ¢nn.- H¢¢.Hm mHH.m¢ ¢H¢.¢ n-.m Dam.mfl mmfl.¢m Nnh.mm ¢¢o.m¢ hwzc nm¢o¢ mmfiom Nomom thooa mwnoHH oomoaa mmwo¢ m¢noh nmhos mmhom hmnom «wooed am¢o¢ cmo.m mmmom m¢moh nchoh mHHom mmm.m ¢Nmo¢ monom mhhom moaom ammow m¢mom N¢H.n ocmom cmmon whao¢ mumo¢ 2Hma omhowm oawohh omooflm awn-mm canomw cohomw ammo¢h owe-Hm cmnomm 6mmo¢m ocNomm ocmohm ammowh émhomw como¢m omaomm cowohm com-mm ocaonw ammo¢m cm¢omm omwahm cum-hm omwomm émmo¢m ocu.wm ammomm ammohm amnomm oohomm 3H ommomm dew-mp amwomw cmmomw acmomm mom-om ammumh omaoww ommo¢m omuohw cowomm omoomm omnomh omoo¢m coaumw omwomm bamoam aowomm oa¢omw ommomm ammohw ammomm domomm ammonm ammomm comohw ammomm ammoom omoomm ammonm ¢h accomm oowomh momoam uomo¢m abmsmm oomomm domo¢h nomoam manomm odaomm aomohm camomm ooaomh oo¢.mm aomomw mo¢ohw ammomw oomoam camomw comomw bamohm oc¢omm damomw bum-am Bomo¢m oomomm camcfiw domomm cmu.am admoum NH coma bacowm manomm adoowm aaoowm uo=.wm oooomm cam-no momonm mow-mm ammonm comono momomw aa¢owm 00¢.ww 6o¢omm do¢omm 60¢.wm ca¢omw oaoonh aco.nh aaoonh Damonh awn-MN aaaonh ban.&p donomh aonomh canomh con-mh canowh minkm comm cmm.w ohnoNH ammoma QHHomN uamahn own-me mmmsm ofinoNH www.ma canowm cam-hm annom¢ ammow ohnoNH awn-ma ofldomm cam-hm cmnom¢ ammom ohnomn ammoma OHH.wN cam-hm omnom¢ ammom abnowa meomH caaomN aflm.hm omnom¢ XDJmI o¢m¢ n 021 10. 11. 133 LIST OF REFERENCES S.J.D. 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