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Growth and collapse of vapour bubbles in convective subcooled boiling of water Farajisarir, Davood 1993

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GROWTH AND COLLAPSE OF VAPOUR BUBBLES IN CONVECTIVESUBCOOLED BOILING OF WATERByDavood FarajisarirB.A.Sc. (Engineering) University of British Columbia, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESMECHANICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAPRIL 1993© Davood Farajisarir, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of  P9 ec^Pi CCGI^c>2e eThe University of British ColumbiaVancouver, CanadaDate  191pL2 30 /??3DE-6 (2/88)AbstractThe growth and collapse of vapour bubbles during convective subcooled nucleate boilingof water in an internally heated annular test section was visualized using the high speedfilming technique. The experiments were performed at atmospheric pressure, mean flowvelocities of 0.08- 0.8 m/s, liquid bulk subcooling of 10-60 °C and heat fluxes of 0.1-1.2MW/m2. High speed photographic results showed that bubbles grew to a maximum radiuswhile sliding on the heated surface; condensed slowly while still attached to the heatedsurface; and ejected into the flow with further condensation. The bubble volume,displacement of bubble centroid parallel and normal to the heating surface, and change inthe bubble maximum and minimum diameters were evaluated during the bubble lifetime.The effects of heat flux, liquid bulk subcooling and mean flow velocity on maximum bubbleradius, growth time, and condensation time were investigated. At low subcoolings, anincrease in the heat flux resulted in a decrease in the maximum bubble radius and growthtime. At high subcoolings, the maximum bubble radius and growth time were independentof the heat flux. The effect of mean flow velocity on bubble parameters was negligible inthe range of this study. Correlations are proposed for the maximum bubble radius, growthtime, condensation time, and growth and collapse rates.Table of ContentsAbstract^ iiList of Tables vList of Figures^ viNomenclature ixAcknowledgment^ xv1 Introduction 11.1 Void Fraction in Convective Subcooled Boiling^ 21.2 Research Background^ 31.3 Research Objectives 42 Literature Review 82.1 Inertia-Controlled Bubble Growth^ 92.2 Heat-Transfer-Controlled Bubble Growth 102.2.1 Bubble Growth in Uniform Temperature^ 102.2.2 Bubble Growth in Non-Uniform Temperature 132.3 Micro-Macro- Layer Evaporation^ 152.4 Bubble Condensation (Collapse) Models 162.5 Flow Visualization studies of Bubble Growth and collapse^ 183 Experimental Apparatus and Data Processing^ 283.1 Test Facility^ 283.2 Instrumentation 293.3 High-Speed Photography Setup^ 303.4 Procedure for Degassing 313.5 Experimental Conditions 323.6 Data processing^ 343.6.1 Digitizing Setup 343.6.2 Evaluation of bubble volume^ 353.6.3 Procedure for selecting an 'average bubble'^ 363.7 Error analysis^ 38iii4 Results and Discussion^ 574.1 Observations of Bubble Dynamics in Convective Subcooled Boiling^574.1.1 Bubble Growth and Collapse Curves^ 574.1.2 Bubble Shape^ 594.1.3 Parallel and Normal Displacements 604.2 Effect of Experimental Conditions on Bubble Parameters^ 614.2.1 Maximum Radius 614.2.2 Bubble Growth Time^ 644.2.3 Bubble Condensation Time 654.2.4 Effect of Subcooling on Bubble Parameters at V=0.08 m/s^674.3 Correlations^ 674.3.1 Normalized Bubble Growth and Collapse Curves^ 674.3.2 Correlations for Bubble Parameters^ 695 Conclusions and Recommendations 895.1 Conclusions^ 895.2 Recommendations 92Bibliography 93Appendices^ 98A Bubble Growth Model (Mikic[22])^ 98B Bubble Growth Model (Unal[28]) 101C Evaluation of Bubble Volume^ 106D Error Analysis^ 111E A Sample of Correlation Procedure^ 116ivList of Tables2.1 Flow visualization studies of vapor bubbles in convective subcooled boiling 222.2 Correlations for condensation rate and condensation time for injected bubblesinto uniformly subcooled liquid223.1 Range of experimental parameters 393.2 Estimated error for measured and calculated experimental parameters 393.3 Estimated error for measured quantities obtained from high-speed photography 394.1 Slip ratio of bubbles in different conditions 744.2 Comparison of experimental maximum bubble radius with predictions of 75Unal[28], Zuber[23], and Mikic et al.[24]4.3 Ratio of growth and condensation time to bubble lifetime 764.4 Comparison of condensation time with predictions of Akiyama[30] and 77Florschuetz et al.[31]4.5 Comparison of experimental maximum radii with literature 78VList of Figures1.1 Bubble behavior in subcooled nucleate boiling (a) Schematic diagram of bubblegrowth and collapse process (b) Typical bubble growth and collapse curve61.2 Void fraction, wall temperature and liquid bulk temperature along an internallyheated channel72.1 Schematic diagram of inertia-controlled bubble growth 232.2 Schematic diagram of heat-transfer-controlled bubble growth 232.3 Comparison of bubble growth models in uniformly superheated liquid 242.4 Comparison of bubble growth models in non-uniform temperature (Mikic et 24al.[24], Zuber[23], and Unal[28])2.5 Schematic diagram of bubble growth model proposed by Unal[28] 252.6 Comparison of bubble collapse models in uniformly subcooled liquid 25(Florschuetz and Chao[31], Akiyama[30], and Zuber[23])2.7 Comparison of condensation time predicted by Florschuetz and Chao[31] and 26Aldyama[30]2.8 Effect of mean flow velocity on bubble maximum diameter and growth time 27(from Akiyama[38])3.1 Schematic diagram and photograph of the test facility 403.2 Schematic diagram and photograph of the test section 413.3 Snap-shots of bubbles with a shutter speed of 1/4000 sec 423.4 Schematic diagram and photograph of high-speed filming setup 433.5 Filmed conditions for subcoolings of (a) 10°C (b) 20°C (c) 30°C (d) 40°C 44(e) 60 °C3.6 Schematic diagram and photograph of image processing system 47vi3.7 Magnified image of a bubble on the monitor^ 483.8 Definitions of bubble parameters^ 483.9 Steps in the evaluation of bubble volume 493.10 Photographs of digitization steps for evaluating bubble volume (a) Discretizing^50bubble (b) Scanning bubble outline (c) Determination of bubble projection areaand centroid (d) Evaluation of centroidal principal axis of bubble projectionarea (e) Evaluation of the volume of revolution of the areas on each side of theaxis of symmetry3.11 (a) Displacement of bubble centroid parallel and normal to the heated surface^53with respect to the nucleation site (b) Diameters along the centroidal principalaxes3.12 Photograph of frame analysis results displayed on the computer monitor^543.13 Distribution of bubble lifetime for conditions D21 and D22^ 553.14 Selection of an 'average' bubble for condition D24^ 564.1 Photographs of bubble growth and collapse (D24-10) for 11=0.4 m/s,^79A Tub =20° C and 4) =0.3 MW/m24.2 Growth and collapse curve for a typical bubble (D24-10)^ 804.3 Change in bubble shape during its lifetime^ 804.4 Comparison of bubble volume obtained in this study with the volume evaluated^81by spheroidal assumption4.5 Normal and parallel displacement of the centroid of bubble^ 814.6 Bubble path in different liquid bulk subcooling^ 824.7 Effect of heat flux and flow velocity on bubble maximum radius^824.8 Effect of heat flux and subcooling on the maximum bubble radius 834.9 Effect of heat flux and subcooling on bubble growth time^ 83VII4.10 Effect of heat flux and subcooling on bubble condensation time^844.11 Effect of subcooling on bubble parameters at V=0.08 m/s 844.12 Comparison of experimental growth and collapse rate with Zuber[23]^854.13 Correlation of bubble growth and collapse rates^ 854.14 Comparison of experimental bubble growth rate Equation (4.6) with^86Aldyama[38], Zuber[23], and Mikic et al.[24], and Unal[28].4.15 Comparison of experimental condensation rate Equation (4.6) with^86Akiyama[30], Zuber[23], and Florschuetz and Chao[31]4.16 Comparison of experimental condensation rate at low subcooling with^87condensation models of Florschuetz and Chao[31] and Akiyama[30]4.17 Correlation of maximum radius with Ja: and 0^ 874.18 Correlation of growth time with Jaw* and 0^ 884.19 Correlation of condensation time with Ja and the non-dimensional maximum^88radius (R,)B.1 Schematic diagram of bubble growth model proposed by Unal[28]^103C.1 Nomenclature used in pixel integration^ 107C.2 Schematic diagram of the centroidal principal axes of the bubble^107C.3 Nomenclature used in evaluating the volume of revolution 108D.1 Repeatability of bubble volume and radius measurements^ 112D.2 Repeatability of normal and parallel displacement measurements^112D.3 Repeatability of measurements of diameters normal and parallel to centroidal^113principal axis of bubbleviiiNomenclatureA^parameter defined in Equation (2.13)B^parameter defined in Equation (2.13)C,^thermal conductivity of heater material (J/kg °C)Cp,^specific heat of liquid (J/kg °C)c^coefficient defmed in Equation (4.14)D instantaneous diameter (m)Dd^diameter of dry area under the bubble (m)Ph^hydraulic diameter (m)Dn^diameter along the centroidal principal axis normal to heater surface (m)Dp^diameter along the centroidal principal axis parallel to heater surface (m)DF^bubble flatness,Dna,tFo^Fourier number, 2RialtcFoc^condensation Fourier number, 2Rig^acceleration of gravity (9.81 mls2)H thermal boundary layer thickness defined in Equation (4.2)ifs^latent heat of vaporization (J/kg)km^convective heat transfer coefficient (W/m2K)kb^convective heat transfer from bubble surface (W/m2K)()ICJa^Jacob number based on liquid subcoohng, PIATsubPlitt,ix-PIC 7' LI)Jacob number based on liquid superheat, ^'1( - pvhfg.13/C T - Tsat)Jacob number based on wall superheat,  P1(pvhfgK^constant defined in Equation (4.4)ki^thermal conductivity of liquid (W/m °C)lc^thermal conductivity of heater material (Wim °C)Lb^normal displacement of bubble centroid w.r.t the nucleation site (m)L1, ^displacement of bubble centroid w.r.t the nucleation site (m)/^location of the filming measured from upstream end of the heater (m)tit^mass flow rate (kg/s)N^constant defined in Equation (4.4)lc,ONB^onset of nucleate boilingOSV^onset of significant voidP^heated perimeter (m)P^ambient pressure (atm)Pv^vapor pressure inside the bubbleP.,^pressure far away from the bubblePIVDhCp1 Pe^Peclet number,2RiVbPeb^bubble Peclet number,aiPrp•IC',Prandtl number, kiJa*Jaw*konDbNu^Nusselt number,k1xAPqqbRRoRtRmR:,ko,RabReRebSt 0,riTTBTinTvTs.TivPv- P—heat flux (kW/m2)heat flux to bubble from the micro-layer (W/m2)instantaneous bubble radius (m)initial radius of cavity (m)bubble growth or condensation rate (m/s)bubble break-off radius (m)maximum bubble radiusnon-dimensional maximum radius defined by Equation (4.9)cavity radiusg( Pi - Pv )4R/2  prbubble Rayleigh number,p1 VDh Reynolds number,A 12piVbRibubble Reynolds number, (1)0sv Stanton number at OSV,p/VCpiAT,,,d,radial distance to the spherical element (m)velocity of the spherical liquid element (m/s)temperature (°C)bulk liquid temperature (°C)inlet temperature (°C)temperature of vapor inside the bubble (°C)saturation temperature (°C)wall temperature (°C)piv 1211,xisuperheated liquid temperature (°C)AT^liquid superheat, T - T (°C)6.7;v^wall superheat, Tv - T (°C)liquid bulk subcooling, T - TB (°C)timetb^bubble lifetime (s)bubble condensation time (s)bubble detachment (ejection) time (s)tm^bubble growth time (s)tw^waiting time (s)t:^non-dimensional bubble condensation time defined by Equation (4.16)t,:,^non-dimensional bubble growth time defined by Equation (4.11)V^mean flow velocity (miS)Vb^bubble velocity (m/s)Veic^bubble ejection velocity (m/s)Vol^measured bubble volume (m3)Vol^Maximum bubble volume (m3)vv^specific volume of liquid (m3 /kg)specific volume of vapor (m3 /kg)coefficient defined in Equation (4.14)normal distance above the heater surface (m)R/R7ncoefficient defined in Equation (4.14)Greek lettersal^thermal diffiusivity of liquid (m2/s)xii(3 non-dimensional bubble radius, —RRIparameter defined in Equation (2.25)sphericity correction factorheat flux (MW/m2)heat flux from the interface to bulk liquid defined in Equation (2.14)gamma functionliquid viscosity (Ns/m2)non-dimensional temperature defined by Equation (4.8)liquid density (kg/m3)density of heater material (kg/m3)density of vapor at saturation (kg/m3)PI Pvnon-dimensional density - ^,defined in Equation (2.25)P1al^liquid surface tension (N/m)SubscriptsB^bulkb^bubblec^condensationcav^cavitycon^convectived^dry areaejc^ejectionh^hydraulicin^inlet1^liquidm^at the end of growth stagemax^maximumn normalp^parallels^solidsat^saturationsub^subcoolingW^waitingw^wallo initialoo^far awaySuperscripts+ non-dimensional quantity* non-dimensional quantity• rate of changexivAcknowledgmentI would like to thank my supervisor, Dr. Martha Sakudean, for her continued support andtrust through all stages of this work. I would also like to thank Dr. Yacov Barnea for hissuggestions and contributions during the analysis of data and thesis write-up and EricBibeau for his generous help during high-speed filming. Technical advice of Don Bysouthin digital image processing and Ed Abell and Tony Besic during various stages of theexperimental setup is greatly appreciated. I also wish to thank my family and friends fortheir support, especially Glenn Stefurak and Zenebe Gete for their continousencouragement and Penny Syroid for her love and understanding during this rewardingexperience.XVCHAPTER 1INTRODUCTIONThe phenomenon of convective subcooled boiling is important in the design ofnuclear reactors which use a liquid coolant that is subjected to high heat fluxes. In some ofthese reactors, the surface boiling is designed into the system or allowed to occur at highloads to increase heat transfer whereas in others the surface boiling is avoided in normaloperation but may be allowed only under emergency and transient conditions. The effect ofvoidl formation on the reactivity of the system is described by the void coefficient ofreactivity. Depending on the design of the reactor and its moderator-to-fuel ratio, a reactorcan have a positive or a negative void coefficient of reactivity[1]. In a reactor with anegative void coefficient, an increase in the amount of void in the system results in adecrease in the reactivity of the system.SLOWPOKE and MAPLE low-pressure, pool-type nuclear reactors, designed byAECL, belong to a class of reactors with negative coefficient of reactivity[2]. The poweroutput of these reactors depends on the density of the moderator (water) which is afunction of the volume fraction of the vapour in the flow, expressed as void fraction. Thesereactors are so designed that, in case of emergencies when the probability of powerexcursions is high, surface boiling occurs along the fuel rod and the increased void fractionin the moderator causes a decrease in reactivity. In this way the power output of thereactor is controlled to safe levels. Therefore, the evaluation of the volume of steam,1 In nuclear industry, vapor generated during the process of surface boiling is termed as'void'.12produced during the process of subcooled flow boiling, is critical for operation of water-moderated low pressure nuclear reactors.Evaluation of the void fraction has been the subject of many studies in the high-pressure range of operation of commercial nuclear-powered reactors. The development oflow-pressure nuclear reactors motivated the study of void fraction at atmospheric pressure.Void fraction experiments conducted at low pressure have revealed differences in themechanism of void formation between high and atmospheric pressures. This study is part ofan extensive project undertaken at the University of British Columbia in collaboration withAtomic Energy Canada Limited, to study the void growth at atmospheric pressure. Thisthesis presents the results of flow visualization experiments of vapour bubbles generated inthe process of subcooled boiling at atmospheric pressure. The flow visualizationexperiments were carried out to obtain insight on the mechanisms of void growth atatmospheric pressure.1.1 Void Fraction in Convective Subcooled BoilingSubcooled boiling is characterized by the growth of vapour bubbles at a heated solidsurface and their subsequent condensation or collapse inside the subcooled liquid. Thesebubbles originate at cavities, pits and scratches on the heater surface where vapour or non-condensable gases are trapped. When the temperature at the liquid-solid interface exceedsthe saturation temperature by a few degrees, nucleation sites become active and boilingcommences. An active nucleation site produces vapour bubbles which go through a typicalperiodic cycle of nucleation, growth, departure and collapse (condensation) followed by awaiting period (Figure 1.1). This cycle, repeated hundreds of time in a second, and athundreds of different locations on the heater rod, results in a two-phase mixture of liquidand vapour.3Figure 1.2 shows schematically the process of subcooled flow boiling and voidgrowth in a vertically mounted annular channel with internal heating used in this study. Thesingle-phase subcooled liquid enters the test section and flows upward parallel to theheater. At some distance downstream where the wall temperature exceeds the saturationtemperature by a few degrees, the nucleation sites on the heater become active and bubblesform on the heater. This point is referred to as ONB or Onset of Nucleate Boiling andsignifies the first appearance of the vapour bubbles. As the liquid flows past ONB andmoves further downstream, the amount of vapour in the mixture increases. The volumefraction of the vapour in the flow is termed 'void fraction' which is defined as the ratio ofarea occupied by vapour over the total cross-sectional flow area. The void fractionincreases in the direction of the flow up to the point of OSV (Onset of Significant Void)which signifies a sudden increase in the void fraction. The point of OSV indicates thecondition at which the amount of void increases exponentially and its prediction is criticalto the modeling of void growth. The void fraction in the system is dependent on theaverage bubble size, average bubble lifetime, growth rate and condensation rate of bubbles,number of nucleation sites, and the frequency of bubble formation. These parameters, inturn, are dependent on experimental conditions such as heat flux, pressure, mass flow rateand liquid subcooling.1.3 Research BackgroundThe project originated at the University of Ottawa with the measurement of voidfraction using the Gamma ray attenuation method. Void fraction measurements, conductedin an annular test section with internal heating at atmospheric pressure and low flow ratesimulated the flow geometry and conditions in the SLOWPOKE reactors [3,4,5]. Theexperimental data were compared to various void fraction models derived from high-pressure experiments without satisfactory results[4]. Further experiments were performed4at the University of British Columbia for different hydraulic diameters of the test section forupflow and downflow [6,7,8]. It was concluded that the discrepancies between themeasured results and those calculated from the existing models were probably because ofthe differences in the hydrodynamics and heat transfer mechanisms at low pressure:• At low pressure the bubble detachment did not coincide with OSV.• The void prior to OSV was not negligible.The research continued at the University of British Columbia in the modeling of voidfraction at low pressure[9]. A model was proposed to 'account' for all the bubbles that aregenerated and condensed in the flow. The present work, carried out as a complement to the'bubble accounting model', evaluates the characteristic bubble parameters employed in themodel. Moreover, in void growth models, a correlation for the generation andcondensation rate of vapour is required[4,10,11,12]. Usually these terms are approximatedwithout a physical basis. Nevertheless, a constant need exists to express the generation andcondensation terms for vapour in terms of basic bubble parameters. This study alsoevaluates the growth and condensation rates for bubbles generated and condensed duringthe process of subcooled flow boiling at atmospheric pressure.1.4 Research Objectives• Flow visualization using high speed photography of vapour bubbles generated on aheated surface for different flow conditions. The mass flow rate, inlet subcooling andheat flux would be changed systematically so that the effect of each parameter on thebubble growth and collapse could be investigated.5• Design an efficient method for analyzing images of the bubbles with the aid of acomputer.• Quantify the effect of experimental conditions on the maximum bubble size, growthtime, condensation time, and growth and collapse rates.• Investigate the applicability of available models of bubble growth and collapse to thepresent research.(b)Figure 1.1. Bubble behavior in subcooled nucleate boiling (a) Schematic diagram of bubblegrowth and collapse process (b) Typical bubble growth and collapse curve.7FLOWFigure 1.2. Void fraction, wall temperature, and liquid bulk temperature along an internallyheated channel.CHAPTER 2LITERATURE REVIEWThe augmentation of heat transfer to the liquid during subcooled boiling is attributedto the processes of growth and collapse of bubbles during which the adjacent liquid isviolently agitated and latent heat of vaporization is transferred to the liquid[13].Ascertaining the relative importance of these two heat transfer mechanisms, requires aknowledge of the heat transfer during growth and condensation of a bubble. This has ledto the development of mathematical models and experimental investigations of bubblegrowth and collapse rates in subcoolecl and superheated liquids.The growth of a bubble is defined as the macroscopic (visible) expansion of thebubble boundary on the heater surface beyond the boundary of the cavity. Research on themechanism and physics of bubble growth has led to three points of view[14,15]:• Inertia-controlled growth;• Growth due to heat transfer at the liquid-vapour interface on the bubble surface;• Growth by micro/macro-layer evaporation at the bubble base.The driving force for bubble growth in an inertia-controlled process is the pressuredifference between the inside and outside of the bubble. In heat-transfer-controlledgrowth, the growth is due to the evaporation of liquid at the liquid-vapour interface onbubble surface, whereas in micro/macro- layer evaporation theory, the evaporation fromthe thin liquid formed at the bubble base is considered to account for all the vapour insidethe bubble.89The following methods are reported in the literature for studying bubble growth andcollapse rates[161:1. Injection of saturated vapour in uniformly superheated or subcooled liquid;2. Local heating of a surface by laser beam or electric pulse;3. Nucleation from prepared sites;4. Nucleation from a random site during actual boiling.The study of bubble growth and collapse is facilitated by the use of the first three methodssince the complexity of the nucleation process is avoided and interaction betweennucleation sites is eliminated. In the present study, the bubble growth and collapse isstudied from a random nucleation site during actual subcooled boiling.This chapter reviews the different bubble growth mechanisms, presents flowvisualization experiments of bubble growth and collapse in flow boiling, and outlines theexperimental correlations for the condensation of bubbles injected into the subcooledliquid.2.1 Inertia-Controlled Bubble GrowthIn an inertia-controlled bubble growth process, a vapour bubble in a uniformlysuperheated liquid is idealized as a sphere expanding from an initial radius Ro to R in aninfinite, incompressible, non-viscous liquid with constant excess pressure. Theconservation of mechanical energy with these assumptions yields the followingequation [17] :—1pi Orr- 2 dr =^(R3 - 1?;3)42 R^3(2.1)where Ap =^P- • This equation, combined with the continuity requirement/^\ 2wiz) = ( ), results in the inertia-controlled bubble growth equation known as theRayleigh's equation:Rk + lie . AP2^P1A solution to (2.2) is approximated by the following[15]:lAr, )6R(=-) tThe vapour inside the bubble is assumed to be at the saturated state corresponding to thetemperature of superheated liquid (Figure 2.1). As long as this assumption holds, thevapour pressure inside the bubble will exceed the ambient pressure and cause the bubbleboundary to expand outward. The pressure difference in Equation (2.3) is approximatedwith the Clausius-Clayperon equation:AP ^i18AT Tfat(vv — v1)where AT = T., - T.. Applying this approximation in Equation (2.3) yields:2^p2h 2 )MR a (^*— .1a , v -fg^t3^p7CpIT.,, piC /ATwhere fa - P^.Pvifg2.2 Heat-Transfer-Controlled Bubble Growth2.2.1 Bubble Growth in Uniform TemperatureIn heat-transfer-controlled growth it is assumed that the growth of the bubble occursdue to the evaporation at the liquid-vapour interface at the bubble surface on account ofheat supplied from the superheated liquid by conduction through the boundary layer. Inthis case the temperature of the vapour inside the bubble is assumed to be at the saturation10(2.2)(2.3)3pi(2.4)(2.5)11temperature corresponding to the ambient pressure (Figure 2.2). A simple energy balanceat the interface (x = 0) of a spherical bubble yields:pvifgR= k1(-Tox toThe temperature gradient at the interface is approximated by the one-dimensional transientheat conduction formulation for a homogeneous semi-infinite body with a plane boundary,i.e.:1 OT -02T- al at ax 2 (2.7)with initial and boundary conditions:t = 0:T(x,0)= T.,t > 0:T(0,t)=t > 0:T(00,0= T.The solution of (2.7) combined with the energy balance (2.6) results in an expression forthe bubble growth rate for the heat-transfer-controlled mode known as the Bosnjakovicequation::,^T., - Ts.pvizeK - ktIntegrating (2.8) along a time period t, the bubble radius is expressed as [18]:R = 2 _.,ffr ja. v.73rit _ 2 frr ( pipc,pii:T)j,--v7Plesset and Zwick[19] and Forster and Zuber[20] extended Rayleigh's equation(2.2) to account for both the inertia- and heat-transfer-controlled growth as well as thesurface tension effect which were ignored both in (2.2) and (2.6):(2.6)170:3Eit(2.8)(2.9)Pr(Rii÷ lie) = (Pv(n - Po.) - 262^R(2.10)12where pv(T) is the pressure inside the bubble and pa, is the pressure of the liquidsurrounding the bubble. The momentum equation is therefore coupled to the energyequation through the vapour temperature. To obtain a solution, the Clausius-Clapeyronequation was used to relate the pressure difference to the temperature difference. Atransient heat conduction equation with a moving spherical boundary was used to evaluatethe temperature of the interface[20,21]. The asymptotic solution, valid at large values ofradius, was obtained by assuming that the bubble wall temperature falls rapidly to thesaturation temperature. This drop in temperature from superheated to saturation isassumed to occur in a "thin boundary layer" near the bubble wall. The solution of (2.10)was given for the heat transfer-controlled growth as follows:R ir7 Ja^(Forster - Zuber)^(2.11)R (12,/)2 ja*^(Plesset -Zwick) (2.12)The different constants in Equations (2.11) and (2.12) are due to different mathematicalschemes used to evaluate the temperature of the interface. These solutions are the same as(2.9) except for the value of the constants mainly because the spherical boundarycondition was used in the evaluation of the bubble wall temperature. The larger values ofthe constant in (2.11) and (2.12) compared to (2.9) implies that the effect of curvature isto increase the rate of bubble growth.In a different approach, Mikic et al.[22] derived a non-dimensional relation that wasapplicable in the whole range of inertia-controlled to heat transfer-controlled growth:R+ = —2[(t+ +^(t+) -1]3(2.13)where13The definitions of A and B are given in Appendix A with the derivation of (2.13). Thisrelation reduces to (2.3) for t+ < < 1 and to (2.12) for t+ >> 1.Figure 2.3 compares the growth rates obtained from Equations (2.5), (2.9), (2.11),(2.12), and (2.13). The growth rate predicted by the inertia-controlled growth model issubstantially higher than the predictions of the heat-transfer-controlled models for thesame Ja* . The growth rates predicted by Mikic et al.[221, Forster and Zuber[20], andPlesset and Zwick[21] are in good agreement with each other whereas the Bosnjakovicsolution predicts substantially lower growth rate.2.2.2 Bubble Growth in Non-Uniform TemperatureThe models mentioned above were based on the assumption that the growth of avapour bubble occurs in a stagnant uniform superheated liquid. However, the actualprocess of subcooled boiling involves a temperature gradient at the vicinity of the wall sothat the liquid near the wall is superheated which decreases in temperature to thesubcooled temperature in the core. None of the above models predict the maximumdiameter reached in subcooled boiling. However, they are a basis for more complicatedmodels that consider non-uniform temperature fields and predict the maximum bubbleradius. The common feature of models for non-uniform temperature fields is that thecontrolling factor is the heat transfer at the interface rather than the liquid inertia andsurface tension.Zuber[23] expressed the non-uniformity in the liquid temperature by including anadditional term, st to account for the heat transfer from the vapour interface to the bulkliquid in Equation (2.8):T.- TuiPviff = c-44 vnalt(2.14)where e =7r/2 is a correction factor for the sphericity of the bubble. Zuber assumed that theadditional heat flux term was approximately the same as the wall heat flux since the14temperature gradient between the vapour phase and liquid was equal to the temperaturegradient which existed between the solid and liquid immediately before nucleation. Zuberobtained a non-dimensional relation for bubble radius by integrating (2.14) andnormalizing with the maximum radius:R . 1-112 _. ^IT)VtmL IF: )The maximum radius, R., and growth time,t., are given by:R. - Picp,(T. - Tat)^1 .nalt„, = — Ja. 7.17O—it,„^2 pvifs, 2where,- k^l(T"' - T )^ilrclt  ^'at .q(2.15)(2.16)(2.17)where q is the wall heat flux.Mikic and Rohsenow[24] expressed the temperature non-uniformity in the liquid asa function of the waiting time, tw, and themiophysical properties of the liquid. Mildc et al.used one-dimensional transient conduction equation to evaluate the bubble walltemperature and the sphericity of the bubble was taken into account by the use of acorrection factor (e = IS):I  Tv - Tsat  _  T - Tb   1I Fror^vii' Vaal(t + tw)The waiting time, tw, was expressed in terms of the growth time by observing that att = t., R = 0. The bubble radius is formulated in a non-dimensional form:m1- -' ' Ii_ e{(1+(e2 -1)1s) - (032 -1).t-,r}}R^(tn.^-^t^rk, 1- e(13 - (62-1)1The maximum radius is:(2.19)pvizei?= eki (2.18)152^.Rai= “Rif—t,t,„11 - e[e - (02 - 1)4])7r(2.20)T T^pIC 1(T. T m)where e - ^- b represents the degree of subcooling and Ja.-^- P^$ .T.- Tat PvlfgFigure 2.4 compares the growth and collapse rates obtained from (2.15) and (2.19)for different values of subcooling. The models agree well for bubble growth, however,Mildc's model results in smaller collapse rates than Zuber's model for 0 < 4.5. For highervalues of 0 (indicating higher degree of subcooling) both theories predict similar collapserates. In Mikic's model the growth rate is insensitive to the change in the degree ofsubcooling.2.3 Micro-Macro Layer EvaporationOther researchers[25-29], assumed that most of the evaporation during bubblegrowth occurs at the bubble base between the vapour-liquid interface and the heatersurface where a very thin liquid is formed. The evaporation from the bubble surface due toconduction from the superheated liquid is assumed to contribute little to bubble growthsince the thickness of the superheated layer was found to be much smaller than that of themaximum radius attained by the bubble[26]. Unal[28] applied this model to bubble growthduring the process of convective subcooled boiling. It was assumed that a spherical bubblegrows on the wall by the evaporation of liquid into vapour at the dried patch whiledissipating heat by condensation to the surrounding liquid at its upper half (Figure 2.5).The following heat balance equation is presented by Unal:702 ^D2,^A^702 it . dD3qb^—^= ricbuisub ^ (2.21)4^D2 2 6 ” dtwhere qb is the heat flux to the bubble from the very thin liquid film under it, and kbis theheat transfer coefficient for condensation at the surface of the bubble. The final expressionfor the bubble radius is cast into a non-dimensional form:161+0 228 Ill•^t„1-i- = 1.368(1-R.,^t„, ) 1 + 0.685X.(2.22)The derivation and solution for the maximum radius and growth time for this model aregiven in Appendix B.In Figure 2.4, Unal's model is compared with Equations (2.15) and (2.19). Unarsmodel predicts lower growth rates and unlike the other two models, fails to predict amaximum radius.2.4 Bubble Condensation (Collapse) ModelsThe collapse or condensation of a bubble is defined as the decrease in the size of thebubble from its maximum size at the end of the growth stage to undetectable microscopicsize. Similar to the growth stage, the bubble collapse is categorized into the inertia-controlled and the heat-transfer-controlled modes.Akiyama[30] solved the extended Rayleigh's Equation (2.10) for the condensationof a spherical bubble in stagnant, uniform subcoolal liquid with the initial condition oft = 0: R = Rni , i? = 0. For an inertia-controlled process, the condensation rate was given interms of the Gamma function:where y = 7R. andt _3 r(4)t,^r(i)r(+) i (1 _ y3)X"-YIT I' (i)r(4-) t -`^6•5 r(4)g ^ifgAT,,,„6 -4.186R, 7",,,, (v, - vi)pspi(2.23)(2.24)(2.25)Zuber[23] solved Rayleigh's equation (2.2) for the condensation of a spherical bubble insubcooled liquid and reached a similar result:17(2.26)Analysis of the heat-transfer-controlled condensation process was given byFlorschuetz and Chao[31] by solving (2.10) for the heat transfer controlled bubblecollapse and by Voloshko and Vurgaft[32] using Bosnjakovic's simpler analysis. Thecondensation rate is given as follows:whereR =1- (—TR.^t,7r-4a/ Ja2•(2.27)(2.28)Figure 2.6 compares the condensation rates obtained by (2.23), (2.26) and (2.27).Akiyama's and Zuber's equations compare well with each other as expected; however, theydiffer drastically from the heat-transfer-controlled models of Florschuetz et al. andVoloshko et al.. In heat-transfer-controlled collapse the condensation rate is rapid at thebeginning and slows at the end of condensation process whereas in the inertia-controlledmodel, the condensation rate is initially slow and substantially faster at the end.The condensation time predicted by Akiyama[30] and Florschuetz and Chao[31] areshown in Figure 2.7 as a function of subcooling for different maximum radii. Thepredictions by Florschuetz et al. were at least one order of magnitude higher than those ofAkiyama at low subcoolings but matched Akiyama's values at higher subcoolings (60 °C)for small values of maximum radii.182.5 Flow Visualization Studies of Bubble Growth and CollapseThe survey of experimental studies on bubble growth and collapse showed that veryfew of the flow visualization experiments were performed to visualize bubble dynamicsduring void growth experiments. Unal[33] and Shoukri et al.[34] used a high speedfilming technique to study the effect of different flow conditions on the bubble populationin void growth experiments. Aside from these studies, other researchers concentrated onvisualization of bubble dynamics and behavior which led to burnout condition orenhancement of heat transfer. Most of the experiments on convective boiling wereperformed at higher velocities and heat fluxes.Table 2-1 summarizes flow visualization studies of vapour bubbles duringconvective subcooled boiling of water with the high speed filming technique. In a pioneerstudy, Gunther[35] studied the influence of heat flux, liquid subcooling, and mass flowrate on bubble size, lifetime and population during convective subcooled boiling. The testsection consisted of a 0.10 mm metal strip suspended lengthwise inside a verticaltransparent channel of rectangular cross-section. The metal strip divided the channel intotwo flow passages and boiling occurred on both sides of the metal strip. The experimentswere done at higher flow velocities and heat flux than those used in the present study. Thesurface boiling activity in these experiments, consisted of small hemispherical vapourbubbles which grew and collapsed (while still attached to the heating surface) slidingdownstream under the influence of the coolant flow. At high heat fluxes, the bubblepopulation increased to the limit at which bubbles coalesced to form vapour clumps on theheated surface. The effect of increasing heat flux, subcooling and mass flow rate was todecrease the maximum bubble size and the average bubble lifetime. For instance, bubblesize and lifetime decreased by 40% with an increase of heat flux from ONB (2.4 wh2) tothe burnout condition (10.4147.2) at flow velocity of 3 m/s and subcooling of 85 °C. Atnear burnout condition, the bubble frequency was estimated at 1000 bubbles per second19for subcooling of 85 °C. No correlations were given to generalize the findings to lowerflow velocities and heat flux.Tolubinsky and Kostanchuk[39] investigated the effect of subcooling and pressureon maximum bubble size and frequency of bubble formation at low flow rates. The testsection was made of an electrically heated stainless steel plate 0.25 mm thick positionedinside a horizontal channel with rectangular cross-section. Bubble frequency and sizedecreased with increasing subcooling and pressure. Bubble size and lifetime wereindependent of heat flux, in contradiction of Gunther's results. The frequency of bubbleformation was reported to be 100 bubbles/second for subcooling of 5 °C and 400bubbles/second for subcooling of 60 °C at flow velocity of 0.2 m/s and atmosphericpressure. The effect of flow velocity was not reported.Abdelmessih et al.[36] studied the effect of flow velocity on the growth and collapseof bubbles in slightly subcooled water (2 °C) during surface boiling. The test sectionconsisted of an electrically heated stainless steel strip, 0.15 mm thick insulated on itsundersurface, and was positioned concentrically inside a vertical channel of circularcrossection. An artificial nucleation site was constructed by making a depression of 0.18mm in diameter on the heated surface. The bubbles slid on the heater surface whilechanging shape and detached from the surface with a shape of an inverted pear. Anincrease in the flow velocity resulted in a decrease in bubble lifetime and average bubbleradius. However, increasing the heat flux resulted in an increase in bubble size andlifetime, in contradiction of the result of Gunther[35] and Tolubinsky and Kostanchuk[39]Akiyama and Tachibana[38] investigated the effect of flow velocity and subcoolingon the maximum bubble size, lifetime and growth time in an annular channel similar to thatof the present study for a wide range of flow rates and subcoolings. The circular heatedsection was made of stainless steel of 0.2 nun thickness. The hydraulic diameter of the testsection was twice the one used in the present study. It was concluded that the effect offorced convection was important only at velocities higher than 0.3 m/s (see Figure 2.8).20Moreover, the distribution of the liquid temperature normal to the heating surface wasinvestigated. The temperature gradient in the thermal boundary layer was controlled by themass flow rate and was independent of the heat flux. The thickness of the superheatedlayer was estimated to be smaller than 0.2 mm for flow velocity range of 0.1 -5 m/s. Theeffect of the heat flux on bubble parameters was not described in this study.Del Valle and Kenning[37] investigated the bubble size, lifetime, frequency and thepattern of the interaction of nucleation sites at constant flow velocity of 1.7 mls andsubcooling of 84 °C for high heat fluxes. The test section consisted of an electricallyheated stainless steel plate, 0.08 mm thick, set into one side of a vertical flow channel ofrectangular cross-section. The surface boiling activity, unlike in Gunthers' observations,consisted of bubbles growing and collapsing at their nucleation sites without sliding on theheated wall. At higher heat flux, activation of nucleation sites became irregular and manysites were observed to become inactive, although some sites were reactivated with furtherincrease in heat flux. The waiting time was estimated to be 0.9-2.9 ins and the maximumradius was found to be normally distributed. Maximum bubble size and bubble lifetimewere independent of heat flux confirming the results of Tolubinsky and Kostanchuk[39].Other researchers[16, 40-44] studied only the bubble condensation by injectingbubbles inside stagnant subcooled liquid. Table 22 presents the experimental correlationsgiven by these experiments for condensation rate and time of bubbles after detachmentfrom the orifice. The initial bubble radius in these experiments is much larger than thatencountered in the actual process of subcooled boiling.Apparently, the experimental observations of bubble behavior and the effect of flowconditions on bubble parameters differ from study to study. However, researchers haveshown that surface boiling is a local effect and is dependent on many parameters e.g., heatflux, liquid subcooling, pressure, surface quality, thermal boundary layer thickness,interaction between the nucleation sites, and the amount of dissolved air in the system.Moreover, surface boiling is a statistical process in which the bubble lifetime and bubble21sizes are statistically distributed. These complexities of the boiling process necessitatemore investigations on the effect of different experimental conditions on bubbleparameters.22Table 2.1 Flow visualization studies of vapour bubbles in subcooled flow boiling.InvestigatorChannelGeometry p(atm) 4)(mw/.2) V(%)Gunther[35] rectangular 1.7 2.3 - 10.7 1.5 - 6.1 33 - 110Tolubinsky[39] rectangular 1-10 0.05 - 1.0 0.08 - 0.2 5 - 60Del Valle et al.[37] rectangular 1 3.44 - 4.67 1.7 84Abdelmessih et al.[36] cylindrical 1 0.19 - 0.46 0.92 - 2.30 1.9Akiyamap8] annular 1 0.1-0.8 0.1 -5 20-80Unal[28] annular 1 -177 0.47- 10.64 0.08 - 9.15 3-86 Present Investigation annular 1 0.1 -1.2 0.08 - 0.80 10 - 60Table 2.2 Correlations for condensation rate and time for injected bubbles into uniformlysubcooled liauid.Investigator p(atm) ATsub (° C) R, (mm) Condensation time Condensation rateBrucker et al.[44] 10.3-62.1 15-100 1.5 Fo, = 55.5 Ja-314 Rai,-'Mayingeret al.[16] / I <Ja <120 2 Fo, = 1.784Re," Pr' Ja-w 0 = (1- 0.56Reb°3 Pr" JaFo)"Simpson et al.[43] 1 -2 5-36.6 4 Fo, = 0 .263Ja' Pe„" 0 = (1- 4.35 Ja" Pebus Fou)161Kamei et al.[40,41] 1 -10 10-70 5 Fo, = 55.5 Ja-31 4 Rab-112Voloshko et al.[32] 1 40 <Ja< 75 5 - 12.5 Foc = 5.90 x 10-3 0 = 1- L694 x104FoP.T. . Tsat + PTTp ( T. ) > p.Figure 2.1. Schematic diagram of inertia-controlled bubble growth.P.,^TT > TCo^vFigure 2.2. Schematic diagram of heat-transfer-controlled bubble growth.23,Rayleigh(Eq.2.5)Ja*-27.7‘\/^ Ja.-83.1a -83.1/^,•-- -.-27.7I/1.21.00.8cr 0.60.40.20.0ZuberMikic (0-1.5) _Mikic (0-2.5) -Mikic (0-3.5) -Mikic (0-4.5) -00^2.0^4.0^6.0^8.0^10.0Time (ms)Figure 2.3. Comparison of bubble growth models in uniformly superheated liquid- — - — -Plesset and Zwick[19], ^ Mikic et al.[22], — Bosnjakovic(Equation 2.9), ^ Forster and Zuber[20] and Rayleigh (Equation 2.5).2400^1.0^2.0^3.0^4.0^50t I tmFigure 2.4. Comparison of bubble growth models in non-uniform temperature (Mikic etal.[24], Zuber[23] and Unal[28]).1.00.80.40.20.01.000.00 0.25 0.50 0.75t/^Thin liquid filmSuperheated liquidlayerDry patch ( Dd )Figure 2.5. Schematic diagram of bubble growth model proposed by Unal[28].25Figure 2.6. Comparison of bubble collapse models in uniformly subcooled liquid(Florschuetz and Chao[31], Akiyama[30], Zuber[23]).0.400.300.200.100.002610^20^30^40^50^60^70^80^90^100Subcooling (° C)Figure 2.7. Comparison of condensation time predicated by Florschuetz and Chao[31] andAkiyama[30].4.02 00.)1.0a)0.4.9^0.20.1270.1^0.3^5Mean flow velocity (m/s)4.02.01.00.40.20.1^0.3^1^5Mean flow velocity (m/s)Figure 2.8. Effect of mean flow velocity on bubble maximum diameter and growth time(from Aldyama[38]).CHAPTER 3EXPERIMENTAL APPARATUS AND DATA PROCESSINGThe flow visualization experiments were performed on the test facility designed atthe University of British Columbia to simulate the thermohydraulic conditions ofSLOWPOKE reactors and used previously for void fraction measurements by Bibeau[6].This chapter describes the facility and the procedure followed prior to filming, discussesthe choice of the experimental conditions under which the films were taken, and elaborateson the flow visualization setup and image processing system for bubble analysis.3.1 Test FacilityFigure 3.1 is a schematic diagram of the test facility. The test section, where theboiling occurred, was located in series with a pump, a condenser, an immersion heater,and flow meters. A 3 H.P. centrifugal pump was used to circulate distilled water throughthe loop and the flow through the test section was adjusted by a by-pass line locateddownstream of the pump. The temperature of the loop was controlled by a 4.5 kWimmersion heater. The flow entered at the bottom of the test section at a presettemperature and flow rate and exited to the condenser at the top of the test section whereall the vapour was condensed. An additional heat exchanger mounted before the mainpump facilitated the cooling of the flow for lower inlet temperature. The distilled water2829was produced by the use of a distiller and collected for later use inside a clean, sealed 100-gallon polyethylene tank.The test section consisted of a hollow stainless steel tube (type 316) , 2.1 mm thick,with outside diameter of 12.7 mm and 480 mm long heating length. The stainless steel tubewas located concentrically inside a bigger glass tube of inside diameter of 21.8 mmforming an annular flow area (Figure 3.2). Both ends of the stainless steel tube (heater)were welded to hollow copper tubes of the same outside diameter (heater assembly). Theheater assembly was vertically mounted on a four-legged support where it was connectedto the rest of the loop via copper piping. The test section was heated by large amounts ofcurrent (up to 2000 amperes) passed through the stainless tube with the use of a 64 kVAa.c. adjustable power supply. The current was carried from the power supply to the testsection by copper bars attached to copper tubes at the ends of the heater at the top and thebottom of the support frame.3.2 InstrumentationThe average inlet temperature was measured at the bottom plenum while theaverage outlet temperature was measured at one meter downstream of the outlet plenumto avoid vapour patches. The thermocouples used were ungrounded, shielded, K-typethermocouples.The heater wall temperature was measured at the location of filming (440 mm fromthe upstream end of the stainless steel heater) with an ungrounded K-type thermocouplespot welded to the heater surface. The thermocouple wires were 0.102 mm in diameter, ina 0.508 mm diameter stainless steel sheath. The heater assembly and thermocoupleattachments were fabricated and designed by Atomic Energy Canada Limited.30Two turbine flow meters each with a different sensitivity (0.006-0.6 kg/s) measuredthe mean flow rate in the test section. The frequency output of the flow meters wereconverted to d.c. voltage using a frequency-to-voltage converter. The current wasmeasured with an induction coil which generated an a.c. signal proportional to the current.The a.c. voltage across the heater element was conditioned to a 0 to 10 volts d.c. voltagesignal.The conditioned output d.c. signals from the instruments were all fed to an analog todigital converter board in an IBM 486 PC computer. The data were collected by scanningthe various channels in the analog to digital converter by the use of a data acquisitionprogram written in C-language. More detailed information on the test facility is inreference [6].3.3 High-Speed Photography SetupA 16-mm Hycam high-speed camera was used to perform the flow visualization dueto high bubble growth and collapse rates. Snap-shots of the boiling process with a shutterspeed of 1/4000 sec provided less expensive means of optimizing the lighting conditionsand magnification (Figure 3.3). These snap-shots revealed the approximate sizes of thebubbles and aided determination of the approximate orientation and the number of lightsto be used for optimum illumination. The setup shown in Figure 3.4 provided the bestlighting and magnification. The camera was operated at 4000 - 6000 frames per second.The images of bubbles were recorded on 100 ft long 16 mm Kodak reversal films withASA rating of 400. The duration of filming corresponded to 800 ms of the boiling process(4500 frames in one roll). A neon lamp inside the camera was activated by a pulsegenerator of 1000 Hz to produce timing marks on the films at an interval of / ms. The testsection was back lit with the use of two racks of lights each consisting of six 300-watt31tungsten halogen projector lamps located 25 cm from the test section. A light diffuserscreen positioned half way between the test section and the lighting source provided auniform illumination of the area of interest. High magnification was achieved on the filmwith the use of a macro-telephoto Tamron SP lens (set at 80 mm focal length) attached toa 40 mm extension tube. When the distance from the base of the lens to the glass tube wasset to approximately 20 cm, the magnification on the film corresponded to the actualdimension of the bubble. The field of view with this magnification covered 8 mm of thelength of the heater with a width from the glass tube up to the surface of the heaterelement(dotted rectangle in Figure 3.4).Due to the requirement of high magnification and frame speeds, many trial and errortests were run to achieve the best possible lighting and magnification. Although highermagnification could be achieved on the film, the depth of view and the field of view wouldbe lessened. With the reduction of the depth of field, the bubble image would be lost if thebubble traveled towards or away from the camera. A smaller field of view would result inthe loss of bubble image if the bubble traveled great distances before condensingcompletely. A maximum of 10,000 fps was attainable with the Hycam though that woulddemand more illumination and also less time of the boiling activity would be captured onthe film. Therefore, for best magnification, illumination and frame speed, aside from thesnap-shots mentioned, about 10 trial and error runs were conducted with the Hycam. Thearrangements and specifications discussed and shown in Figure 3.4 were the results ofthese lengthy trial and error tests.3.4 Procedure for DegassingEexperiments were started by first degassing the system to get rid of the dissolvedair in the loop. The flow was directed inside the test section (the by-pass line was almost32closed) and the pressure in the loop was raised to three atmospheres to avoid surfaceboiling on the heater surface. The heater was turned on and set at maximum power(approx. 24 kW) to raise the temperature of the water. When the temperature in the loophad reached approximately 105 °C (45 minutes, 2 °C/min), the heater was shut off and thepressure was dropped to atmospheric pressure. The system was degassed by opening thevent valves located at the top of immersion heater and condenser and also at variouselevated points in the loop where the chance of trapped air was high. Degassing wasrepeated two or three times at the beginning of every experiment to ensure that all the airwas removed from the system before the filming. Before the condition was set for anexperiment, surface boiling at the heater surface was initiated (for about 15 minutes) byraising the power in the heater at relatively small flow rates so that air adhered to theheater surface would detach. When the system had been thoroughly degassed (three hourslater), the experimental conditions for filming were set. These variables included the flowrate (iii), heat flux(), and the subcooling (AT).3.5 Experimental ConditionsAs has been noted, the purpose of these flow visualization experiments was tovisualize the bubbles produced under the same conditions as those of the void growthexperiments performed by Bibeau[6]. In these experiments, the flow rate and inlettemperature were kept constant while the heat flux was varied from ONB toapproximately 35% void fraction. This procedure implied that, at the location of voidmeasurement, both the heat flux and subcooling changed. In this study, the flowvisualization were performed at constant bulk liquid subcooling and flow rate by varyingthe heat flux (Table 3.1). The loop was set at atmospheric pressure and the flow rate wasset only at three different values of 0.02, 0.10 and 0.20 kg/s (corresponding to 0.08, 0.4,330.8 m/s receptively). The inlet temperatures corresponded to the bulk liquid subcoolings of10, 20, 30, 40, 60 °C at the location of filming. The inlet temperature was related to thebulk liquid subcooling by the heat balance equation from the upstream end of the heater tothe location of filming (1):4)P1ATsub = sat —in MCI,/where 1= 440 mm, P = 39.89 mm and Tsa = 102.1 °C. The range of heat flux extendedfrom values corresponding to the onset of nucleate boiling (ONB) to the vicinity of onsetof significant void (OSV). Heat fluxes corresponding to ONB were obtained from thecorrelation of Hahne et al[45] as:= hcon 20/Tsa^X),) + 6,7"mb (3.2)Rcavl fgwhere Rco, = 4.5 x 10-6m given by [9] and k was calculated by Dittus-Boelter correlation[46]:Nu = 0.023 Reg Pr°33^ (3.3)The heat fluxes for OSV were obtained from Bibeau[9] as:= a1Pea2^ (3.4)where the coefficients al = 136 and a2 = -0.88 were given by [9] obtained from the voidfraction experiments for the present experimental conditions. Figure 3.5 illustrates therelative position of each experiment with respect to ONB and OSV heat fluxes evaluatedfrom (3.2) and (3.4). A total of 45 different conditions were filmed with each conditiondenoted by a dot in Figure 3.5. Experiments were performed at constant subcooling and34mass flow rates by varying the heat flux from ONB to OSV. The choice of flow conditionswere limited by two constraints of the test facility: both the inlet temperatures of less than15 °C and heat fluxes larger than 1.2 MW/m2 were unattainable. Due to the firstlimitation, the point of OSV was not achieved for subcoolings larger than 10 °C at lowflow rate. Due to the second limitation, the point of OSV was not attainable atsubcoolings of 40 and 60 °C at high flow rate.3.6 Data Processing3.6.1 Digitizing SetupThe films were analyzed by a digital image processing system shown in Fig 3.6. Thesystem consisted of a video adapter (Photovix11) with a Tamron CCD solid state camerafocused on a high intensity light source. The film was placed on top of the light source andthe image was captured by the camera. Passing the 16 mm film, frame by frame, throughPhotovixII converted each frame to a video signal. The video signal was fed to aPCVision-Plus frame grabber which resided in a host PC 486 computer. The framegrabber digitized the video signal into 640 by 480 pixel digital image with 256 levels ofgray scales. With this setup, great magnifications (of up to 30 times the actual bubble size)on the monitor were obtained (see Figure 3.7). For analysis of the digitized images ofbubbles and evaluation of the bubble parameters, a computer program in C-language wasdeveloped and interfaced with the frame grabber.353.6.2 Evaluation of Bubble VolumeMost researchers used the average of the major and minor axes of the assumedspheroid to evaluate an average diameter for the bubble. However, this study firstevaluates the volume and second, deduces an equivalent spherical radius by the use of:R- 31/00L 47r )(3.5)Observations of images of the bubbles showed that the bubbles possessed at least one axisof symmetry during most of their lifetime. The bubble volume was evaluated by finding thevolume of revolution of the areas on each side of the axis of symmetry of the bubble.Depending on the flow conditions, the growth and collapse process of a typical bubblewas recorded on 10 to 60 frames. The volume-versus-time graph for bubbles was obtainedby evaluating bubble volume at successive frames from its birth to its total collapse. Fromthe volume-versus-time graph, the maximum bubble volume (Vol.), bubble growth time(t,,,), condensation time (tc) and lifetime (tb) were deduced (see Figure 3.8).Figure 3.9 is a schematic diagram of the procedure used to evaluate the bubblevolume with the pixel integration technique. The outline of the bubble was discretized withline segments of 10 to 40 pieces, depending on the bubble size (Figure 3.10a). The pixelscomprising the image of the bubble were scanned (Figure 3.10b) and the area of theprojection of the bubble and its centroid were calculated (Figure 3.10c). The orientation ofthe symmetry axis was found by observing that the axis of symmetry coincides with one ofthe principal centroidal axis of the area for a symmetric body[47]. The principal centrokialaxis were drawn on the bubble (Figures 3.10d) and the symmetry axis was selected fromthe two choices of the axes. The areas and centroids on each side of the symmetry axiswere evaluated (Figure 3.10e) and the volume of the revolution of each area around theaxis of symmetry was calculated. The bubble volume was defined by the average of the36two volumes of revolution. In addition to the bubble volume, the displacement of thecentroid parallel and normal to the heater wall (La, Lp) and change in bubble shape(4, D ) with time were sought (Figure 3.11). For more information on the computerprogram and pixel integration refer to Appendix C.The inputs to the program were the coordinates of the boundary of the bubble, thereference point, the location of the nucleation site, the scale and the time marks. Thecoordinates of the pixels at the edges of the bubble were obtained by selecting points atthe bubble outline with the use of a mouse. Although different edge-enhancement imageprocessing softwares were tested to avoid this tedious task, no outcome was satisfactory.The reference point was the center of the cross-hair marking built in the camera lens whichappeared on every frame. The location of the nucleation site corresponded to the mid-point of the bubble on the wall in the first frame where the bubble was visible. A scale inmm was placed on the side of the glass tube and was visible on every frame. The scale andthe nucleation site location were entered by the use of a mouse, once at the beginning ofthe digitization process; however, the reference point had to be entered for every frame.The output of the program was the volume( Vol), equivalent spherical radius(R),displacement of bubble centroid from the nucleation site(L„, Lp) and the diameters alongthe principal axis of inertia of the bubble(D„,Dp) as shown in Figure 3.12.3.6.3 Procedure for selecting an 'average bubble'The statistical nature of the process of growth and collapse of vapour bubbles insubcooled water has been reported by many researchers[35-38]. Therefore, for a setcondition, variations in bubble parameters from one nucleation site to another areexpected. Moreover, given a specific nucleation site, the bubble parameters also exhibitstatistical variations with time. Since the employment of rigorous statistical methods for37measuring and evaluating the bubble parameters would have been extremely difficult andtime-consuming, different researchers have used varied approaches in evaluating thebubble parameters and in avoiding statistical analysis. For instance, Gunther estimatedbubble lifetime and maximum radius by 'digitizing' four to eight bubbles for one conditionand taking the average value of radius and lifetime from these observations. Akiyama[30]digitized the largest and smallest, and a few in-between, bubbles and used an averagevalue based on these bubbles.This study takes a different approach in the selection of an average bubble. First, anucleation site which was active in most of the films was located and all the bubblesemerging from that nucleation site were marked. Therefore, all the bubbles analyzed wereinitiated from one specific nucleation site eliminating the spatial variation of bubbleparameters from site to site. For the random variation of bubble parameters from onenucleation site, the following procedure was implemented. The lifetime of all markedbubbles was found for every film, and an average bubble lifetime was defined. Then, threeto five bubbles with closest lifetime to the average bubble lifetime for the condition weredigitized. From the digitized bubbles, one with maximum radius closest to the averagemaximum radius of the digitized bubbles was chosen to represent the bubble behavior forthat condition. This method of selection of an average bubble is justified since thedistribution of the bubble lifetime from a nucleation site was found to be approximatelynormal (Figure 3.13). Moreover, Del valle and Kenning[37] reported that the distributionof the maximum radius is also normal. Depending on the flow conditions about 15 to 45bubbles were available for analysis in one film.Figure 3.14 shows the volume versus time graph for the three bubbles digitized forthe following conditions (D24): V = 0.4 (%) ATsub = 20 (° C) and (1) = 0•3(4%2). For thiscondition, the average bubble lifetime based on 15 bubbles observed in the entire roll of38the film was 8.35 ms . Since bubble # D24-10 had a maximum radius closer to the averagemaximum radius, this bubble is selected to represent the typical behavior of bubbles in thatcondition.3.7 Error AnalysisTables 3.2 and 3.3 list the experimental errors for the measured and calculatedparameters. The errors in the measured quantities (7:4,, Ti„,rit) were either estimated fromthe manufacturers' specifications or reference[9]. The estimation of uncertainties in thecalculated parameters (4), AT,,,„ ) is given in Appendix D. The estimated errors formeasured quantities from image processing (Vol, R, D., Dp, L,,, L) are obtained bymeasurement of the volume, centroid, and maximum and minimum diameters of a knownshape and are further discussed in Appendix D.Table 3.1. Range of experimental parameters.Experimental promoters I Range of parametersPressure, P (atm) 1Mass flow rate, ??? (kr) 0.02, 0.10, 0.20Mean flow velocity, V (%) 0.08, 0.4, 0.8Subcooling, AT(° C) 10, 20, 30, 40, 60Heat flux, (1) ("72) 0.1 - 1.239Table 3.2. Estimated error for measured and calculated experimeMeasured or CalculatedquantityI^ErrorInlet temperature, Tin ±1 ° CWall temperature, K, -2.2 / +1.2 °CSubcooling, ALI, ±2 °CHeat flux, 4) ±2 %Mass flow rate, ??? ±0.3%ntal parameters.-speed photography.Table 3.3. Esti nated error for measured quantities obtained from hieMeasured or Calculatedquantityr^ErrorVolume, Vol ±5 %Radius, R ±1.7 %Parallel/Normaldisplacement, L., Lp±0.08 mmParallel / Normaldiameters, D., Dp±5 %Time, t ±0.02 ins40Figure 3.1. Schematic diagram and photograph of test facility.41Figure 3.2. Schematic diagram and photograph of the test section.42Figure 3.3. Snapshots of bubbles with a shutter speed of 1/4000 sec.43- 11^.^... ...^-.41 1^i............-.^ , ...i .....t^. ^ . i.; .:t.. .^, -.:  ill 111 : MI 6..^t-, lk,. ^., •^'''" -^1■•••i•^, ....CI:, ^-"‘ . ^..... ill if. '' '-, ^r.-. ..,,^.^,...i.^.. ,^ „ f ',^",^-^‘. i^1. 1-"•„ ,,,^a• *1.,_- I^:V:',„^, '•^.^fi'.1P".,^. • -/:..-^. ' " -;:^.!... ,. ....^4116•*: 1A.^••r-..^MN•, ..--- i^I 1_ .• ..,-^.^--- -.. - -"•:•f-i...:,^-. ,..^. -•■•--......40 141^-.'^............ .^-..^....^.Figure 3.4. Schematic diagram and photograph of high speed filming setup.0.200.16cr)^0.12_se0.080.040.0000 0.2 0.4 0.6 0.8 1.0 1.2Tfr, < 15 °C03 027 028 _ — —• •^•-— —I I0.200.16ri)^0.12_se0.080.040.0000 0.2 0.4 0.6 0.8 1.0 1.2I^I^I^.^I^'^I^I019 020 D47 021 022 D48• • • • •^•AT,,,,,, -20 °C _ONB^ OSV(b)D23 024^D25^D26^050• • • • •44(MW/m2)Figure 3.5. Filmed conditions for subcoolings of (a) 10 C (b) 20 C.1 10.2 0.4 0.6 0.8 1.0 1.20.200.16ci)• 0.120.080.040.0000(1) (mw/m2)0.200.16• 0.120.080.040.0000^0.2^0.4^0.6^0.8^1.0^1.2^1.4^1.6^1.8^2.0^2.2(I) (mw/m2)Figure 3.5 Filmed conditions for subcoolings of (c) 30 C (d) 40 C.4506 012^1313 014^D49• • • • • -ONB^ OSV015^D5^D16^D17 018^051• • • • • •_ - -__-------^AT, -30 °C _037^- - - - - - 1", < 15 °C(c)--1^•^I^I^I^I^I 46Figure 3.5. Filmed conditions for subcoolings of (e) 60 C.47Figure 3.6. Schematic and photograph of image processing system.Figure 3.7. Magnified image of a bubble on the monitor.48Figure 3.8. Definitions of bubble parameters.49EvaluateBubble CentroidEvaluate BubbleProjection AreaScan Pixels Boundedby Bubble OutlineFind Orientation ofPrincipal Centroidal axisEvaluateCentroidal Momentsof Inertia^ 1Figure 3.9. Steps in the evaluation of bubble volume.Figure 3.10. Photographs of the digitizing steps for evaluating bubble volume (a)Discritizing bubble outline.5051%Figure 3.10. Photographs of digitization steps for evaluating bubble volume (b) Scaningbubble outline (c) determination of bubble projection area and centroid.52Figure 3.10. Photographs of digitization steps for evaluating bubble volume (d) evalutionof centroidal principal axis of bubble projection area.53Figure 3.10. Photographs of digitization steps for evaluating bubble volume (e) evaluationof the volume of revolution of the areas on each side of the axis of symmetry.Nucleation site(a)^ (b)Figure 3.11. (a) displacement of bubble centroid parallel and normal to heated surface withrespect to the nucleation site (b) diameters along the centroidal principal axes.54Figure 3.12. Photograph of frame analysis results displayed on the computer monitor.55Figure 3.13. Distribution of bubble lifetime for conditions D21 and D2256Figure 3.14. Selection of an 'average bubble' for condition D24.CHAPTER 4RESULTS AND DISCUSSIONThis chapter describes the characteristics of a typical vapour bubble in subcooledboiling through the analysis of high-speed photographs, discusses the effect of experimentalconditions (heat flux, subcooling, flow rate) on bubble parameters (R„„ tc, t„„tb), andpresents simple correlations for the bubble parameters based on the experimental data.4.1 Observations on Bubble Dynamics in Convective Subcooled BoilingFigure 4.1 shows the high-speed filming results of the growth and collapse process ofa typical bubble photographed at mean flow velocity of V=0.4 mls, bulk subcooling ofAT.b=20 °C and heat flux of 4) =0.3 MW/m2 (Reference condition D24-10). Figures 4.2 -4.6 shows the digitized results for this bubble.4.1.1. Bubble Growth and Collapse CurvesFigure 4.2 shows the temporal variation of the bubble volume and the equivalentspherical radius. The bubble lifetime is divided into two regions of growth andcondensation separated by the solid line. The condensation region is further divided intotwo sub-regions: condensation on the wall and condensation after ejection (distinguishedby the dashed line). The growth region included the period from nucleation to the5758maximum bubble size and the condensation region comprised the remaining portion of thebubble lifetime where bubble size decreased first while attached to the heater surface andlater after being ejected' into the flow. The duration of each region depended on theexperimental conditions (see Section 4.2).Based on Akiyama's[38] conclusions on the superheated layer thickness(section 2.5),the bubble spends only a small fraction of its growth in the superheated layer (t<0.10 t.).Therefore the bubble growth is influenced more by micro/ macro-layer evaporation, than byconduction through the superheated layer. At the end of the growth period, characterizedby the maximum bubble size, evaporation from the bubble base is balanced withcondensation at the bubble top surface. At this part of the bubble lifetime, the bubble topsurface has intruded well into the subcooled core, and the condensation at the bubbleinterface becomes dominant while the bubble is still in contact with the heater surface.Meanwhile, a surface tension gradient is formed along the bubble interface due totemperature gradient across the flow[9]. This surface tension gradient is the driving forcefor the bubble ejection from the wall. The condensation rate increases slightly after bubbledetachment due to the lack of bubble contact with the heater surface and due to the bubbledistance from the superheated layer. The following observations were made on bubbleejection:• In high subcooling (60 °C) most of the condensation occurred while the bubblewas attached to the wall, although ejection was still present. This differs from theresults of Gunther[35] who observed that bubbles grew and collapsed on theheater surface as hemispheres.• Contrary to void growth model assumptions that the OSV point coincided withbubble ejection, ejection was observed well before the point of OS V.'The term 'ejection' used in this thesis refers to the departure of the bubble from the heated surface.59• Unlike pool boiling, the ejection of a bubble did not occur at its maximum size.This confirms the observations of Tolubinsky and Kostanchuck[39].4.1.2. Bubble ShapeFigure 4.3 shows the change in bubble shape characterized by the variation of thebubble diameters along the bubble principal axes (D,,, D„) with the ratio F = DpD„representing the flatness of the bubble shape. In the growth region, the bubble shape wasellipsoidal with a maximum flatness of approximately 1.6 reached at —t ,• 0.2 where teic isteicthe time at detachment. As the bubble grew, the shape changed from ellipsoidal tospherical. At the point of detachment, the shape of bubble resembled a tear drop (pearshape) with a flatness of approximately 0.8. In the condensation region after detachment,the bubble shape became highly irregular and was approximated by an ellipsoid for thepurpose of analysis. The observations on bubble shape agree with similar observations ofAldyama[38]. The bubble face adjacent to the heater underwent the greatest and mostirregular deformation immediately after detachment. This deformation is perhaps due tosurface tension gradient adjacent to the heater surface.Contrary to the observations of continuous transformation in bubble shape, mostresearchers have assumed that the bubble shape approximated a spheroid throughoutbubble lifetime with an effective radius defined by the average of the maximum andminimum radii of the irregular shape. Figure 4.4 shows the volume measured in this studycompared with the volume evaluated with the spheroidal assumption. The value of themaximum volume is underpredicted by approximately 1 5 % with the spheroidal assumption.For comparison of the bubble sizes obtained in this study with those of the literature,the measured volume is converted to an equivalent spherical radius from:60R _ ( 3 Vol )) (4.1)47r )In Figure 4.2, the measured volume and the equivalent spherical radius with the abovedefinition (4.1) are shown for reference condition D24. The growth and collapse regionsare defined from the volume graph since the maximum bubble size is clearly defined by thecurve fitted through the experimentally obtained points. The curve fitted through thecalculated radius points has a flatter maximum due to the definition of the radius withequation (4.1) where the radius is given as the function of the third root of the volume.4.1.3 Parallel and Normal DisplacementsFigure 4.5 presents the normal and parallel displacement of the bubble centroid withrespect to the nucleation site on the heater surface. The bubble translation velocity parallelto the heater, defined by the slope of the parallel displacement curve, is constantthroughout the growth and collapse process and is of the order of magnitude of the meanflow velocity. Table 4.1 lists the slip ratio, defined as the ratio of bubble translation velocityparallel to heater surface to mean flow velocity, for the different conditions. The values ofthe slip ratio ranged from 0.71 - 2.33, dependent on local conditions. No dependence ofslip ratio on bubble size was found unlike Gunther[35] who reported an average value of0.8 increasing slightly with the bubble size. Akiyama[38] reported values of 0.3 - 0.8 forthe slip ratio, constant throughout the process of growth and collapse and independent ofthe bubble size.The normal velocity of the bubble, defined by the slope of the normal displacement ofbubble centroid with respect to the heater surface, is shown in Figure 4.5. The growth andejection regions are marked by high normal velocity of the bubble centroid while at themaximum bubble size the normal velocity is approximately zero. The ejection velocity,defined by the slope of the line through the points past the dotted line, was evaluated for61most conditions (see Table 4.1). The values of ejection velocities fell into the range of 0.36to 1.13 m/s. With higher temperature gradient anticipated at higher subcooling, the ejectionvelocity was expected to depend on the bulk liquid subcooling. However, such adependence was not established from the experimental data.Figure 4.6 displays the path of the bubble centroid for different subcoolings atconstant flow velocity and heat flux. The origin in the graph corresponds to the location ofthe nucleation site with the y-axis representing the heater surface. The flow is in thedirection of positive y-axis. The bubble path curves in the direction of the cross-flow beforebubble ejection which indicates the influence of the cross-flow. However, the ejection ofbubble into the flow marks a change in the slope of the displacement curve whichdemonstrates the high normal velocity of the bubble compared to the mean flow velocity.At high subcoolings (ATsub =60 °C), the bubble normal and parallel displacements werelimited to the vicinity of the wall due to the rapid condensation process; at low subcooling,the bubble traveled farther and penetrated more deeply into the flow. The bubble behaviorat high subccoling might explain the reason why some researchers described a distinctregion close to the heater surface as the 'bubble boundary layer' (Jiji and Clark[48]).4.2 Effect of Experimental Conditions on Bubble Parameters4.2.1 Maximum RadiusFigure 4.7 shows the effect of flow velocity and heat flux on bubble maximum radiusfor constant subcooling of 30°C and for flow velocities of 0.40 and 0.80 m/s. As indicatedby the scatter of the data points for the two flow velocities, the effect of flow velocity onmaximum bubble radius is negligible. The effect of flow velocity is appreciable when arelative velocity between the bubble and the flow exists. However, in section 4.1.3, it was62shown that bubbles translated with the velocity of the flow. Aldyama[38], in similarexperiments evaluating the effect of flow velocity on bubble size, concluded that increasedflow velocity decreased the bubble maximum size at mean flow velocities greater than 0.3rn/s (see Figure 2.8). The scatter of Akiyama's data points at flow velocity of 1 m/s and thesmall change in the values of maximum diameter for flow velocity range of 0.1 to 1 m/s atlow subcooling do not support his proposed limit of 0.3 m/s. The same is valid for the otherbubble parameters. From the present experimental data and Akiyama's data, the effect offlow velocity on bubble parameters is concluded to be negligible for flow velocities smallerthan 1 m/s.Figure 4.8 presents the effect of heat flux and subcooling on the maximum bubbleradius for subcoolings of 20 to 60 °C. At low subcoolings, an increase in heat flux reducedthe maximum bubble size. At high subcoolings, the maximum radius was independent ofheat flux. For a given heat flux, increased subcooling resulted in smaller bubble sizes at thevicinity of ONB. At high heat fluxes (near the OSV point), the maximum radius wasindependent of both the heat flux and liquid bulk subcooling. The decrease of the maximumbubble radius with increasing heat flux and the constant value of maximum radius at highersubcoolings are consistent with the experimental results of Gunther[35] and Del Valle andKenning[37] respectively. The maximum radii obtained in this work are slightly larger thanthose of Akiyama[38] for the same subcooling (see Figure 2.8). This could be either due tothe choice of the nucleation site or the selection of the 'average' bubble.Table 4.2 compares the experimental maximum bubble radii with maximum radiipredicted by theories of Unal[28], Zuber[23] and Mikic et al.[24]. Unal derived anexpression for the maximum radius based on the micro-layer evaporation theory. Heassumed that bubble growth resulted from the evaporation of the thin liquid film formed atthe bubble base balanced by the dissipation of heat to the surrounding subcooled liquid atthe bubble top surface. The expression for the maximum radius, Equation (B.18), is derived63in Appendix B. Unal underpredicted the maximum radius for all the conditions (see Table4.2). The range of predicted radii fell between 0.17 to 0.46 mm. In Unal's model anincrease in the heat flux resulted in an increase in the bubble size, contrary to theobservations of this investigation. Moreover, referring to Equation (2.22), the expressiongiven by Unal does not contain a maximum and the model does not predict the entire cycleof bubble growth and collapse as shown in Figure 2.4.Zuber[23] derived an expression for the maximum bubble radius by assuming thatbubble growth was due to the evaporation of the liquid to vapour at the bubble interface bythe supply of heat from the superheated layer (see section 2.2.2). The energy balanceyielded an expression in which the maximum bubble radius is inversely proportional to theheat flux and directly proportional to the wall superheat, (T 2. - ..)  , (see Equations 2.16qand 2.17). Therefore, in evaluating the maximum radius with Zuber's expression, theexperimental wall superheat was used. Contrary to Unal's predictions, Zuber predicted arange of radii that was closer to the experimentally obtained radii except at low flow rate(V=0.08 m/s) at which the predictions were up to three times the maximum radii obtainedin this study. In this study the wall temperature increased with increased heat flux;however, the trend was not linear (see Table 4.2). Due to the dependence of the wallsuperheat on the heat flux, Equation (2.16) predicts increasing as well as decreasingmaximum radii with increased heat flux.Mikic et al [24] used a similar approach to Zuber in analyzing bubble growth (seeSection 2.2.2). The expression derived for the maximum radius, Equation (2.20), unlikeZuber's model, contained the effect of liquid subcooling as well as wall superheat. Theexpression, more complicated than that proposed by Zuber, contained an additionalparameter, the growth time, the value of which was taken from this experiment. Mikic'spredictions were comparable to Zuber's predictions except at low flow rates which Mikic64predicted lower values closer to those of the present study. The effect of increased heatflux on bubble maximum radius was inconsistent, perhaps due to the experimental values ofwall superheat and growth time input into Mikic's model.In none of these models are the phenomena of decreasing bubble size with increasingheat flux embedded in the theory and the theoretical results do not predict the trend in theexperimental observations. Gunther has shown that with increased heat flux the density ofnucleation site and the frequency of bubble formation increase significantly. It follows that,as heat flux is increased, the energy input to the flow will be distributed among morenucleation sites. The result is a smaller amount of energy per nucleation site and hencesmaller bubble sizes. Therefore, the inability of these models to predict the observed trendof decreasing maximum bubble radius with increasing heat flux indicates a need for acorrelation based on the experimental results of the present study.4.2.2 Bubble Growth TimeThe effect of heat flux on the bubble growth time for subcoolings of 20 to 60 °C isshown in Figure 4.9. The trend, similar to the trend of decreasing maximum radius withincreasing heat flux, implies that the growth time is proportional to the maximum radius,i.e., the larger the maximum radius, the longer the growth time. Aldyama also showed thatthe maximum growth time followed the same trend as that of the maximum radius when theeffect of flow velocity was investigated. Gunther[35] and Del Valle and Kenning[37]showed that the bubble lifetime followed the same trend as that of the maximum radiusversus heat flux.Table 4.3 shows the ratio of growth and condensation time to bubble lifetime for allthe experiments. The values for the ratio of bubble growth time to bubble lifetime fell in therange of 10.27 <L'-' <O.44 with an average value of 0.33± 0.04 based on all thetb65experiments. Aldyama[38] reported a range of 0.2-0.5 and found a range of 0.3-0.55 forGunther's data.4.2.3 Bubble Condensation TimeFigure 4.10 presents the effect of heat flux on the condensation time for subcoolingsof 20 to 60 °C. An increase in heat flux is accompanied by a decrease in condensation time.However, this decrease is not the result of the direct effect of heat flux or superheat butthat of the small maximum bubble sizes obtained at high heat fluxes. Since the growth timewas found to be proportional to the maximum bubble radius, the condensation time is alsoexpected to be proportional to the maximum bubble radius. At a given subcooling, thelarger bubbles will take longer to condense.Table 4.4 compares the condensation time obtained in this study with the analyticalpredictions based on inertia-controlled collapse by Akiyama[30] (Equation 2.24) and heat-transfer-controlled collapse by Florschuetz and Chao[31] (Equation 2.28). Aldyama'spredictions were up to two orders of magnitude lower than the experimentally obtainedcondensation times. Florschuetz' predictions at low subcooling of 10 °C compared wellwith the experimental results but at higher subcoolings the predictions were up to twoorders of magnitude lower than the experimental values. These discrepancies might be dueto the assumption of uniform subcooling in the derivations of the models. This assumptionmight not be valid in subcooled boiling since, as shown earlier, the condensation processcommences adjacent to heater where large temperature gradients exist and local subcoolingdiffers from the bulk subcooling. Better agreement at low subcooling between theexperimental values and the predictions of Florschuetz et al. could be explained by the factthat, at low subcooling, the difference in temperature between the main flow and the wall issmaller so that the assumption of uniform temperature during the condensation stage maybe justified.66A better estimation of the local subcooling should include the effect of the radialtemperature gradient in the flow. In this study, the temperature across the flow was notmeasured. However, the temperature across the flow during subcooled nucleate boiling isgiven by Forster[49] as:-YT(Y) = T., + (AT„ + AT,)e II - ^ (4.2)where AT is the wall superheat and H is the thermal layer thickness defined as the distancewhere the non-dimensional temperature difference in Equation (4.2) drops to lie. Aldyamaobtained values of 0.05 to 0.2 mm for the thermal boundary layer thickness for a velocityrange of 0.08 to 0.8 m/s, respectively. An estimate of the local subcooling, based on thetemperature of the liquid at a distance equal to bubble diameter and the saturationtemperature is given by:(7")10.1- T(Y =2R.)+ at 2(4.3)Since the thermal boundary layer thickness is small compared to the maximum bubblediameter, the liquid temperature at Y=2 R, can be approximated by the bulk liquidtemperature. This approximation limited the range of local subc,00ling to 5 - 30 °C frombulk subcoolings of 10- 60 °C respectively. The condensation time was recalculated fromEquation (2.28) using the local subcooling from Equation (4.3). This recalculation resultedin higher condensation times overall as expected. However at low subcooling a smallchange in the value of local subcooling resulted in a drastically changed value of thecondensation time because Equation (4.28) has a steep slope at low subcooling (see Figure2.7). The refinement of this approach was not pursued since Equation (4.3) was found torepresent poorly the condensation rates obtained in this experiment and is further discussedin Section 4.3.1.674.2.4 Effect of Subcooling on Bubble Parameters at V=0.08 m/sThe lowest inlet temperature that could be achieved with the loop was approximately15 °C. Since reaching the point of OSV at low flow rates (V=0.08 m/s) required an inlettemperature lower than 15 °C, the effect of subcooling was investigated at only one valueof heat flux. Figure 4.11 presents the effect of subcooling on the maximum radius, bubblegrowth time, condensation time and bubble lifetime for a heat flux of 0.20 MW/m2. Thesame trend of decreasing values of bubble parameters with increased subcooling isobserved as previously shown for higher flow rates.Over the entire range of the present experimental conditions, the maximum bubbleradius ranged from approximately 0.50 mm at high heat fluxes and high subcoolings up to1.75 mm at low heat flux and low subcoolings. Table 4.5 compares the experimentallyobtained values for the maximum radius and bubble lifetime with similar experimentsperformed at atmospheric pressure. The range of maximum radii and bubble lifetimeobtained in this study is larger than that of Akiyama's similar study due to the range of bulksubcoolings (20-80 °C) used by Akiyama compared to the present range of (10-60°C).43 Correlations4.3.1 Normalized Bubble Growth and Collapse CurvesZuber's[23] non-dimensional expression (Equation 2.15) for the instantaneousbubble radius was based on heat-transfer-controlled growth and collapse of a singlebubble. Figure 4.12 shows the experimental data normalized with maximum radius andgrowth time and compared to Equation 2.15. In the growth region, Zuber's growth-ratepredictions matched the experiments; however, the normalization procedure failed in thecondensation region.68Akiyama[38] suggested a correlation for the bubble growth and collapse curves interms of maximum bubble radius and bubble lifetime:R K1-2'Rm1 ( t ri — : ) (4.4)where N and K are constants. N was evaluated from the fact that at t/tm=1, R/Rm= 1:N(tm ) _ 1tb^2(4.5)and the parameter K was found by the curve being fitted to the data. Aldyama used a valueof K=3 and found a value of K=2 for Gunther's data. Figure 4.13 compares theexperimental data normalized with the maximum bubble radius and bubble lifetime withequation (4.4) for the adjusted values of K=2.2 and N=0.67 2 based on experimentalresults:2.2!= 1- 221R. )0.671 ( t2^tb(4.6)A good representation is obtained for both growth and condensation regions by the use ofEquation (4.6).Figure 4.14 compares the growth rate obtained by Equation (4.6) with thepredictions of the growth models described in Chapter 2, and Akiyama's correlation withN=0.66 and K=3. Growth rates obtained in this work are in good agreement with thegrowth models of Mikic and Zuber. Unal predicted lower growth rates with the micro-macro layer evaporation model.Figure 4.15 compares the collapse rates obtained with Equation (4.6) with thecollapse rates predicted by the inertia-controlled and the heat transfer-controlled collapse2 The values of tm/tb are shown in Table 4.5. In evaluating N, a value of tm/tb =0.36 was used.69models[30,31]. The shape of the experimental curve is similar to those of the inertia-controlled models with the experimental collapse rates lower at the beginning of thecondensation stage. This result contrasts with the heat-transfer-controlled collapse modelsin which the condensation process is fast at the beginning and slow at the end of thecondensation stage. It was shown in Section (4.2.3) that at low subcooling, thecondensation time was in good agreement with the heat transfer-controlled predictions.Figure 4.16, which compares an experiment at low subcooling to the Florschuetz' model,shows that even though the condensation times for the experiment and the theory areapproximately the same, the collapse rates differ significantly. In the experiments, asbubbles condense on the heater surface, slower collapse rates are expected. When bubbleseject inside the subcooled liquid, higher condensation rates are expected due to the largertemperature gradients between the vapour and the bulk liquid. Higher temperaturegradients imply higher heat transfer rates through the bubble wall and lower bubble walltemperatures with lowest possible wall temperature of 1. This assumption implies anisothermal collapse which is the assumption in inertia-controlled collapse models. In theactual case, due to the lack of perfect heat transfer rates, the bubble wall temperature ishigher than the saturation temperature so that a slower condensation rate is expected (seethe experimental curve Figure 4.15).4.3.2 Correlations for Bubble ParametersThe experimental results compared to those of different theoretical models led to theconclusion that the expression given by Mikic, Zuber and Unal for the maximum radius ofthe bubble did not predict the experimental results, i.e., their prediction of increasing bubblesize with wall superheat contradicted those of Gunther, Del Valle and Kenning and thepresent study. Comparison of the experimental values of the condensation time did notcompare well with models proposed by Akiyama and Florschuetz et al.. Therefore,70correlations had to be developed in order to predict the maximum radius and the lifetime ofthe bubble at the subcooled nucleate boiling for heat flux range corresponding from ONBto OSV. The result of these correlations for bubble maximum radius, growth time andcondensation time is the subject of this section.The bubble lifetime is divided into two regions for the purpose of the correlations:the growth region and the condensation region. In the growth region, the effect of heat fluxand subcooling are considered the most significant parameters that limit the maximumbubble size and the growth time is assumed to be directly proportional to the maximumradius. In the condensation region, the time for the bubble to condense is assumed to be afunction of the degree of subcooling and the maximum bubble size.In the correlation of the maximum bubble radius two non-dimensional numbers areused:ja* _ PICpl(7v — Tsat) Pvifg(4.7)e _ Tw - TB (4.8)Tw - 7",.The effect of heat flux is shown with modified Jacob number, Jaw* . In this study, its valueranged from 45 to 110 with higher values of Jaws indicating larger wall superheat. Theproperties pl and Cp, are evaluated at saturation temperature since during growth thebubble is close to the heated surface where the bulk temperature of the liquid is close to thesaturation temperature. The non-dimensional temperature difference, 0, represents thedegree of liquid subcooling. The values of 0 ranged form 1.3 to 4 with the larger values of0 indicating higher degree of subcooling.The maximum bubble radius is non-dimensionalized with 12:,:(4.9)71where ai, pi, a are evaluated at the saturation temperature. This non-dimensional number,used by Cooper and Chandratilleke[50] in the analysis of vapour bubble growth at a wallwith a temperature gradient, was derived as a result of a non-dimensional analysis.Dimic[51] arrived at the same non-dimensional number (R:) in his analytical work onbubble condensation in a subcooled liquid. A different approach for non-dimensionalizingthe maximum radius was applied by Mikic[24] as  R.  This required a knowledge of the°ITC.growth time to obtain the maximum bubble radius, i.e., coupling the effect of the twobubble parameters.The experimental data for the maximum bubble radius were correlated with Jaw* and0 as follows:= 5.01 x 109Ja,:-(650 -L65^ (4.10)The data points and the correlating line are shown in Figure 4.17. The coefficient ofdetermination for this correlation was 0.70 (see appendix E). The correlation predicts adecrease in the maximum bubble size with increasing superheat and subcooling as expected.The equal exponents of Jaw* and 0 indicate that wall superheat and subcooling are of equalinfluence in determination of the bubble maximum size.Since the growth time is proportional to the maximum radius as shown in Section(4.2.2), the growth time is correlated with the same non-dimensional parameters as themaximum radius. The growth time is non-dimensionalized as3:ng+ -t ^aitm 2p,a, )( 0' )(4.11)3 This non-dimensional number was also derived from dimensional analysis by Cooper andChandratilleke[50].72This non-dimensional time is similar to the Fourier number:alt.Fo„, -^(length scale) 2(4.12)However, the length scale used in the denominator is consistent with the length scale used+in the definition of R. - [ R m 2 ) . Based on the experimental data, the followingPrat acorrelation was obtained for the growth time:= 3.21 x 1014 Jaw* -1580 -188^(4.13)The data points and correlating line are shown in Figure 4.18. The coefficient ofdetermination for this correlation is slighlty lower than the correlation for the maximumradius. Since the exponents for Ja: and 0 are almost equal, the growth time is assumedto be proportional to the maximum bubble radius, i.e.:t. = cR,.:,^ (4.14)where c and x are found by correlating t„, with R. from the data:t„, = 56.7 gi49^ (4.15)Equation (4.15) provides a simpler expression to determine the growth time when themaximum radius is obtained.The condensation time is expressed in terms of liquid subcooling and as a function ofthe maximum radius. The condensation time is non-dimensionalized with:73°,t,(131(112 )2La jand correlated with the Jacob number and the non-dimensional maximum radius:piC i(T.- TB)Ja- 'Pvifgme IC,17Pia't: - (4.16)(4.17)(4.18)Based on the experimental data , the correlating equation for the condensation time wasgiven by:t: = 106.8 Ja-u5 R,+„ 13°^ (4.18)The data points and the correlating line are shown in Figure 4.19. The coefficient ofdetermination for this correlation was 0.96. As expected, increasing the liquid bulksubcooling Ja, reduced the time of condensation. Moreover, the condensation time isdirectly related to the maximum size of the bubble.Table 4.1 Slip ratio of bubbles in different conditions.NumberRef ATsub(°C) V(%) 4)(mw/.2) Vb(%)_Vb// Vvejc^scy)D35 10 0.08 0.2 0.25* 3.13* 0.42D36 10 0.08 0.3 0.05* 0.63* 0.36D33 10 0.40 0.3 0.61 1.53 0.43D27 20 0.08 0.2 0.35* 4.38* 0.60D28 20 0.08 0.3 -0.11* -1.38* 0.64D24 20 0.40 0.3 0.44 1.10 0.79D25 20 0.40 0.6 0.50 1.25 0.95D26 20 0.40 0.7 0.93 2.33 0.42D50 20 0.40 0.9 0.45 1.13 0.45D21 20 0.80 0.6 1.08 1.35 0.49D22 20 0.80 0.7 0.84 1.05 0.82D48 20 0.80 0.9 0.89 1.11 1.28D37 30 0.08 0.2 0.076 0.95 1.13DOS 30 0.40 0.3 0.37 0.93 0.75D16 30 0.40 0.6 0.48 1.20 0.93D17 30 0.40 0.8 0.54 1.35 0.44D18 30 0.40 0.9 0.37 0.93 1.06D51 30 0.40 1.2 0.80 2.00 1.03D06 30 0.80 0.6 0.76 0.95 0.71D13 30 0.80 0.8 0.81 1.01 1.01D14 30 0.80 0.9 0.94 1.18 0.98D49 30 0.80 1.2 0.83 1.04 0.69D39 40 0.80 0.6 0.81 1.01 **D40 40 0.80 0.9 0.60 0.75 **D41 40 0.80 1.2 0.84 1.05 **D42 60 0.80 0.6 0.60 0.75 **D43 60 0.80 0.9 0.70 0.88 **D44 60 0.80 1.2 0.57 0.71 **, *Bubbles in these conditions were affected by the growth and collapse ofneighboring bubbles.** Not available.7475Table 4.2. Comparison of experimental maximum bubble radius with predictions ofUnal[28] (Equation B.18.), Zuber[23] (Equation 2.16) and Milcic et al.[24] (Equation2.20).RefNumberATsub(2 C) *KM d)(117.2) 7' (°C) R1(mm)Unal[28]R.(mm)Zuber[23]R.(mm)Mikic[24]R.(mm)ExperimentD35 10 0.02 0.2 130.3 0.40 3.04 1.47 1.36D36 10 0.02 0.3 131.8 0.46 2.24 1.13 1.16D33 10 0.1 0.3 127.1 0.45 1.59 1.07 1.23D27 20 0.02 0.2 128.3 0.28 2.62 1.17 1.77D28 20 0.02 0.3 132.0 0.32 2.28 1.61 1.60D24 20 0.1 0.3 124.6 0.30 1.29 0.99 1.33D25 20 0.1 0.6 127.7 0.40 0.83 0.89 1.03D26 20 0.1 0.7 129.9 0.42 0.84 0.87 0.73D50 20 0.1 0.9 142.0 0.46 1.35 0.92 0.56D21 20 0.2 0.6 126.0 0.35 0.73 0.71 0.79D22 20 0.2 0.7 126.1 0.38 0.63 0.69 0.74D48 20 0.2 0.9 141.1 0.42 1.29 0.80 0.64D37 30 0.02 0.2 131.2 0.22 3.23 0.85 0.83DOS 30 0.1 0.3 120.6 0.24 0.81 0.64 0.86D16 30 0.1 0.6 126.7 0.32 0.77 0.66 0.79D17 30 0.1 0.8 1263 0.36 0.57 0.62 0.53D18 30 0.1 0.9 126.7 0.37 0.51 0.56 0.48D51 30 0.1 1.2 132.3 0.42 0.58 0.67 0.46D06 30 0.2 0.6 119.9 0.26 0.46 0.49 0.68D13 30 0.2 0.8 123.5 0.32 0.44 0.55 0.61D14 30 0.2 0.9 124.5 0.33 0.43 0.54 0.46D49 30 0.2 1.2 131.0 0.37 0.53 0.54 0.51D39 40 0.2 0.6 123.2 0.23 0.57 0.52 0.66D40 40 0.2 0.9 125.1 0.28 0.45 0.67 0.71D41 40 0.2 1.2 129.8 0.32 0.49 0.68 0.51D42 60 0.2 0.6 123.6 0.17 0.59 0.43 0.52D43 60 0.2 0.9 126.6 0.22 0.51 0.57 0.61D44 60 0.2 1.2 130.1 0.25 0.50 0.60 0.54Table 4.3. Ratio of condens .......^.....^.-....... ....war ana VIal.l.■,/ •RefNumber Ailth CC) th(KgX) 4'7m2) (%) t(%)D35 10 0.02 0.2 67 33D36 10 0.02 0.3 72 28D33 10 0.1 0.3 66 34D27 20 0.02 0.2 73 27D28 20 0.02 0.3 67 33D24 20 0.1 0.3 66 34D25 20 0.1 0.6 68 32D26 20 0.1 0.7 69 31D50 20 0.1 0.9 63 37D21 20 0.2 0.6 70 30D22 20 0.2 0.7 71 29D48 20 0.2 0.9 73 27D37 30 0.02 0.2 66 34DOS 30 0.1 0.3 70 30D16 30 0.1 0.6 71 29D17 30 0.1 0.8 65 35D18 30 0.1 0.9 65 35D51 30 0.1 1.2 65 35D13 30 0.2 0.8 68 32D14 30 0.2 0.9 62 38D49 30 0.2 1.2 71 29D39 40 0.2 0.6 67 33D40 40 0.2 0.9 56 44D41 40 0.2 1.2 56 44D42 60 0.2 0.6 71 29D43 60 0.2 0.9 67 33D44 60 0.2 1.2 67 337677Table 4.4. Comparison of condensation time with predictions of Aldyama[30] (Equation2.24) and Florschuetz et al. 31 (Equation 2.28).RefNumberAT.b(°C)_ni(Kg/, ) tkinv/.2) t(ms)Akiyamat(ms)Florschuetzt(ms)ExperimentD35 10 0.02 0.2 0.1280 11.02 10.2D36 10 0.02 0.3 0.109 8.02 7.2D33 10 0.1 0.3 0.126 9.02 6.4D27 20 0.02 0.2 0.118 4.74 8.1D28 20 0.02 0.3 0.130 5.75 9.1D24 20 0.1 0.3 0.088 2.67 5.5D25 20 0.1 0.6 0.069 1.60 3.8D26 20 0.1 0.7 0.049 0.81 3.3D50 20 0.1 0.9 0.037 0.47 1.5D21 20 0.2 0.6 0.053 0.94 3.0D22 20 0.2 0.7 0.050 0.83 2.9D48 20 0.2 0.9 0.043 0.62 1.9D37 30 0.02 0.2 0.045 0.47 2.3D05 30 0.1 0.3 0.047 0.50 3.7D16 30 0.1 0.6 0.043 0.42 2.4D17 30 0.1 0.8 0.029 0.19 1.7D18 30 0.1 0.9 0.026 0.16 1.3D51 30 0.1 1.2 0.025 0.14 1.3D06 30 0.2 0.6 0.037 0.31 2.2D13 30 0.2 0.8 0.033 0.25 1.9D14 30 0.2 0.9 0.025 0.14 1.3D49 30 0.2 1.2 0.028 0.18 1.2D39 40 0.2 0.6 0.031 0.17 1.6D40 40 0.2 0.9 0.034 0.19 1.4D41 40 0.2 1.2 0.024 0.10 1.0D42 60 0.2 0.6 0.020 0.05 1.2D43 60 0.2 0.9 0.024 0.07 1.4D44 60 0.2 1.2 0.021 0.05 1.278Table 4 5. Comparison of experimental maximum radii with literature.Investigator P(atm) 4)(1%2) V(%) AT.th(`) C) R.(mm) tb(ms)Gunther [35] 1.7 2.3 - 10.7 1.5 -6.1 33 - 110 0.13 -0.50 0.10 - 0.40Tolubinsky et al.[39 ] 1 0.05 - 1.0 0.08 - 0.2 5 - 60 0.20 - 0.65 N/AAbdelmessih et al.[36 ] 1 0.19 - 0.46 0.92- 2.30 1.9 0.15 -0.25 1.5 -5.5Akiyama[38] 1 0.1-0.8 0.1 - 5 20-80 0.20 - 1.0 0.40 - 5.0Del Valle et al.[37] 1 3.44 -4.67 1.7 84 0.20 0.40This investigation 1 0.1-1.2 0.08 - 0.80 10- 60 0.50 - 1.75 2 - 150.20^0.41^0.61^0.81^1.01^1.22^1.42^1.62^1.822 .03^2.23^2.43^2.63^2.84^3.04^3.24^3.44^3.65^3.854.25^4.46^4.66^4.86^5.06^5.67^5.87^6.08^6.28^6.486.89^7.09^7.29^7.49^7.70^7.90^8.10^8.30 (ms)^ Scale 3:1Figure 4.1, Photographs of bubble growth and collapse (D24-10) for V=0.4 in/s. A7.,=20 'C and (1)=0.3 win-Figure 4.2. Growth and collapse curve for a typical bubble (D24-10)80Figure 4.3. Change in bubble shape during its lifetime.Figure 4.4. Comparison of bubble volume obtained in this study with volume evaluated byspheroidal assumption.81Figure 4.5. Normal and parallel displacement of the centroid of bubble82Figure 4.6. Bubble path in different liquid bulk subcooling.Figure 4.7. Effect of heat flux and flow velocity on bubble maximum radius.Figure 4.8. Effect of heat flux and subcooling on maximum bubble radius.83Figure 4.9. Effect of heat flux and subcooling on bubble growth time.Figure 4.10. Effect of heat flux and subcooling on bubble condensation time.84Figure 4.11. Effect of subcooling on bubble parameters at V=0.08 m/s.Figure 4.12. Comparison of experimental growth and collapse rate with Zuber[23].85Figure 4.13. Correlation of bubble growth and collapse rates.1.00.80.40.20.01.000.00 0.25 0.50 0.75t /Figure 4.14. Comparison of experimental bubble growth rate Equation (4.6) withAkiyama[38] Zuber[23], Mikic et al.[24], and Unal[28].86Figure 4.15. Comparison of experimental condensation rate Equation (4.6) withAkiyama[30], Zuber[23], and Florschuetz and Chao[31].Figure 4.16. Comparison of experimental condensation rate at low subcooling withcondensation models of Florscuetz and Chao[31] and Akiyama[30].87Figure 4.17. Correlation of maximum radius with Ja* and 0 (average correlation error =20%).Figure 4.18. Correlation for growth time with Ja* and 0 (average correlation error = 28%).Figure 4.19. Correlation for condensation time with Ja and the non-dimensional maximumradius (average correlation error =12%).CHAPTER 5CONCLUSIONS AND RECOMMENDATIONS5.1 ConclusionsThe growth and collapse of vapour bubbles in subcooled convective boiling of waterwere investigated by high-speed photography to obtain insight on the mechanism of voidgrowth at atmospheric pressure, mass flow rate of 0.02-0.20 kg/s, liquid bulk subcoolingsof 10-60 °C, and heat fluxes of 0.10-1.20 MW/m2. The effect of mean flow velocity, heatflux and liquid bulk subcooling on maximum bubble radius, bubble growth time, and bubblecondensation time were investigated. Observations were made on the bubble translationalvelocity, ejection velocity and change in bubble shape during the bubble lifetime. Based onthe analysis of high-speed photography the following were concluded:1. The bubble lifetime was divided into two distinct regions of growth and condensation.The condensation region was further subdivided into condensation with bubble slidingon the wall and condensation after bubble ejected into the flow.2. At high bulk liquid subcooling most of the condensation occurred while bubbles weresliding on the wall, though ejection was still present. The bubble radius at ejection wassmaller than the maximum bubble radius attained at the end of the growth stage.89903. Bubbles translated parallel to the wall with a constant velocity approximately equal tothe mean flow velocity during both the growth and condensation periods. The ejectionvelocities of the bubbles were in the range of 0.36-1.13 m/s.4. The effect of flow velocity on bubble parameters was found to be negligible in therange of this study. This was due to the translation of the bubbles with the cross-flow.5. At low subcooling, the bubble radius, bubble growth time and condensation timedecreased with an increase in the heat flux. The density of the nucleation sites andfrequency of bubble formation were increased with an increase in the heat flux. Athigh subcooling, the bubble maximum radius, growth time, and condensation timewere independent of the heat flux.6. Bubble growth time and condensation time were proportional to the maximum radius.The ratio of bubble growth time to bubble lifetime fell in a range of 0.27-0.44 with anaverage value of 0.33±0.04.7. Bubble growth and collapse curves were normalized with maximum bubble radius andbubble lifetime as follows: 2.2R =1- 22-2g.)0.671_[ t2^tb(4.6)8. Bubble growth rate and maximum bubble radii obtained in this study were comparedwith bubble growth models of Unal[28], Zuber[23] and Mikic et a1424]. Theexperimental growth rates were well predicted by Zuber and Mikic et al.; however the91predictions of the maximum bubble radii did not agree well with the experimentalresults.9. Bubble collapse rate and bubble condensation time were compared with thepredictions of Akiyama[30] and Florschuetz and Chao[31]. The shape of the collapsecurves were similar to the predictions of Akiyama; however the condensation timespredicted by Akiyama were two orders of magnitude smaller than found in thepresent work. The shape of the collapse curve predicted by Florschuetz et al. deviatedsignificantly from those measured in the present experiment.10. Maximum bubble radius was correlated with wall superheat (Ja,,,* ) and liquid bulksubcooling (e) ( average correlation error =20%):= 5.01 x 109 Ja,,* -1.650 -1.65^ (4.10)11. Bubble growth time was correlated with the same non-dimensional parameters as themaximum bubble radius. A simple expression was found relating the growth time tomaximum bubble radius (average correlation error =28%):t,n+ = 3.21 x 1014 Jau," -2.580 -2"88^(4.13)tm = 56.7 R1„;49^(4.15)12. Bubble condensation time was correlated to the maximum radius (R7) and liquid bulksubcooling (Ja) (average correlation error = 11.7%):t: = 106.8 Ja -m5 R:1313^ (4.18)925.2 Recommendations1. Measure the temperature profile across the flow to obtain the local subcooling and thethickness of the superheated layer. The temperature measurements would determinethe effect of true liquid subcooling and superheating on the bubble growth andcollapse.2. Perform additional experiments with higher flow velocities and different hydraulicdiameters to investigate the effect of flow and geometery on the bubble parameters.3. Investigate the effect of heat flux, local and bulk subcoolings and flow velocity on thedensity of nucleation sites and frequency of bubble formation as the present models ofbubble growth do not include the effect of increased nucleation site density andfrequency of bubble formation on bubble parameters.4. Evaluate the variation of bubble parameters for different nucleation sites.5. Develop a better method for analyzing the films so that more bubbles are digitized forone condition and statistical methods can be used for analyzing the data.6. Simulate the bubble growth numerically by the use of different boundary conditionsmatching the bubble shape observed experimentally. This simulation for differentboundary conditions will promote better understanding of the important parameters inbubble growth.93BIBLIOGRAPHY[1] El-valdl M.M., Nuclear Heat Transport, The American Nuclear Society, (1978).[2] Kay R.E., Stevens-Guille P.D. and Hillbom J.W., Jervis R.E. 'SLOWPOKE: A NewLow-Cost Laboratory Reactor', International Journal of Applied Radiation andIsotopes, Vol. 24, pp. 509-518, (1973).[3] Rogers J.T., Salcudean M., Abdullah Z., Mcleod D. and Poirier D., 'The onset ofsignificant Void in Upflow Boiling of Water at Low Pressure and Velocities', Int. J.Heat Mass Transfer, Vol. 30, No. 11, pp. 2247-2260, (1987).[4] Mcleod R.D., 'Investigation of Subcoolecl Void Fraction Growth in Water Under LowPressure and Low Flow rate Conditions', M.A.Sc. Thesis, Carleton University,Ottawa, (1986).[5] Abdullah Z., 'Investigation of Onset of Significant Void and Void Fraction UnderConditions of Low Pressures and Flow Velocities', B.A.Sc. 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Heat Transfer Conference, 8th, San Fransisco, USA, Vol.4, pp.1919-1924, (1986).[44] Brucker G.C. and Sparrow E.M., 'Direct Contact Condensation of Steam Bubbles inWater at High Pressure', Int. J. Heat Mass Transfer, Vol.20, pp .371-381, (1977).[45] Hahne E., Spindler K. and Shen N., 'Incipience of Flow Boiling in Subcooled WellWetting Fluids', Int. Heat Transfer Conference, 11th, Proc, Jerusalem, Vol. 2, pp. 69-74, (1990).[46] Hino R. and Ueda T., 'Studies on Heat Transfer and Flow Characteristics in SubcooledFlow Boiling-Part2. Flow Characteristics', Int. J. Multiphase Flow, Vol. 11, No. 3, pp.283-297, (1985).[47] Beer F.B. and Johnston E.R., Vector Mechanics for Engineers, McGraw-Hill, (1984).[48] Jiji L.M. and Clark J.A., 'Bubble Boundary Layer and Temperature Profiles for ForcedConvection Boling in Channel Flow', J. of Heat Transfer, Transaction of the ASME,Vol.86, pp. 50-58, (Feb. 1964).[49] Forster K. E., 'Growth of a Vapor-Filled Cavity near a Heating Surface and SomeRelated Questions', The Physics of Fluids, Vol. 4, No.4, pp. 448-455, (April 1961).[50] Cooper M.G., Mori K. and Stone C.R., 'Behaviour of Vapour Bubbles Growing at aWall with Forced Flow', Mt. J. Heat Mass Transfer, Vol.26, No.10, pp. 1489-1507,(1983).97[51] Dimic M., 'Collapse of One-Component Vapor Bubble with Translatory Motion', Int.J. Heat Mass Transfer, Vol. 20, pp.1325-1332, (1977).[52] Devore J.L., Probability and Statistics for Engineering and the Sciences, WadsworthInc., (1987).98Appendix ABubble Growth Model (Mikic[22])In this approach the total kinetic energy of the moving liquid at any time is equal tothe work done at the liquid boundaries. The bubble is assumed to be spherical, andexpanding in an infinite incompressible liquid. The kinetic energy of the liquid is given by:00K.E.=^u2d( Vo0^ (A.1)2 Rwhere u is the radial velocity of the liquid element. The equation of continuity is given by:u=(-1?2)Substituting (A.1) into (A.2) and integrating yields:•(R)22K.E.= 47r -p,—$ R — 1 r 2 dr =27rp1R3i?22 R^rThe net work to the liquid is expressed as:W = 47r5(p,- pjR2dRAssuming that the variation in the vapour pressure during the bubble growth is not large,(A.4) can be approximated by:4W —3 R3(Pv P..)Equating the net work done on the liquid boundary (A.5) with the total kinetic energy(A.3), one obtains:_ 2 P, 3^p,(A.6)(A.2)(A.3)(A.4)(A.5)Al?^A 2t= — and t+ =B2 B2(A.13)99The pressure difference in Equation (A.6) can be approximated with the Clausius-Clayperon equation:Pvifg(Tv Tsar) Py P-TsatUsing (A.7), Equation (A.6) becomes:k2 = A2  Tv - TsatATWhere2 if^- T 112A =(^p (T^Sat and AT = T - Tsar3 PiTsatA relationship expressing the rate of bubble growth with the vapour temperature was givenby Plesset and Zwick [19] for bubble growth in an initially superheated liquid due to aconstant temperature difference (T., - Tv):where1 B^T - Ti?=^1^v2 Vt^ATB .(12 oc1)) ja.n (A.10)(A.11)T - T  )Solving for^.( Equation (A.10), substituting in (A.8) and non-dimensionlizingATthe resulting expression, one obtains:dt+^(t+^(t,^ (A.12)where(A.7)(A.8)(A.9)Equation (A.12) integrates to:100R+ = —2[(t+ + 0 -(t+)% -1}3 (A.14)This equation simplifies to Rayleigh's Equation (2.3) at t+ < < 1 and to Plesset and Zwick'sEquation (2.12) at t+ >> 1.101APPENDIX BBubble growth model (Unal[28])Unal[28] assumed that a spherical bubble grows on a very thin, partially dried liquidfilm formed between the bubble and the heated surface (micro-layer). The bubble growthwas due to the evaporation of the microlayer balanced by the dissipation of heat at thebubble top surface (see Figure B.1). The dry area under the bubble is assumed to becircular in shape. Over its growth period, the bubble takes up heat by the evaporation ofrrD2^ D2^Dthe very thin liquid film over the area — 1 - —(1,) in which --d— is assumed to be4( D` Dconstant for a given pressure. The process of growth is assumed to be isobaric. The heatinput to the bubble from the superheated layer is neglected compared to the heat from thethin liquid film, since the ratio of the thickness of the superheated layer to the maximumbubble diameter is assumed to be small. The dissipation of heat is assumed to occur at thebubble top surface since the bottom surface faces the heater, and is ineffective in dissipatingheat. An overall energy balance on the bubble yields the following equation:702 ^D2, ^A , 702 ir . dD3qb — k 1 — 4) = richt-limb — + — p i,^(B.1)4^D 2 6 " dtwith initial condition of t = 0 D = 0. qb in Equation (B.1) is the heat flux from the verythin liquid film under the bubble and is given by Semas and Hooper[27] as follows:ATiatylciqb — 3.frc—ritwhere A1 ^the initial superheat of the very thin liquid layer under the bubble:AT. _ p sub  )(  q- h AT )(B.2)(B.3)[)Y -kspsCs7., rpi,nipi,....,ifill/ (^CI:1^17 jC* -km is evaluated from:^Nu = 0.023 Reg Pr°33^ (B.6)The condensation heat transfer coefficient at the surface of the bubble, kb, in (B.1) is givenby:CcloifgDkb -^2(ypv- Xi)(B.7)where)0.47VcD =(—^for V> 0.61 (%)^Vb = 0.61 ("X)^(B.8)V.cl) = 1^for V ^ 0.61 ("X) (B.9)and C is pressure dependent constant. Substituting (B.2) and (B.7) in equation (B.1) yieldsthe following equation:where—dD = aat - Col•Ddt(AT.TarklY) a -2p,ifs(nai);5(B.10)0.0135,g Pr '(B.11)102(B.4)3(B.5)( ^a  )g(Pi - Pv) Y2103b=  ATs'4'2(1 - %)a = (1 - 44)Solution of equation (B.10) is given as follows:2aat34(1 + 4b0:14)D(t) -(1+ abbt)Differentiating (B.14) and equating to zero, the maximum diameter is obtained:D = 1.21 aa(balcI)'1tm - 1.46bCcI)(B.12)(B.13)(B.14)(B.15)(B.16)To be able to calculate D(t),Dm and t„, with the equation (B.14), (B.15) and (B.16), a andaC must be known. Unal has shown that the value of^is constant for a given pressureCXand its value is found empirically from the experimental data available in the literature. Theavalue of —cx is therefore correlated to the pressure as follows:a = 2 x 10-5Pm90(B.17)By substituting (B.17) in (B.15), the maximum bubble diameter for atmospheric pressurebecomes:D 2^.42 x 10-5a-m (WI(B.18)where a, b and (Dare defined by (B.11), (B.12), (B.8) and (B.9). The range of applicabilityof (B.18) is:P = 0.1 -17.7 Mpa,q = 0.47 - 10.64 MW/m2,V = 0.08 -9.15 m/s,A Tsub =3-86 K,D.= 0.08 -1.24 mm104105Figure B.1. Bubble growth model proposed by Unal[28].106APPENDIX CEvaluation of Bubble VolumeThe following algorithm, written in C programming language, was employed to evaluatethe bubble volume:1. Pixels comprising the bubble projection area were scanned.2. The area of projection of bubble was evaluated:A = dA = ApixelNpuel h2 Npixel^ (C.1)where Apud (mm2) is the area of a single pixel and Npird is the total number of pixelscontained inside the contour of the bubble and including the pixels on the contour. Apixel was assumed to be square in shape with the dimension h (mm/pixel). For amagnification of twenty times on the monitor, the value of h (screen resolution) wasapproximately 0.02 (mm/pixel).3. Bubble centroid was found next by integrating the pixels as follows:11 bottom^right^ bottom^rightA A^A pixel= — Xdfl = — E E(hrpue, — 4h)h2 — — E^()Cud —^(C.2)...top pixel-left^ N 1 pixel-top pixel-left1bottom^right^ h^bottom^rightY = j'YdA= E Dhypuei — ih)h2 —^E DY pixel — 4)A^ri pixel-top pixel-left^ pixel pixel-top pixel-leftwhere xpixd,ypixd are the coordinates of the pixel (see Figure C.1).4. The x-, y- and xy-moments of inertia of the projection area were found as follows:bottom^right /x =^x' AptrelY2) = h4 E^E^(y pixel — 4)2)A pixel-top pixel-left(C.3)(C.4)107bottom^right i 2 \/), = Viy, + Apixe/X2) = h4 E^I ( 112- + ( x pixel — -1-) )A^ pixel-top pixel-left,^tbottom^right rIx), = E(Ix,y, + Axy) = h4 E E xpL„, — +xypixe, — 4)1(A^ pixel-top pixel-left(C.4)(C.6)whereI x, = ly, = 112-h3h and /xy = 0^(C.7)5. The centroidal moments of inertia were found by the use of the parallel axis theorem:(see Figure C.2):Ix„ = .rx - Ay2 (C.8)1„ = /y - A.2 (C.9)= I ^Avy (C.10)6. The orientation of the of the principal centroidal axis of the area was found from [47]:21 —tan20 - -  _ x YIx„ — ry.(C.11)where() is the angle shown in Figure C.2.7. These axis were drawn on the bubble and the axis of symmetry was chosen.8. The area on both side of the axis of symmetry was evaluated and the centroid of eacharea was found in the same manner.9. The volume of revolution of the areas on each side of the axis of symmetry was found asfollows:Vo/i = 27r/i4^ (C.12)Vo/2 = 2/r/2A2 (C.13)where 11 and 12 are distances as shown in Figure C.3.10. The total volume was defined by the average volumes of revolution from equations(C.12) and (C.13):108Vol - Vo/i + Vo/22(C.14)A pixel = h2Ix ,^ y = I , = (1/12) if1^=0x' y'^,d10110•1111.EN ■ x(XpiXel 9 Ypixel )x = hx - 0.5hpixely = hypixel - 0.5h•YFigure C.1. Nomenclature used in pixel integration.Figure C.2. Schematic diagram of the centroidal principal axes of the bubble.109Figure C.3. Nomenclature used in evaluating the volume of revolution.110111Appendix DError AnalysisTable D.1. lists the errors in the measured quantities in the experiment. The errors wereeither estimated from the manufacturers' specifications or obtained from reference[9].Table D.1. Estimated errors in the measured quantities.Measured Quantity EstimatedErrorFlow rate ±0.3%Current ±1%Voltage ±1%Inlet temperature ±1 °CWall temperature -2.21+1.2 °CGlass tube diameter ±0.09%Heater diameter ±0.15%Heater length ±0.2%Inlet and wall temperature: The error in the temperature measurements consisted of theinherent error in the calibration of the thermocouple plus the error in the calibration of theinstrumentation (d(Tin)=± 1 ° C, d(74,) =± 1.7 ° C). In the case of the wall temperaturemeasurements, an additional error was present due to convection of heat from the strippedend of the thermocouple (7 mm). The error in the temperature measurement due to effectof forced convection was estimated to be -0.5 °C [9].112Heat flux: The error in the heat flux measurements was calculated mathematically from theuncertainty of the input power measurements (± 2%) i.e. error in the measurements ofvoltage and current.Bulk subcooling: The error in the calculated bulk temperature at the filming location wascalculated mathematically by differentiating the following with respect to inlet temperature,heat flux and mass flow rate:(OPIT = T +^ (D.1)B^in thC pidTB - -OTB dTin + OTB di) + OTB chit (D.2)OTin^4^arildTB =d7 + (TB - Tinfl + 1-]^(D.3)The maximum temperature difference between the inlet and the filming location was 60°C.The various error terms in (D.3) are given in table D.1.d(AT.th) = dTB a (1° C) + (60°C)(0.020 + 0.003) = ±2.4°CTime: The error in the time measurement is made up of: error in the assumption ofconstant film speed (0.01 ms); accuracy of the pulse generator (±0.01 ms); and the error inzero time. In this experiment, the zero time corresponds to the frame preceeding the firstappearance of the bubble. At a camera speed of 5000 fps the zero time error will be1/(5000fps) = 0.2 ms. In this experiment since the same convention is used to determine thezero time for every bubble cycle, this error is not added to the overall error in the timemeasurement.Volume, Normal and Parallel diameters: Errors were calculated by measuring thevolume, and maximum and minimum diameters of an apple with the pixel integrationtechnique and comparing it with the direct measurement of the volume of the apple (±5%).Radius: Error in the radius was obtained by differentiating Equation (3.5):113dR 1 d(Vol) 1- x 0.05 = ±1.67%R 3 Vol^3Normal and Parallel Displacement: Errors included uncertainty in the location of thenucleation site (2 pixels) and uncertainty of the centroid (2 pixels). The resolution ofmagnified images were 0.02 mm/pixel.Repeatability of Results Obtained from Film Analysis: Figure D.1 -D.3 show thedigitization results for condition D22-30 for two different measurements of the samebubble cycle. The error involved in the repeatability of the digitization results is due to thetracing of the bubble outline and is caused by human error.4.03.0?-^2.01 .00.0 I^II^II^11111^III^I^ II^I^I^1^II 0.0^1.0 2.0^3.0 4.0 50Figure D.1. Repeatability of bubble volume and radius measurementsTime (ms)114Figure D.2. Repeatability of normal and parallel displacement measurements.Figure D.3. Repeatability of measurements of diameters normal and parallel to centroidalprincipal axis of bubble.n^Eln Ja^EineEln Ja ln 0Eine ElnOlnJa: ENV ,DIA+.I, ln kiln Ja:Elnk,Ine_ln K-x_ Y _(E.3)Eln Ja: EOnfa:32116Appendix EA Sample of Correlation ProcedureThe following general form was assumed to correlate the bubble maximum radiuswith experimental conditions:lt:, = KJa0Y^ (E.1)where K, x, and y are constants to be determined from multiple regression analysis.Equation (E.1) was linearised by taking the log on both sides of the expression:ink, =lnK+xlnJa: -Fyln0^(E.2)Using the least square method, the values of the constants in (E.2) were obtained from thesolution of the following matrix[52]:where n is the number of different conditions tested and I, = E . The coefficient ofnmultiple determination (R2) is defined as:117R2 _ 1 _ E(Yi - 502 (EA)E(Yi - Yi)2where y is the experimental value, j; is the predicted value based on the correlation, and yis the average of experimental values (y is denoted as the parameter to be correlated, i.e.,in this case R,:).

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