Bubble Formation in a Horizontal Channel at Subcooled Flow Condition

Transcription

1 Bubble Formation in a Horizontal Channel at Subcooled Flow Condition by Saman Shaban Nejad A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Mechanical and Industrial Engineering University of Toronto Copyright by Saman Shaban Nejad, 2013

2 Bubble Formation in a Horizontal Channel at Subcooled Flow Condition Abstract Saman Shaban Nejad Master of Applied Science Mechanical and Industrial Engineering University of Toronto 2013 Bubble nucleation at subcooled flow boiling condition in a horizontal annular channel with a square cross section by the use of high-speed camera is investigated. The channel represents a scaled-down version of a single rod of CANDU reactor core. The experiments were performed by the use of water at pressures between 1-3 atm, constant heat flux of MW/m 2, liquid bulk subcooling of 32-1 o C and mean flow velocities of m/s. Bubble lift-off diameters were obtained from direct high speed videography. The developed model for the bubble lift-off diameter was obtained by analyzing the forces acting on a bubble. Furthermore, a model for the bubble growth rate constant was suggested. The proposed model was then compared to experimental data and it has shown a good agreement with the experimental data. Additionally, the effects of liquid bulk subcooling, liquid pressure and mean flow velocity on bubble lift-off diameter were investigated. ii

3 Acknowledgments First of all, I would like to thank my supervisor, Dr. Nasser Ashgriz, for his guidance, continued support and trust through all phases of this research work as well as his suggestions and contributions during the data analysis and thesis write-up. I would also like to thank Lu Liu for his help during image analysis. Technical advice of my fri, Dr. Reza Karami during high-speed videography and digital image processing as well as Osmond Sargeant and Terry Zak during various stages of the experimental setup is greatly appreciated. Finally, I wish to thank my family and fris for their great support and continuous encouragement during this rewarding experience which made this investigation possible. iii

4 Table of Contents Abstract... 2 Acknowledgments... 3 List of Tables... 7 List of Figures... 8 Nomenclature Chapter 1 Introduction Introduction CANDU Power Plant- Overall View Need to Characterize the Nucleation Process... 5 Chapter 2 Research Objectives Research Objectives Tasks Approach... 9 Chapter 3 Literature Review Literature Review Reactors Operating Conditions CANDU Nuclear Fuel Rod System Parameters Boiling Overview of Two-Phase Flow Models Nucleate Boiling Wall Heat Flux Models for Departure and Lift-off Diameters in Subcooled flow iv

5 3.3 Acting Forces on a Sliding Bubble Chapter 4 Experimental Procedure Experimental Procedure Scaling Criteria and Experimental Conditions Scaling Subcooled Boiling Region Water Scaled-down facility Digital Photographic Method for Visualization Errors and Uncertainty Analysis Chapter 5 Results and Discussion Results and Discussion Visualization and Image Analysis Coalescence Experimental Analysis Balance of forces acting on a bubble at the departure Balance of forces acting on a bubble at the lift-off Comparison between the experimental and predicted results Chapter 6 Summary and Conclusions Summary and Conclusions Bibliography Appix A: Force Balance in x-direction (departure moment) Appix B: Bubble size measurement technique B.1. 3-D Bubble Lift-off Diameter Approximation using 2-D Image B.2. Bubble Lift-off Velocity B.3. Bubble Upstream, Downstream, and Inclination Angles at Lift-off v

6 Appix C: MatLAB code for image analysis C.1. Procedure C.2. MatLAB Code Appix D: Mechanical Properties of the Zirconium tubes vi

7 List of Tables Table 3-1: Operating conditions of various nuclear reactors 12 Table 3-2: Suggested correlations for the bubble departure 31 Table 3-3: Suggested correlations for the bubble lift-off diameter 37 Table 4-1: Set points for CANDU nominal operating conditions and the modeled chamber 54 Table 5-1: Advancing and Receding contact angles of the bubble shown in the Fig Table 5-1: Data bank 90 vii

8 List of Figures Figure 1-1: Overall diagram of a typical CANDU Power Plant [2]... 2 Figure 1-2: CANDU nuclear reactor core [5]... 3 Figure 1-3: Fuel Rods, Fuel Bundles, Pressure Tubes and Calandria [7]... 4 Figure 3-1: Fuel rod configuration [8] Figure 3-2: Typical boiling curve for water at 1 atm pressure [11] Figure 3-3: Stages of Bubble Formation [16] Figure 3-4: Illustration of bubble protruding out of the superheated liquid layer, by Guan [17] Figure 3-5: Schematic representation of subcooled flow boiling, Kandlikar [19] Figure 3-6: Boiling curve from the Bowring [23] model Figure 3-7: Boiling curve for the Bergles and Rohsenow [27] model Figure 3-8: Force balance of a vapour bubble at a nucleation site Figure 3-9: Schematic diagram of bubble nucleation phenomenon Figure 4-1: The axial void fraction distribution during forced convection subcooled boiling 49 Figure 4-2: Axial profiles of the flow quality and thermodynamic equilibrium equality in the case of a constant wall heat flux Figure 4-3: Overall view of the experimental setup Figure 4-4: Schematics of the Tank Assembly Figure 4-5: Tank assembly setup Figure 4-6: The Schematics of the Chamber Assembly Figure 4-7: Chamber assembly setup Figure 4-8: Camera Setup viii

9 Figure 4-9: A sample bubble for image processing Figure 4-10: A sample of the cropped image Figure 4-11: Binarized image of the sample bubble Figure 4-12: Schematic of a bubble at the final stage of image processing Figure 4-13: The sample bubble before filtering the noise Figure 5-1: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1 atm, Mass Flux: 350 kg/m 2 s, Heat Flux: 124 kw/m 2, Subcooling: 4 o C) Figure 5-2: Growth and collapse curve for a typical bubble at Pressure: 1 atm, Mass Flux: 350 kg/m 2 s, Heat Flux: 124 kw/m 2, Subcooling: 4 o C Figure 5-3: Normal and parallel displacement of the centroid of a typical bubble at Pressure: 1 atm, Mass Flux: 350 kg/m 2 s, Heat Flux: 124 kw/m 2, Subcooling: 4 o C Figure 5-4: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1.5 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 9 o C) Figure 5-5: Bubble growth in superheat layer (same flow conditions as those of the Fig. 5-4) Figure 5-6: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1.0 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 9 o C) Figure 5-7: Consecutive images of the Bouncing phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass Flux: 350 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 16 o C) Figure 5-8: Consecutive images of the Sliding phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 26 o C) Figure 5-9: Schematic of the bubble Coalescence in Pool and Flow Boiling [69] ix

10 Figure 5-10: Consecutive images of the Coalescence phenomenon in subcooled flow boiling (Pressure: 2.5 atm, Mass Flux: 400 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 15 o C) Figure 5-11: Consecutive images of the Coalescence phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass Flux: 350 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 16 o C) Figure 5-12: Force balance of a vapour bubble at lift-off Figure 5-13: Bubble lift-off diameters vs. Subcooling for all the cases at 1 atm and their corresponding standard deviations Figure 5-14: Effect of the liquid pressure on the bubble lift-off diameter (heat flux: 124 kw/m2) Figure 5-15: Effect of the mass flux on the bubble lift-off diameter (heat flux: 124 kw/m2) Figure 5-16: Effect of the fluid subcooling on the bubble lift-off diameter (heat flux: 124 kw/m2, mass flux: 300 kg/m2.s) Figure 5-17: Comparison of the experimental data with the predicted data at different pressures and for different flow conditions Figure 5-18: Comparison of the experimental data versus the predicted data in different conditions (mass flux) Figure 5-19: Comparison of the experimental data versus the predicted data in different conditions (subcooling) Figure 5-20: Prediction results of the proposed model against the first set of the experimental lift-off diameter (average error: 21.07%) Figure 5-21: Prediction results of the proposed model against the second set of the experimental lift-off diameter (average error: 16.81%) x

11 Figure 5-22: Prediction results of the proposed model against the entire experimental lift-off diameter (average error: 19.91%) Figure 5-23: Prediction results of five model against the present lift-off diameter data Figure B-1: Images taken 0.25 apart at inlet conditions of 100 o C, 1.5atm, 2gpm. The indicated bubble detached from the heater during this period Figure B-2: Bubble Contact angle lines xi

12 Nomenclature 1. Symbols b Bubble growth constant C Dimensionless coefficient as indicated by its subscript C p D D 2 O D w F F f Specific Heat Capacity Diameter Deuterium Surface contact diameter Force Pool boiling heat transfer suppression factor Bubble Frequency [s -1 or Hz] G Average Mass flux, [Mg/m 2 s] g Acceleration due to Gravity [9.81m/s 2 ] G s h H Dimensionless shear rate Heat transfer coefficient Bubble height H fg Latent heat of evaporation (Ch. 3) h fg Latent heat of evaporation (Ch. 4) Ja Jakob Number k Thermal Conductivity [W/m 2 K] l length M Molecular weight of the liquid Mass flow rate N pch N S Nu p Pe Pr p r Phase Change Number Subcooling Number Nusselt Number Pressure Pecelt Number Prandtl Number Critical pressure xii

13 Heat flux r Radius Re Reynolds Number S Suppression factor S Single-phase heat transfer enhancement factor St Stanton Number t Time [s] T Temperature [K] u x-component velocity [m/s] U 235 u r Uranium-235 Relative velocity between bubble centroid and liquid flow [m/s] V Volume [m 3 ] v Y-component velocity [m/s] W Width We Weber Number (dimensionless) X Quality x distance or position 2. Greek Letters Thermal Diffusivity [m 2 /s] Friction Factor Dynamic Viscosity [Ns/m 2 ] Density [kg/m 3 ] Surface Tension [N/m] Contact angle [deg or rad] Shear Stress [N/m 2 ] ν Kinematic Viscosity [m 2 /s] Difference xiii

14 3. Subscripts a b b cp d du e eqb f fc fdb fg g h h i inl int l liq lo m nb pb pool qs r s advancing bubble- bulk buoyancy (for forces) contact pressure contact unsteady drag effective equilibrium fluid forced convection fully developed boiling fluid-gas (phase change) gas (or vapour) hydraulic (for diameter) hydrodynamic (for forces) inclination inlet intersection liquid liquid lift-off mean contact angle nucleate boiling partial boiling pool boiling quasi-steady receding surface xiv

15 s sat sl sub TP w or wall x y surface tension (for forces) saturation shear lift subcooling Two-Phase wall x-direction y-direction 4. Abbreviations BWR Boiling Water reactor CANDU CANada Deuterium Uranium CHF Critical Heat Flux DNB Departure from Nucleate Boiling DOF Degree Of Freedom FDB Fully Developed Boiling ONB Onset of Nucleate Boiling OSV Onset of Significant Void PB Partial Boiling PHWR Pressurized Heavy Water Reactor PNVG Point of Net Vapour Generation PWR Pressurized Water Reactor VVER Russian-type pressurized water cooled reactor xv

16 xvi

17 Chapter 1 Introduction 1

18 2 1 Introduction 1.1 CANDU Power Plant- Overall View CANDU (CANada Deuterium-Uranium) reactor is a Canadian pressurized water nuclear reactor in which heavy water is used as a coolant. Therefore, it is classified as a Pressurized Heavy Water Reactor or PHWR. In Ontario s Power generation system, CANDU has a vital role since it generates almost 50% of Ontario s electricity (16% of Canada s overall electricity requirements). This Canadian designed and built reactor is efficient and relatively low capital cost, and has been in service with high reliability and safety for over 35 years [1]. Figure 1-1: Overall diagram of a typical CANDU Power Plant [2] Fig. 1-1 shows a CANDU power plant consisting of the following three compartments: a control system building, a reactor building, and a building for the steam turbine and the electrical generator. The main component in this plant is the nuclear reactor where the required heat is generated as a result of fission reactions. The CANDU reactor is designed to use two indepent water loops in order to remove the heat from the nuclear core. The primary loop, in which heavy water, D 2 O, is used as the heat transfer fluid, and contains high pressure tubes. All the fuel bundles are placed inside these pressure tubes. The released heat due to the nuclear fission reactions is removed by the heavy water flow, through the pressure tubes. Heavy water at very high pressures is used to allow it to be heated to higher temperature, and therefore more heat to be removed from the reactor core. The inlet temperature of the heavy water is lower than the saturated temperature and therefore, the

19 3 flow is subcooled and single phase at the entrance to the core. Pressurized heavy water enters the pressure tubes as a subcooled liquid at around 11MPa at ~260 o C with a degree of subcooling (or subcooling margin) of around 50 o C at 24kg/s [3], [4]. Subcooled liquid is a liquid that its temperature is below its saturation temperature and the degree of subcooling is the difference between the subcooled liquid temperature and the saturation temperature of the liquid at the specified pressure. The heavy water flows through the fuel channels over 37- element bundles and by absorbing the generated heat, it eventually becomes close to saturated mixture. The heated flow exits from the fuel channel as a low quality (~3% to 4%) two-phase mixture and enters the feeders with a pressure drop of around 1MPa [3]. After exiting the core and reaching the steam generator, all of the heat from the hot heavy water is absorbed by the light water in the secondary loop and then, the light water becomes steam which is fed to the steam turbine in order to generate electricity. 1. Fuel Bundles; 2. Calandria; 3. Control Rods; 4. Pressurizer; 5. Steam Generator; 6. Light water Pump; 7. Heavy water Pump; 8. Fuel Loading Machine; 9. Moderator; 10. Pressure Tube; 11. High Pressure Steam (to Steam Turbine); 12. Water Condensate (from Condenser); 13. Reactor Containment Building; 14. Primary Loop Figure 1-2: CANDU nuclear reactor core [5] Calandria is where all the pressure tubes are placed and contains another loop of heavy water used as a moderator. The moderator, in contrary to the primary loop with heavy water, is kept at low pressures, i.e. atmospheric pressure. Cadmium rods (28 rods in some moderators) are submerged into the heavy water of the moderator in the Calandria. these rods absorb the

20 4 radiation and are control rods which serve as an emergency shutdown system in case of an accident, by a gravitational drop. One of the main design advantages of the CANDU reactor is the use of a horizontal core containing many small diameter pressure tubes (about 4 ID) in which the uranium fuel bundles are placed. These horizontal pressure tubes are typically 6 m long and can sag in the middle after many years of service. As a result of having horizontal orientation, on-line refueling of the reactor at full power can be accomplished. A refueling machine pushes in a new fuel bundle at one of the pressure tube and removes an old bundle at the other of it. In contrast, light water reactors which are more popular in other countries must be shut down for re-fueling purposes. Each fuel rod is approximately 50 cm long and 1 cm in diameter and is placed inside a zirconium alloy tube. Fuel rods contain natural uranium. The heat energy is generated via a fission reaction by the fissile uranium -235 (U 235 ) which make up about 0.72% of the fuel mass [6]. Figure 1-3: Fuel Rods, Fuel Bundles, Pressure Tubes and Calandria [7] The heavy water in the primary loop serves the dual purpose of the neutron moderator from the nuclear fission reaction and cooling the fuel rod bundles. Since the main purpose of this work is on the heat transfer characteristics around the fuel bundles, an electric heater and light water have been used instead of the uranium fuel rod and heavy water, respectively.

21 5 Therefore, no nuclear fission reaction is involved and no need of heavy water is required (the neutron moderating properties are not required if nuclear fission reaction is not present). This system was scaled down in ter of pressure, mass flux, heat flux, and temperature to investigate the bubble characteristics (although the fuel rod will be 1:1 scale). The horizontal orientation of the pressure tubes, fuel bundles and subcooled two-phase flow phenomenon are closely related to the objectives and scope of the present project as are discussed later. It should be noted that the only heat source for the coolant flow in the fuel channel is from the fuel bundles. These bundles comprise of 37 (in most CANDU reactors) fuel rods, which are the main interest for this project. This study particularly focuses on the interface between the heat supply and the coolant. 1.2 Need to Characterize the Nucleation Process Because of the high heat generation rate on fuel bundles in the pressure tubes, boiling phenomenon is used to remove heat from the fuel bundles. In CANDU, heavy water flows over the horizontal tube bundle and removes heat from the tubes. Subcooled water enters the channel and due to high heat transfer rate, evaporation occurs and finally two-phase flow leaves the channel. In the nuclear rod bundles, critical heat flux (CHF) limits the amount of power which can be obtained. Consequently, understanding the heat transfer characteristic in CANDU reactor is critical since the heat transfer from the reactor fuel rods is bounded by the Critical Heat Flux (CHF). If CHF is reached, the coolant cannot provide sufficient cooling for the heat removal from the heater surface, and this leads to an uncontrolled temperature rise and eventual failure of the fuel rod cladding material. This is normally characterized either by a sudden increase in the surface temperature or by a small temperature spikes on the heated surface. Thus, exceeding the critical heat flux is associated with safety risks as well as economic losses. Water-cooled reactors should be designed with sufficient safety margins to prevent such occurrences. The flow inside the CANDU reactor core is subcooled flow. However, since the heater surface is usually hot, bubbles may form on the surface. These bubbles grow in size and separate into the core flow, but they usually collapse since the core flow is subcooled. The characteristics of the bubbles can change by the flow parameters, such as heat flux, mass flux, subcooling, and pressure. Changing from a single-phase subcooled flow to a two-phase

22 6 subcooled flow starts by the bubble formation on the heater rod. This phenomenon can eventually lead to CHF. In spite of a great quantity of experimental and theoretical studies, knowledge of the precise nature of CHF and subcooled boiling, i.e. bubble nucleation, is still incomplete and the mechanis of a boiling crisis are still not well understood. This is mainly due to the very complex nature of the two-phase flow with heat transfer. Due to an incomplete knowledge of boiling crisis mechanis, experimental investigations on the subcooled boiling have to be performed for each specific design of nuclear reactors. Validated prediction methods for the design condition must be derived. This leads to a large amount of subcooled boiling data banks and bubble nucleation prediction methods. Because of the complexity of the problem, the experimental investigations on the bubble formation have to be performed for each specific design and flow conditions. Due to the limitation of the technical feasibility and financial expense, these experiments have often been performed in a scaled model system. Two different modeling techniques are available: geometric modeling and fluid modeling. In the geometric modeling, simplified flow channels, e.g., circular tubes, instead of typical rod bundles are used. By using such simple flow channels, it is possible to systematically study the effect of different mentioned parameters on heat transfer and gain detailed knowledge of the nucleation process for a wide range of test parameters. In the fluid modeling, a substitute fluid, e.g. Freon-12, is used instead of the water. By a proper selection of a model fluid, the operating pressure, operating temperature, and the heat power required can be reduced significantly. Using such modeling methods, a large number of empirical correlations has been developed for the bubble formation and CHF conditions.

23 Chapter 2 Research Objectives 7

24 8 2 Research Objectives A better understanding of a thermal-hydraulic phenomenon taking place inside a nuclear reactor core is necessary for its safe and efficient operation. The scope of the present study is to obtain experimental data on the bubble formation and its characteristics in CANDU nuclear reactor. For this purpose, a set of experiments have been performed on a horizontal and uniformly heated channel. Bubble nucleation information is obtained and based on the gathered data, a new analytical model for the bubble growth and departure from the heater surface is proposed. 2.1 Tasks The following tasks are achieved: 1. Development of scaling parameters to scale down the CANDU reactor core conditions: In order to design a scaled down test section, a detailed analysis of the bubble formation inside the tube bundles is performed and a set of dimensionless numbers are developed. These dimensionless numbers are then used to design the scaled down test section. 2. Design and construction of an experimental facility: An experimental facility to allow for the measurement of bubble nucleation process on a horizontally oriented heated tube was constructed. The heated tube is inside a channel having similar dimensions as those in channels of a 37-element fuel bundle. The design is inted to nearly duplicate a scaled down model of a CANDU reactor pressure tube together with only one replica of 37-element fuel bundles placed inside. Also a preliminary photographic study including image analysis was performed in order to develop correlations that characterize bubble properties. 3. Scoping Study: Experimental investigation of the bubble formation and migration throughout the system at various operating conditions was performed. Thermal and physical characteristics of the rod-liquid interface were observed and data on the bubble lift-off diameter were collected. 4. Validating and Comparison: The experimental data were compared with other investigators experimental data. In addition, proposed models and correlations were

25 9 validated by the use of experimental data, and then compared with previous proposed models. 2.2 Approach A better understanding of the bubble nucleation in subcooled flow is needed and thus, is investigated through a review of experimental visualization at several conditions. Various two-phase flow regimes occurring at ONB-OSV region are reported and classified. Theoretical and experimental bubble and wall heat flux models developed by others and used in the past studies are also reviewed and related to the current experimental findings. An appropriate wall temperature model as well as the bubble lift-off diameter approach is then selected (chapter 3). Required experimental setup is described in chapter 4. Two-phase flow experiments were performed and the flow is characterized using a high-speed camera. The selected bubble lift-off and wall temperature concepts from chapter 3 are then theoretically developed for the practical applications. Validation and sensitivity analysis are then performed and the average errors are reported in chapter 5. The conclusion of the current work and the recommations for the future works are further explained in chapter 6.

26 Chapter 3 Literature Review 10

27 11 3 Literature Review 3.1 Reactors Operating Conditions Bubble formation and CHF highly deps on the geometrical conditions as well as thermalhydraulic conditions. The followings are the most important parameters affecting the bubble formation and CHF in a fuel element: Pressure Mass flux Steam quality Fuel rod diameter Pitch to rod diameter ratio Fuel rods configuration Power distribution Spacers Table 3-1 gives an example of the operating conditions for different reactor designs [8]. This table is just an example of each reactor group and it does not show all the operating conditions that one design can have. For instance, operating pressure for different designs of PWR s can range from 15.0 to 16.0 MPa. The changes of the mass flux are more significant. In designs of PWR, PHWR and VVER reactors, it was tried to avoid high void fraction in sub-channels and therefore, the temperature of the coolant is always below the saturation temperature. On the other hand, BWR s have an average steam quality of 0.15 at the core outlet due to high steam fractions at the core outlet [8].

28 12 Table 3-1: Operating conditions of various nuclear reactors [8] PWR BWR CANDU (PHWR) VVER Pressure, p, [MPa] Ave. Mass flux, G, [Mg/m 2 s] Ave. Outlet steam quality X, [-] Fuel rod diameter d, [mm] Pitch to diameter ratio, [-] Fuel configuration rods Square Square Hexagonal Hexagonal ** PWR: Pressurized Water Reactors; BWR: Boiling Water Reactors; CANDU: Canada Deuterium Uranium; VVER: Russian-type pressurized water cooled reactor For water-cooled reactors, there are usually two different kinds of fuel rod configurations, i.e. square and hexagonal, as shown in Fig. 3-1: a) Square lattice b) hexagonal lattice Figure 3-1: Fuel rod configuration [8]

29 13 In forced convective channel flow, two different types of boiling crisis are considered. In the subcooled or low steam quality region a boiling crisis occurs by the transition from nucleate boiling to film boiling or departure from nucleation boiling (DNB). In the higher steam quality region, mostly in annular flow, the boiling crisis originates from a depletion of the liquid film (dryout). In the fuel assembly of PWR, PHWR and VVER reactors, the first kind of boiling crisis (DNB) is mostly expected because of low steam quality in sub-channels. In the fuel assembly of a BWR, attention is paid to the boiling crisis of the second kind (dryout) [8] CANDU Nuclear Fuel Rod System Parameters Each CANDU reactor contains horizontal channels deping on its model, and in each of the horizontal channels a Calandria tube is placed which consists of the fuel rods, heavy water coolant and pressure tube. These channels have a square lattice pattern at a standard pitch of which form an approximately circular array [9]. On the other hand, each fuel rod is approximately 50 cm long and 1 cm diameter. 3.2 Boiling Subcooled flow boiling is one of the main methods in many industrial applications in order to achieve the highest possible heat transfer. Subcooled means that the bulk of the liquid, e.g. water, is below its saturation point and the saturation temperature is exceeded only at a heated surface. Thus, both convective (i.e. forced) and conductive heat transfer methods are in use in this mechanism. Once the temperature of the heated surface and consequently, the layer of subcooled liquid, which is in contact with it are high enough, bubbles form. These steam bubbles grow and leave the heated surface once they reach their critical sizes, which are function of the flow regime of the surrounding fluid, surface roughness and heat flux. At this level of heat transfer, heat is not only removed by turbulent convection but also by transient conduction and evaporation as a result of nucleating and departing bubbles. After departing the heated surface, the bubbles condense as they release their latent heat to the surrounding liquid. Therefore, to accurately model the wall heat flux distribution, all the information regarding the nucleation site density, size of the departing bubbles, and the bubble formation frequency should be taken into account. In subcooled flow boiling, the bulk

30 14 liquid is subcooled while vapour is generated near the heating surface due to the local superheat. The local superheat activates the nucleation sites on the heater surface for bubble nucleation. There are two mechanis of boiling that are responsible for the bubble nucleation, pool boiling and flow boiling. The main difference between the two is that in pool boiling the liquid is in static mode and no velocity is involved, while on the other hand, in flow boiling there is fluid flow and therefore velocity effects are involved. After the bubbles formation, they migrate to the subcooled flow and therefore, somewhere downstream, the flow becomes two-phase flow. The two-phase flow behavior has been extensively studied theoretically and experimentally since it occurs in wide industries such as in nuclear reactors, boilers, oil wells and pipelines, etc. In spite of the large amount of research effort in this field, there is still some level of uncertainly associated with it Overview of Two-Phase Flow Models In the early literature, the flow boiling was considered to be the same as pool boiling. But later it was shown there are differences between the two, in particular, the bubble formation process and the critical heat flux. Therefore, different models for each flow patterns and tube or annuli orientation are developed. In addition to the mechanis which are explained below, flow instability is also found to lead to CHF. However, here it is assumed that the two-phase flow is stable and no discussion of this effect is provided. Boiling is classified as pool boiling or flow boiling, deping on the presence of bulk fluid motion. Boiling is called pool boiling in the absence of bulk fluid flow and flow boiling (or forced convection boiling) in the presence of it. In the pool boiling, any motion of the fluid is due to the natural convection currents and the motions of the bubbles are under the influence of the buoyancy. In the flow boiling, the fluid is forced to move in a heated pipe or over a surface by external means such as a pump. Therefore, flow boiling is always accompanied by other convection effects. Pool and flow boiling are further classified as subcooled boiling or saturated boiling, deping on the bulk liquid temperature. Nukiyama has performed the pioneering work on the boiling by using an electrically heated

31 15 nichrome and platinum wires immersed in liquids [10]. He found that boiling takes different for, deping on the temperature difference between the liquid and the heater surface. The four different boiling regimes which are shown below are: Single phase convection, Two-phase nucleate boiling which is further divided into partial and fully developed subregions, transition boiling, and film boiling. Figure 3-2: Typical boiling curve for water at 1 atm pressure [11] On the other hand, flow boiling exhibits the combined effects of convection and pool boiling. The flow boiling is also classified as either external or internal flow boiling deping on whether the fluid is forced to flow over a heated surface or inside a heated tube. External flow boiling over a plate or cylinder is similar to pool boiling, but the added motion increases both the nucleate boiling heat flux and the critical heat flux considerably. Internal flow boiling is much more complicated in nature because there is no free surface for the vapor to escape, and thus, both the liquid and the vapor are forced to flow together. Forced convective nucleate boiling is very effective in achieving a high heat flux with a small temperature difference between the heated surface and the cooling fluid; however, there is a boundary for this effective heat transfer regime, which is referred to as the departure from nucleate boiling (DNB). Reliable understanding of this DNB phenomenon is important for effective and safe

32 16 operation of nuclear syste and other thermal-hydraulic equipment [12]. In general, DNB is a transition which causes the heat transfer regime move from nucleate boiling to film boiling (or partial film boiling). This transition also involves the change from bubbly flow to inverted annular flow. In spite of broad research in this field, detailed physical mechanis leading to DNB have not been clearly understood. The main reason for that is the difficulty in observing the near wall region [13]. Three different flow regimes in flow boiling are as follows: Type 1: Bubbly flow Bubbly flows happen at high mass flux and high subcooling. In this type of flow, individual bubbles nucleate, sometimes slide and detach but not a large number of them coalesce. Wall rooted bubbles are observed to coalesce with neighboring bubbles along the flow stream in some cases [14]. Bubble sizes increase with decreased subcooling, decreased velocity and lower pressure. Type 2: Vapour clots This can be seen usually at moderate subcooling, and the formed bubbles detach from the nucleation sites. At regions close to CHF, most of the formed bubbles stay within the bubbly layer and vapour clots form as a result of the coalescence among the bubbles. The length of vapour clots are governed by Kelvin-Helmholtz instability. One may observe liquid film or bubbly layer between the vapour clots and heated wall. In general, with increasing the subcooling and flow rate, overall bubbly layer thickness and bubble size decreases. Type 3: Slug flow It can be observed at low mass flux and near saturation. Vapour slugs usually have a thin liquid film along the wall. The wall temperatures fluctuate as a result of high temperatures corresponding to the vapour slugs. In many cases the liquid film is not observed to dry out at CHF [15] excluding the occurrence of dry-out type boiling crisis at these conditions. In conclusion, it can be said that in these types of DNB regimes there is no sudden change in macroscopic two-phase flow pattern as CHF is reached. For instance, transition to slug flow

33 17 at high heat flux was not observed to trigger DNB. Note also that due to strong nonequilibrium conditions at CHF, conventional adiabatic or low heat flux two-phase flow regime map cannot be used to predict DNB flow regimes [13] Nucleate Boiling The bubble formation is referred to as the nucleation. Nucleation can be divided into two categories. The first one is called homogeneous nucleation, which can occur as a result of perfect heated surface without any preferential nucleation sites. The other type is called the heterogeneous nucleation and it is attributed to the imperfection in the heated tube and presence of susped particles in the subcooled liquid. In this type, nucleation happens on cavities. First, the vapor trapped in these cavities receives energy from the hot surface and starts growing. This is Stage I as shown in Fig. 3-3 and is called the waiting period. Then, the bubbles keep increasing their volume and reach the mouths of the cavities. This is Stage II and is called the growth period. The last stage happens when the radius of the bubbles and the cavities are equal. This is Stage III, the departure period. After this point, the bubbles can collapse or continue to grow and depart the surface deping on the conditions. Figure 3-3: Stages of Bubble Formation [16] The asymptotic growth phase starts once the bubble reaches a certain size after which the bubble no longer grows monotonically [17]. When a bubble reaches outside of the superheated liquid layer and into the bulk liquid flow, condensation occurs due to the presence of the subcooled bulk liquid. Therefore, both phenomena, i.e. vapour generation in the microlayer at the nucleation site and condensation at the top interface of the bubble,

34 18 happen at the same time and result in fluctuation of the bubble size. Deping on the wall superheat, temperature of the superheated liquid layer, and the liquid subcooling, a bubble may collapse on a nucleation site before departure as observed by Situ et al. [18]. This occurs if the rate of condensation at the bulk liquid interface is higher than the rate of vapor generation at the microlayer. Once bubbles grow to a certain critical size on the nucleation site, as a result of convective flow related forces, the bubble will depart by either sliding on the heater surface and then lift-off or detach from the heater surface without sliding. Figure 3-4: Illustration of bubble protruding out of the superheated liquid layer, by Guan [17] Wall Heat Flux Kandlikar [19] divided the heat transfer area under the subcooled flow into three main regions named as follows: i) Single-phase heat transfer prior to ONB (Onset of Nucleate Boiling), in which the wall temperature of the heater is below the local saturation temperature of the liquid or just a few degrees more. In this region, the heat transfer coefficient, h fc, remains constant (only if one neglects the minor changes of the liquid properties with temperature), and the raise of the wall temperature is linear and parallel to that of the bulk liquid. From Fig. 3-5 at location B, as Kandlikar mentioned, the wall temperature passes the local liquid saturation temperature, but nucleation will not occur instantly, since some amount of wall superheat is necessary to activate cavities existing on the wall. ii) The second region starts at location C, which is called the Onset of nucleate boiling, or ONB. Starting from the nucleation sites, cavities become active, and therefore, the

35 19 nucleate boiling heat transfer increases its contribution to heat transfer and gradually reduce the single-phase convective heat transfer. This region lasts until point H on Fig. 3-5 and is broke down into three sub-regions. The first sub-region, which starts from point C, is called Partial Boiling region (PB). The generated bubbles in this region due to the exposure to the subcooled liquid flow, cannot grow and thus, they are condensed. By increasing the bulk liquid temperature downstream of the ONB, a thin layer of bubbles form on the heater wall and becomes populated by more bubbles slowly. Fully Developed Boiling (FDB) starts from point E, which is a point where convective heat transfer (single-phase heat transfer) becomes insignificant. In FDB, wall temperature remains constant up to the point where the newly defined Significant Void Flow (SVF) sub-region starts. In this region, the convective heat transfer becomes significant once again due to the two-phase flow existing in SVF. This region starts at point G, which is called Net Vapor Generation, or NVG (also called OSV, onset of Significant Void). Upstream of this point, the vapor volumetric flow fraction is very small. The main focus of this report is on this region and the experimental results are mostly for late Partial Boiling Region and early Fully Developed Region. iii) Further downstream, point H is located where the saturation condition under thermodynamic equilibrium is reached and the flow beyond this point is covered under saturated flow boiling. This is the third region and will not be covered in this report.

36 20 Figure 3-5: Schematic representation of subcooled flow boiling, Kandlikar [19] Various models were developed to predict the heat flux and heat transfer rate in each region. According to Warrier [20], developed models to predict the heat transfer rate during the subcooled flow boiling can be divided into the following three categories: 1) Empirical correlations for the wall heat flux, which is mostly limited only to the prediction of total wall heat flux for a specific flow situation. This group does not include modeling of the heat transfer mechanis involved and therefore, it is not able to give any additional information in regards with the partitioning of wall heat flux between the liquid and vapor phases. 2) Empirical correlations for partitioning of the wall heat flux, which are based on the relevant heat transfer mechanis and can provide information of each heat flux components

37 21 individually. As a result these correlations can be used for both the prediction of the wall heat flux and the partitioning of the wall heat flux between the liquid and vapor phase. The main goal of these correlations is to calculate the bulk void fraction, and therefore they mostly focus on how the given total heat flux is partitioned and not the prediction of the total wall heat flux itself. 3) Mechanistic models for the wall heat flux and partitioning. These models can be used to predict both the wall heat flux partitioning and the overall wall heat transfer. Since in this work, the wall temperatures at all nucleation sites were not precisely measured, empirical correlations for wall heat flux were used to estimate the wall temperature. Therefore, two commonly used methods in literature, named Liu and Winterton [21] method and Chen [22] method, were selected and their results were compared. Results from other researchers are also shown here. The commonly used approach in obtaining the empirical method for the partial and fully developed boiling regions is to combine the single-phase forced convection and saturated pool nucleate boiling heat fluxes. In partial nucleate boiling, which is a transition region between single-phase region and fully developed nucleate region, Bowring [23] used a superposition method to get the partial nucleate boiling heat flux as shown in Fig. 3-6: eq. 3-1 where, is the heat flux during partial boiling, is the single-phase forced convection heat flux, and is the fully developed pool boiling heat flux. For the fully developed region, the heat flux is given by Engelberg-Forster and Greif [24]: eq. 3-2

38 22 where, is the heat flux at the intersection of the single-phase and fully developed nucleate boiling curves. For the single-phase region heat flux is calculated as below: ( ) eq. 3-3 where, is the liquid saturation temperature, is the liquid temperature, and is the singlephase heat transfer coefficient which is obtained as below from the Colburn [25]: eq. 3-4 where, is the liquid Nusselt number, is the pipe hydraulic diameter, is the liquid thermal conductivity, is the liquid Reynolds number, and is the liquid Prandtl number. From the Figure 3-6, it is evident that at, then, where is the wall temperature, and at, then. Figure 3-6: Boiling curve from the Bowring [23] model

39 23 Rohsenow [26] likewise proposed a similar method to Bowring except for as: was calculated ( ) ( ) eq. 3-5 where, And also pool nucleate boiling correlation is: ( ) ( [ ( )] ) eq. 3-6 where, is an empirical constant that deps on the fluid-solid combination, m and n are empirical constants that dep on the fluid properties, is the gas-liquid enthalpy difference, is the liquid viscosity, and is the liquid heat capacity. Later, Bergles and Rohsenow [27] suggested a correlation for the partial nucleate boiling heat flux as: [( ) ( )] eq. 3-7 where, is the heat flux computed from the fully developed boiling curve at. The heat flux at ONB is given as: [ ] eq. 3-8 where, p is in kpa, is in degree centigrade, and is in W/m 2. Bjorge et al. [28] suggested the following correlation for the prediction of the boiling curve in subcooled flow boiling:

40 24 [ ( ) ] eq. 3-9 where,, and Figure 3-7: Boiling curve for the Bergles and Rohsenow [27] model Liu and Winterton [21] suggested a model by combining the concepts proposed by Kutateladze [29] and Chen [22]. The main advantage of their method is that they assumed single-phase heat transfer would enhance by increasing the liquid velocity while the pool boiling heat transfer is suppressed as a result of a lower effective wall superheat in flow boiling compared to that in pool boiling. The overall subcooled flow boiling (q w ) which is a combination of single-phase and nucleate pool boiling heat fluxes is obtained as: ( ) ( ) ( [ ]) ( ) eq where, [ ( )], it is called the pool boiling heat transfer suppression factor, it is called the single-phase heat transfer enhancement factor Pr l and Re l are the Prandtl and Reynolds number based on liquid properties. Also for the pool boiling heat transfer rate, the following is proposed by Cooper [30]:

41 25 ( ) eq where, M is the molecular weight of the liquid, q is the heat flux, and p r is the critical pressure of the liquid. Liu and Winterton obtained the following correlation to calculate the temperature difference between the heater surface and bulk of the liquid. By having the bulk of liquid temperature, one can easily calculate the wall temperature: where, [ ( ( )( ))] ( ) eq The older but still widely quoted 1966-Chen correlation [22] is another method to calculate the wall superheat. The Chen correlation has been reported by Liu and Winterton [21] to have the second lowest mean error in subcooled flow boiling among the commonly cited wall superheat correlations, after their own 1990 correlation. The Chen correlation postulates that heat transfer in convective boiling flow is a function of both nucleate and convective heat transfer: where, ( ) eq and where, the F factor is set to 1. Chen s correlation was restated by Situ et al. [18] as:

42 26 ( ) ( ) eq In order to create a numerically solvable non-linear equation in wall temperature, equation was rewritten as:, the ( ) ( ) ( ) eq As was done with the surface temperature obtained from the Liu and Winterton method, the surface temperature obtained by solving this equation for each case tested was used in order to calculate the effective Jakob number. This was then used to obtain the expected bubble lift-off diameter using the suggested modification of the Zeng et al. model and will be presented later. The predictions for bubble lift-off diameter made using Liu and Winterton s correlation for wall superheat, along with mean experimental bubble size and the boiling region for each case are presented in the form of a database in Table 5-1. A total of 802 bubbles across 44 cases were observed. Also correlations for and are presented by Hsu [31], and Satu and Matsumura [32]: [ ] eq [ ] [ ] eq Furthermore, in fully developed nucleate flow boiling (FDB) region, only pressure and wall temperature affect the heat flux and the flow velocity does not have any influence on it [33]. Thom et al. [34] have proposed a model to find the difference between the wall temperature and the coolant temperature for a relatively clean surface: ( ) eq. 3-18

43 27 where, is the heat flux in Btu/hr.ft 2, is the pressure in psi, and is in degree F. Several correlation by many investigators have been proposed the over past fifty years in order to predict OSV, such as correlations from Bowring [23], Thom et al. [34], Ahmad [35], and Saha and Zuber [36]. The empirical correlations of Saha and Zuber are the most widely used for the determination of the OSV point. They define two OSV regimes as their conditions and correlations are presented below: The thermally controlled regime: eq where, is the wall heat flux, is the pipe hydraulic diameter, and. The hydrodynamically controlled regime occurs at: eq where, is the mass velocity Models for Departure and Lift-off Diameters in Subcooled flow By obtaining appropriate correlations for the wall temperature and heat flux, proposing models for departure and lift-off bubble diameters will be feasible. In this work, the main focus is on the bubble lift-off diameter under varying flow conditions. The proposed model will be then compared with the experimental data. There are many empirical and theoretical

44 28 correlations existing in literature for bubbles at the departure and lift-off. In spite of various correlations for pool boiling, not many works have been done on flow boiling. It should be noted that as Klausner et al. [37] reported, pool boiling correlations for bubble diameter do not fit well for bubbles in flow boiling conditions. Klausner et al. [37] were the earliest to differentiate the difference between the two types of bubble motion. Bubble departure is used to characterize the sliding as the mechanism in which bubble leaves the nucleation site. Bubble lift-off is used to characterize bubble detachment from the heater surface, either from the nucleation site or after some finite sliding distance. For this project, bubble lift-off diameter is measured as opposed to the departure diameter. The reason is that the departure diameter is difficult to determine visually. In addition, the departure diameter may be difficult to measure as the bubble may slide while it is still early in the growth phase. For a horizontal surface, Klausner et al. [37] found that the majority of bubbles will slide some distance before lift-off. In addition, Situ et al. [18] observed that for vertical test surfaces that some bubbles t to slide first and did not directly lift-off. Thorncroft et al. [38] reported that bubbles t to not lift-off in upward flow boiling conditions. As shown by Zeng et al. [39], lift-off diameters for flow boiling is typically smaller than that of pool boiling since the wall superheat is lower for flow boiling. This results in a lower growth rate due to the presence of single-phase convective heat transfer. Basic force balance (with varying simplifying assumptions) is the most popular analytical method used in developing bubble departure and lift-off diameter in flow boiling of a bubble departing a nucleation site or the heated wall. It is typically found that these analytical correlations are validated by an empirical study to compare the correlations with experimental data. Analytical and experimental correlations from several authors are presented in Tables 3-2 and 3-3 for departure and lift-off diameters, respectively. The work done by most of these authors were based on a vertical flow channel and thus these correlations cannot be directly applied on a horizontal CANDU channel since buoyancy is not considered at lift-off. However, the procedure in developing these correlations can be incorporated for the development of departure and lift-off diameter in the CANDU case and the relationship between bubble size and experimental conditions can be readily seen.

45 29 The bubble departure phenomena in pool boiling have been studied since 1950s. A correlation for the bubble departure diameter was obtained by Zuber [40] by assuming the bubble growth occurs in a superheated and thin thermal layer near the surface. He found that bubble departure and the flow regimes are similar to the formation of gas bubbles at orifices. Cole [41] stated that the bubble departure diameter is proportional to the inverse of the absolute pressure. Then, Cole and Rohsenow [42] modified the Cole s correlation by replacing the wall superheat with a critical temperature. Kocamustafaogullari and Ishii [43] fitted 135 data points obtained from existing experimental results performed from to bar. They reported that the bubble departure diameter is a function of the contact angle and pointed out that the active nucleation site density on a heated channel surface is the key parameter in the prediction of the bubble number density. Farajisarir [44] carried out a critical review and pointed out the limitations of existing models and correlations regarding the bubble departure diameter. He examined forced convective boiling flow at atmospheric pressure in a vertically oriented test section and proposed nondimensional models for the departure diameter and time. Zeng et al. [39] derived the bubble departure diameter from the balanced force equations affecting the departing bubble based on experimental data acquired under flow boiling conditions. He performed his tests on a horizontal test section but the derived equations we done for both vertical and horizontal orientations. He did not propose an explicit model for the bubble departure diameter. Thorncroft et al. [45] summarized the literature that describes the forces acting on growing bubbles and identified each force balance equation used for conditions of horizontal pool boiling, vertical pool boiling, and flow boiling. Basu et al. [46] assumed that all of the energy from the wall is first transferred to the superheated liquid layer and that a fraction of the energy is then used to generate vapor and to heat bulk liquid due to forced and transient convection. Basu suggested an empirical correlation of the bubble departure diameter. After her, Sateesh et al. [47] determined the bubble departure diameter from the force balance between the buoyancy force and the surface tension force. Duhar and Colin [48] suggested a force balance model to predict the departure radius by referring to the theoretical results of Magnaudet et al. [49]. An experimental study was also performed to measure the growth of air bubbles injected into silicon oil by using high-speed video pictures for validation. The

46 30 model of Duhar for the bubble departure radius predicted his experimental data well, but the injected gas flow rates were required. Among the correlations reviewed above, the correlations developed for a vertical heated surface are not suitable for predicting the bubble departure in a horizontal surface due to the reason that the inclination of a heated surface affects the bubble s behavior and heat transfer near the wall. The studies of Farajisarir, Zuber, and Basu fall into this category. Furthermore, the correlations reported by Cole, and Kocamustafaogullari were developed using existing data from the literature, but most of the data were obtained under horizontal pool boiling conditions. Farajisarir, and Basu examined the effect of high heat flux and high velocity conditions. In addition to these, some correlations were developed using coolants other than water and therefore, constant values used in these correlation might not be applicable to water. Although the force balance equations suggested by Zeng and Thorncroft are very useful, an explicit form of the departure diameter was not given.

47 31 Table 3-2: Suggested correlations for the bubble departure Author Bubble Departure Diameter Comments Cole and Rosenhow model [42] [ ( ) ] - Kocamustaf aogullari and Ishii model [43] (modified version of Fritz) ( ) Farajisarir [44] ( ) is in degrees. Applicable range is where, is the shear lift coefficient, and is the bubble growth constant. Basu et al. [50] ( ) [ ] ( ) Cho et al. [51] [ ( ( ) ( ) ) Klausner et al. formulated [ ] [ ( ) ] ( ) ( ( ) ( ) ) ] ( ) Literature review shows that extensive researches have been carried out on bubble departure size, while there is only limited number of studies have been done on the bubble lift-off size in convective boiling. So far, correlations and models for the bubble lift-off diameter have not received as much attention as the correlations for the bubble departure diameter. This is mainly due to the fact that most studies on the bubble-sliding phenomenon have focused on enhancing heat transfer itself. As a result, it is essential that a proper model for the bubble lift-off diameter be developed that is applicable to the conditions of CANDU. In here, some

48 32 of the previous models are presented. Staub [52] considered several different forces acting on a nucleating bubble, including surface tension, momentum change of the liquid due to the growth of the bubble, liquid inertia force, evaporation vapor thrust force, buoyancy force, and drag force. He then assumed that the surface tension, buoyancy, and drag forces were the dominant forces. In his model, the force balances is applied on a layer of hemispherical bubble. Unal [53] yielded a semi-empirical correlation to predict the bubble departure and maximum diameters using experimental data in the literature. He assumed that a spherical or ellipsoidal bubble grows on a very thin, partially dried liquid film formed between the bubble and the heated surface. He used this model for an energy balance for a bubble in order to predict the maximum bubble diameter when a spherical or ellipsoidal bubble grows on a very thin, partially dried liquid film formed between the bubble and heated surface in subcooled boiling flow. Unal s correlation is the most popular, due to its widely applicable range. However, he did not propose a model for the bubble lift-off diameter. Klausner et al. [37] performed an investigation to find the effects of wall superheat and flow velocity on the nucleation characteristics of cavities of different radii for flow boiling of subcooled water near atmospheric pressure in a narrow rectangular channel by using a highspeed camera. Their results show that higher flow rates require larger wall superheats to activate the cavities. Furthermore, they investigated the effect of wall superheat and found out the fact that as the wall superheat increases, smaller cavities are activated and the heat transfer coefficient increases with increased nucleation activity. They measured the bubble departure diameter in a horizontal rectangular channel using saturated R-113. They used a 25 x 25 mm 2 transparent rectangular channel, and a 20-mm-wide nichrome strip was adhered to the bottom surface of the channel. The mass flux, heat flux, and pressure ranged from 112 to 287 kg/m2, 11.0 to 26 kw/m 2, and 132 to 213 kpa, respectively. They observed that the overwhelming majority of bubbles left the nucleation site by sliding a finite distance along the heated surface before lifting off the wall. The bubble departure was defined as the instant that the bubble left the nucleation site, and the bubble lift-off was defined as the instant that the bubble was detached from the heated surface. They analyzed the force balance in the flow

49 33 direction for bubbles growing at the nucleation site in order to predict their departure diameter. They found that an asymmetrical bubble growth force (so-called unsteady drag force) and surface tension force are important factors holding the bubble at the nucleation site before departure. Zeng et al. [39] proposed improved models for the bubble departure and lift-off diameters by including the bubble inclination angle, following Klausner s work. He carried out pool boiling and flow boiling experiments and solved the force balances on a bubble for different experimental conditions without proposing any explicit model for them. He studied the forces acting on a bubble in saturated horizontal forced convection boiling. At the point of bubble departure and bubble lift-off, several forces such as surface tension, hydrodynamic pressure force, and contact pressure force were neglected because the bubble contact area on the wall was approximated to be zero. The bubble departure diameter and bubble lift-off diameter were modeled based on the simplified force balance equation. They measured the bubble growth rate and bubble lift-off diameter for a saturated R-113 boiling flow using the same test channel as Klausner et al. s [37]. A total of 37 lift-off diameters were obtained for a mean liquid velocity of m/s, heat flux of kw/m2, and pressure of kpa. In a similar manner as Klausner et al. [37], they analyzed the force balance both in and normal to the flow direction for the bubble in order to predict the departure and lift-off diameters, respectively. The quasi-steady drag force, bubble growth force, and shear lift force were considered for the departure diameter, but the surface tension force was neglected in a manner different from that in Klausner et al. s work [37]. The buoyancy and bubble growth forces were considered for the lift-off diameter. The shear lift force was neglected based on their observation that the bubble sliding velocity after departure was close to the local liquid velocity. They proposed a bubble growth constant in Zuber s bubble growth model [15] based on their sample measurements for the bubble growth rate. The constant ranged from 1.0 to 1.73, and the constant of 1.7 gave the best prediction results for the departure and liftoff diameters. Zeng mentioned that their bubble lift-off diameter model could be applied to a vertical boiling flow with some modifications. For a vertical up flow, they expected that the shear lift force would push the bubble against the wall, hampering bubble detachment, and that the bubble detachment would be due to large fluctuations in transverse liquid velocity.

50 34 Thorncroft et al. [38] performed a visual study of bubble growth and departure in vertical up flow and down flow forced convection boiling. They reported that the departure diameter increases with increasing Jakob number and that the bubble-sliding phenomenon increases the heat transfer rate from a heated wall to the fluid. Chang [54] photographically studied the behavior of near-wall bubbles in subcooled flow boiling for water in vertical, one-side heated, rectangular channel at mass fluxes of 500, 1500, 2000 under atmospheric pressure. His main focus was on the bubble coalescence phenomenon and the structure of the near-wall bubble layer. He observed three characteristics layers at sufficiently high heat fluxes (>60-70% CHF): a) a superheated liquid with small bubbles attached on the heated wall, b) a flowing bubble layer consisting of large coalesced bubbles over the superheated liquid layer, c) the liquid core over the flowing bubble layer, as well as the existence of a liquid sublayer under coalesced bubbles was identified photographically. Prodanovic et al. [55] reported that the bubble diameters decreased with an increase in the subcooling and mass flux, while the effect of mass flux became less pronounced as the OSV (onset of significant void) was neared. For the heat flux effect, they concluded that the maximum bubble diameter generally dropped with an increase in heat flux. This was particularly evident at lower heat fluxes, while at a higher heat flux, the bubble diameter remained roughly constant. They also measured the wall superheat at the film location, and the experimentally measured Jakob number was used for the development of their correlation. Furthermore, they measured the bubble maximum and lift-off diameters, and the maximum bubble diameter time, bubble lift-off time, and bubble condensation time for a subcooled boiling flow of water in a vertical annulus. The heater at the center had a diameter of 12.7 mm, the outer glass tube had an inner diameter of 22 mm, and the hydraulic equivalent diameter was 9.3 mm. A total of 54 data sets were presented for pressures of 1.05, 2.0, and 3.0 bar, a bulk liquid velocity of 0.08 to 0.8 m/s, a heat flux of 0.2 to 1.2MW/m 2, and a subcooling of 10 to 30 o C. They suggested five correlations for each of the five parameters above as a function of Jakob number, non-dimensional sub-cooling, boiling number, and

51 35 density ratio. The coefficients and exponents of the correlations were determined based on their data. They observed that the sliding velocity of small bubbles was about 0.8 of the bulk liquid velocity for an isolated bubble region, and larger bubbles under a lower liquid velocity, lower heat flux, and lower subcooling slid at higher velocities than the bulk liquid flow. Basu [46] developed an empirical correlation for the bubble lift-off diameter using the correlation of the bubble departure diameter from his experimental data and from the literature. A reduction factor was introduced to quantify the actual number of bubbles lifting off per unit area. Situ et al. [18] employed the force balance equation suggested by Zeng to formulate the dimensionless form of a bubble lift-off diameter as a function of the Jakob number and the Prandtl number. Their experimental setup was a BWR-scaled upward annular channel (vertical). The working fluid was water and a high-speed digital video camera was used in order to capture the dynamics of the bubble nucleation process. To validate the correlation, forced-convective subcooled boiling experiments were carried out under atmospheric pressure. The conditions of their experiments were at of inlet temperature, pressure of 1 atmosphere, inlet velocity of m/s, and heat flux of The results of the experimental data and proposed model agreed within the averaged relative deviation of 35.1%. they observed both bubble departure and bubble lift-off phenomena and reported that bubbles slid a longer distance as the subcooling was lower and the mass flux was higher, similar to the results of Okawa et al. [56]. To predict the bubble lift-off diameter, they set the force balance normal to the flow direction, and analyzed the shear lift and the bubble growth forces. They adopted the shear lift force derived by Mei and Klausner [57] and assumed that the bubble sliding velocity was half the local liquid velocity. They also used Zuber s bubble growth model with a bubble growth constant of 1.73 to evaluate the bubble growth force. The effect of liquid subcooling on the bubble growth was indirectly reflected by introducing the nucleate boiling suppression factor of Chen s correlation [22] to the bubble growth model. Their lift-off diameter model was validated against their experimental data, and the average prediction error was 35.1%. Bae [58] proposed a description of the bubble lift-off diameter derived from the force balance equation by referring to Situ s study. By modifying the function of the bubble growth rate, he expressed the bubble lift-off diameter as a function of the bubble departure diameter. Bae

52 36 defined a fitted curve to simplify the force balance equation and used Unal s correlation of the bubble departure diameter to calculate the lift-off diameter. Chu [59] investigated phenomena from bubble nucleation to lift-off for a subcooled boiling flow in a vertical annulus channel by the use of a high-speed camera in ter of heat flux, mass flux, and degree of subcooling. It was found that the bubble lift-off diameter decreased as the mass flux and subcooling increased. On the other hand, the effect of the heat flux on the bubble lift-off diameter was neither significant nor consistent, except for when the mass flux was around 500 kg/m 2 s and the subcooling was o C. In his work, the bubble lift-off diameter and nucleation frequency showed stochastic behaviors, such as depence on the nucleation site and competition between them in removing the thermal energy from the heated surface. Therefore, it was recommed that a sufficient number of nucleation sites should be examined in order to obtain unbiased bubble characteristics. Also, the combined parameter, (f b D lo ), showed a clear depence on the subcooling, mass flux, and heat flux. Among the existing models correlation for the bubble diameters in a forced convective boiling flow, Unal s model agreed well with his database of the bubble lift-off diameters. According to Cho et al. [51] and Zeng [39], the developed model for the bubble departure diameter deps strongly on the bubble contact angle. On the other hand, bubble lift-off diameter deps on the buoyancy and the growth forces in a horizontal channel, while in vertical channels, lift-off diameter is a function of the lift-off number (this dimensionless number indicates the ratio between the shear lift and growth forces). It was, therefore, postulated that the developed models for vertical channels are not suitable for horizontal surfaces as it is found out that the inclination of a heated surface affects the bubble s behavior and heat transfer near the wall, Chu [59].

53 37 Table 3-3: Suggested correlations for the bubble lift-off diameter Author Bubble Lift-off Diameter Comments Unal [53] ( ) ( ) ( ), Applicable range for this relation is, Prodanovic et al. [55] ( ) ( ) ( ) A= , B= , C= , D= 1.747, E= Basu et al. [50] ( ) [ ] ( ), The parameters A,B,C,D,E are empirically correlated parameters. Prodanovic et al. derived the lift-off diameter using similar procedure as Farajisarir [44]. Valid within: Basu et al. observed a high scatter in empirical results. of water on Zr-4 was measured to be 57 o. Situ et al. [18] Bae et al. [58] and Cho et al. [51] ( [ ( ) ] ) Bae et al.: Cho et al.: The shear lift coefficient is an adjustable constant which Zeng et al. [39] recommed as Bae et al. and Cho et al. assumed an inclination angle of zero. Bae et al. recomms Unal's model for the departure diameter. 3.3 Acting Forces on a Sliding Bubble The main focus of the present study is on bubbles formation and bubble departure sizes in a CANDU reactor. The bubble size when it detaches from the heater surface (i.e. lift-off bubble size) can be different from the bubble departure size. The bubble departure size is the size a bubble detaches from the nucleation site and starts to move on the surface. A bubble is

54 38 formed at a nucleation site, and starts to gradually grow. It is found out that once the bubble reaches a certain diameter (size), it detaches from the nucleation site; in most of the cases, the bubble slides for a finite distance on the heater surface and continues to grow. During this period, vaporization happens at the inner surface of the bubble, while condensation occurs at the outer surface if the tip of the bubble is out of the superheated layer. At some point downstream of the nucleation site, bubbles lift-off from the surface. For bubble departure, the force balance along the flow direction is to be considered; whereas, for the bubble lift-off size, the force balance perpicular to the flow direction has to be considered. While the bubbles are attached to the heater surface and their nucleation site, they are heated by the heater and vaporization occurs at a micro-layer under the bubbles. Obviously the heat transfer mechanism at the wall is not the same as that in the bulk water. Also while the bubble is attached to the heater surface and slides, it contributes to the micro-convective heat transfer process. The departure diameter of the bubble deps on the contact angles, while on the other hand, the lift-off diameter of the bubble is a function of different forces applied on the bubble such as the growth force and the shear lift force. Also, the main parameter for the evaporation heat flux and vapour generation is the bubble diameter. Once again, the main reason for choosing the lift-off diameter rather than the departure diameter in this report is that, it is fairly difficult to define the instant of bubble departure from the nucleation site. In this part, a force balance analysis on a growing bubble is performed in order to predict the bubble departure and lift-off sizes. It is postulated that the dimensionless form of the bubble departure and lift-off diameters are functions of various non-dimensional numbers such as Jakob, and Prandtl numbers. According to Fig. 3-8, the forces acting on a bubble at its nucleation site are as follows (the dynamic effects of turbulence and wave motion are ignored), Klausner et al. [37]: x-direction: eq y-direction:

55 39 eq where, Fx: the force acting on bubbles at x-direction, F sx : the surface tension force at x- direction, F dux : the unsteady drag force at x-direction (also called growth force because the bubble grows asymmetrically, and the unsteady liquid flow such as the added mass force has a dynamic effect), F qs : the quasi-steady force in the flow direction, ρ g : vapor density, V b : bubble volume, v gx : bubble velocity at x-direction, t: time, Fy: the force acting on bubbles at y-direction, F sy : the surface tension force at y-direction, F duy : the unsteady drag force at y- direction, F sl : the shear-lift force, F b : the buoyancy force (effect of liquid buoyancy and gravity of bubbles), F h : the hydrodynamic force, F cp : the contact pressure force, and v gy : the bubble velocity at y-direction. In addition to the applied forces, it is notable that inclination angle, i.e. θ i, is the angle between the line from nucleation site to the bubble center and y-direction. Also, θ a and θ r are advancing contact angle and receding contact angle, respectively. The correlations for all the mentioned forces are provided next. Surface tension force The surface tension forces at x- and y-directions were given by Klausner et al. [37]: ( ) ( ) ( ) eq where, is the contact diameter. and ( ) eq. 3-24

56 40 Y Θ i X F b F sl H F dux F h, F cp F duy F qs Θ a F sx Θ r F sy Figure 3-8: Force balance of a vapour bubble at a nucleation site. Flow Condensation Heat Flux Sliding Departure Vaporization Lift - off Figure 3-9: Schematic diagram of bubble nucleation phenomenon.

57 41 Growth force The unsteady drag force (growth force) is given by Chen [60] as the following for a spherical bubble attached to a wall; the virtual added mass, V f is: where, r b : bubble radius which is changing over time during the forming and growing phases. eq By assuming that the growth force can be estimated as the inertial force of this added mass, the following is obtained: ( ) ( ) eq where, ρ f : liquid density (kg/m 3 ), H: the bubble height measured from the wall (m), u b y: the bubble front velocity on y-direction (m/s). Therefore, a relation between H and u b y can be written as u b y = dh/dt. In this case, it was assumed that the bubbles are spherical and as a result, H is the bubble diameter (i.e. 2r b ). Thus: u b y = dh/dt u b y = 2dr b /dt eq From Eqs (3-26) and (3-27) the final correlation of the growth force is obtained as: ( ) eq where, : the first derivative of the bubble radius with respect to time, the second derivative of the bubble radius with respect to time. By the use of inclination angle, the growth force can be calculated in x- and y-directions: and F du x=f du sinθ i eq. 3-29

58 42 F du y=f du cosθ i eq One of the commonly used bubble-growth models is that of Zubers model [15] which also shows the depence of bubble s growth on the temperature of the liquid surrounding it: where, is the liquid Jakob number, b is growth rate constant, and t is time. eq It should be noted that the wall superheat can be used as the superheat in the Jakob number in this case, i.e. saturated boiling. While this statement is correct, in forced convection subcooled boiling, it is much more complex. At the beginning of the bubble s growth process, its size is small and therefore, all the liquid around it is superheated, and this makes the bubble to grow. Bubble will continue growing till its tip reaches the subcooled water and the bubble starts to collapse from its tip. Therefore, the wall superheat would be more than the effective superheat surrounding the bubble (Kocamustafaogullari et al. [43]). It then can be concluded that the bubble radius is a function of the following dimensionless numbers and time: r = f(ja e ) ( ) eq. 3-32

59 43 where, ( ), with being the suppression factor and equals to (by Situ et al. [18]): where Re TP : the two-phase Reynolds number calculated by setting vapor quality as zero, ( ). According to the short length of the test section and its small heater power, the estimation of the point of net vapor generation does not considerably affect the calculation of the wall temperature. where, ( ) Shear lift force The shear lift force on a solid sphere at low Reynolds number was obtained by Saffman [61]. Auton [62] also derived a correlation for the shear lift force on a sphere in an inviscid shear flow. Then, Saffman s model was modified by Mei and Klausner to suit for a bubble, and interpolated with Auton s equation to derive an expression for shear lift force over wide range of Reynolds number: where, u r : the relative velocity between the bubble center of mass and the liquid phase (i.e. u r = u f u g ), and C l : the shear lift coefficient given by Klausner et al. [37] which is: eq ( ) eq. 3-34

60 44 where, : a dimensionless shear rate of the oncoming flow,, Re b : the bubble Reynolds number. Buoyancy force According to Klausner et al. [37] the buoyancy force can be obtained as follow: F b = (ρ f ρ g )gv b = ( )(ρ f ρ g )g where, V b : the bubble volume,. eq Quasi-steady drag force Klausner et al. [37] modified the correlation which was obtained by Mei and Klausner [57] by taking into account the effect of the wall: where, n = 0.65 and [( ) ] ( ) eq [( ) ] Contact pressure force Klausner et al. [37] correlation for the contact pressure force is used here. It is important to mention that this force is applied to the bubble over the contact area with the heater because of the pressure difference inside and outside of the bubble at the reference point.

61 45 eq where, r r : the radius of curvature of the bubble at the reference point on the surface y = 0, σ: surface tension (N/m). Hydrodynamic force According to Klausner et al. [37] hydrodynamic force is calculated as follow: eq where, U is evaluated at y = r b. This force was estimated by considering an inviscid flow over a sphere in an unbounded flow field and according to the symmetry over the majority of the bubble surface, the contribution to hydrodynamic force is from the pressure on the of the bubble over an area.

62 Chapter 4 Experimental Procedure 46

63 47 4 Experimental Procedure The flow visualization experiments were carried out to simulate the thermo-hydraulic conditions of CANDU reactors. In this chapter, the facility and the experimental procedure including the flow visualization are described. Also the choice of the experimental conditions under which the fil were taken will be described. Elaboration on the flow visualization setup and image processing system for bubble analysis will be discussed. 4.1 Scaling Criteria and Experimental Conditions Due to the difficulties of conducting the experiments in a real reactor, an electrically heated fuel assembly was built which represents a scaled-down CANDU s 37-element fuel rod. The operational conditions were much lower than those of the real CANDU. The assembly needs to correspond to the real CANDU in all other ways and therefore, dimensionless numbers were obtained in order to maximize the similarities between the real CANDU and its prototype. The focus is on correct development of the flow quality and the different flow regimes that are present inside the assembly. Thus, a loop facility was built as it is explained in Section 4.2: an assembly of only one fuel rod placed in a horizontal channel with one inlet and one outlet on each side was built. Furthermore, to make sure that a fully developed turbulent flow of water is established right at the entrance to the test section, another section with similar geometry and hydraulic diameter is added just before the main chamber. The test section is equipped with several glass sections so that visual inspection of the two-phase flow was made possible. Attention has to be paid in deriving the appropriate scaling criteria. Local bubble characteristics, the flow pattern distribution and the flow development along the test section are among the main objectives of this work. For the purpose of proper local bubble characteristics, an analytical force balance at the moments of departure from the nucleation site as well as the lift-off moment of the bubble was done and the main forces which result in bubble departure or lift-off were obtained. Also, thermo-hydraulic analysis was performed to observe the flow pattern distribution and its development along the test section. Since the local void fraction is an important parameter, two dimensionless numbers were used to perform the system scaling.

64 Scaling Subcooled Boiling Region In a typical CANDU reactor, heavy water enters the reactor core several degrees centigrade lower than its saturation temperature; due to this reason, the supplied heat from the heater rod is added to the subcooled water as it flows over the rod. In literature, the flow of subcooled fluid is divided into four regions as indicated by Fig. 4-1 [23]: Before reaching point 1, no vapour is present in the flow and all the supplied heat is used to increase the temperature of the subcooled flow (forced convection is cooling the heater surface). Right at the point 1, vapour bubbles form for the first time, and from point 1 to point 2 more bubbles are produced along the heater surface. In this region, the superheated liquid layer has small thickness close to the wall of the heater and therefore, bubbles cannot sufficiently grow to reach their critical sizes to be able to leave the surface. At point 2, bubbles with sufficiently large sizes are formed and can depart from the heated wall. The vapour volumetric fraction starts to rise rapidly. In the region between point 2 and 3, although the vapour volumetric fraction is large, thermal equilibrium condition does not exist. This means that part of the flowing water is still subcooled and the real vapour volumetric fraction is larger than the volumetric fraction obtained from a heat balance. In some models, point 2 is called the Point of Net Vapour Generation, PNVG (it is also called Onset of Significant Void, OSV). At point 3, all of the liquid is at saturation temperature and both real and thermal equilibrium volumetric fractions are equal.

65 49 Void Fraction ONB OSV Channel Length Figure 4-1: The axial void fraction distribution during forced convection subcooled boiling Figure 4-2: Axial profiles of the flow quality and thermodynamic equilibrium equality in the case of a constant wall heat flux

66 50 After defining the four regions in a subcooled flow, it would be beneficial to see how these properties are correlated. At the beginning of the heater cooling process by the use of subcooled fluid, all the absorbed heat from the heater rod, is forced to increase the liquid enthalpy up to its saturation temperature. Upon this time, no vapour is formed yet and therefore the thermodynamic equilibrium quality,, can be defined as follow (this quality is a function of x-coordinate which is parallel to the rod axes): ( ) ( )- where, h liq (x): the enthalpy of the liquid at the position x, : the enthalpy of the liquid at saturation for a given pressure, and h fg : the heat of evaporation. eq. 4-1 According to Eq. (4-1), the value of is negative in the subcooled region; but as the experiments have shown, some vapour bubbles form at the wall of the rods in the subcooled region. As a result, part of the generated heat is consumed to form the bubbles and the rest is used to increase the enthalpy of the liquid. Thus, the actual flow quality, ( ), is larger than zero: ( ) where, : the vapor mass flow rate : the total mass flow rate ( ) eq. 4-2 A modified version of the thermodynamic equilibrium quality, ( ), is given as: ( ) ( )- where, ( ): the enthalpy of the two-phase mixture flow at the position x eq. 4-3

67 51 By continues heating the fluid, the whole bulk of the fluid will reach the saturation point and the flow quality,, becomes equal to the thermodynamic equilibrium quality,. This equilibrium point is the start point of the thermodynamic equilibrium. Fig. 4-2 shows these properties. At the first point where the bubbles form, i.e. x x d, the thermodynamic equilibrium quality is less than zero. Onset of boiling is where is zero (also called bulk boiling). Moreover, x = x eqb shows the area where the flow is considered as in thermodynamic equilibrium. Eq. (4-4), which is obtained from an energy balance of Eq. (4-3), shows the increase of the thermodynamic equilibrium quality along the flow path: ( ) ( ) eq. 4-4 where, : the added enthalpy to the inlet enthalpy of the flow at distance x from the inlet (It can be calculated by using ( ) and converting it to mass and heat fluxes) Then, it can be obtained that: where, are heat and mass fluxes, respectively eq. 4-5 ( ) ( ) ( ( ) ( ) ( ) ( ) ( ) - eq. 4-6 ) ( ) - where, : heat flux (assuming constant) : fluid mass flux l: length of a rod D h : the hydraulic diameter of a flow channel in the assembly h inl : the enthalpy of the pure liquid at the inlet of the assembly To obtain this expression, the enthalpy of the two-phase fluid at the distance x from the inlet was calculated based on the fluid inlet enthalpy plus the added energy to the amount of the

68 52 existing mass at a given geometry. Then, it was rearranged to give two dimensionless numbers which are presented below: The phase change number: ( ) ( ) eq. 4-7 and the subcooling number: eq. 4-8 According to the previous discussion, the actual quality is the main concern in any flow conditions in CANDU and the modeled chamber; therefore the actual quality has to be properly modeled rather than the thermodynamic equilibrium quality. Levy offered a profilefit model in which the flow quality is coupled to the thermodynamic equilibrium quality [63]. The fit ensures that: ( ) = 0 at the departure point ( ) ([ ] ) where, [ ] is the thermodynamic equilibrium quality at the departure point and is defined as: [ ] eq. 4-9 where is the specific heat of liquid is the saturation temperature minus local bulk fluid temperature, i.e., correlation is obtained from Levy [63] (Its i) the further downstream the departure point, the smaller the difference between and : [ ] => - 0 eq. 4-10

69 53 ii) the slope of ( ) at the departure point is zero: [ ] [ ] [ ] [ ] eq Since, Therefore, [ ] [ ] According to Levy [63], the following fit fulfills the specified conditions and agrees with experiments (Fig. 4-2): [ ] exp ( [ ] [ ] ) eq It can be concluded that the proper scaling of the flow quality in the subcooled region can be done if the dimensionless numbers, i.e. N pch and N s, are matched for both CANDU and the modeled chamber. According to Cheng and Muller, the void fraction of a typical CANDU is zero which is around the middle point of BWR and PWR cores. CANDU s actual quality is less than 5% [8]; therefore, the flow does not need to be modeled in thermal equilibrium region and consequently, not all the dimensionless numbers, which are applicable to BWR modeling studies, are necessary to be used in this report. Only two dimensionless numbers, i.e. the phase change number and the subcooling number, are going to be used in order to properly scale down the real CANDU core conditions. In the following table conditions of a typical CANDU core and our modeled chamber are compared:

70 54 Table 4-1: Set points for CANDU nominal operating conditions and the modeled chamber [64] CANDU Modeled Chamber geometry Length (m) Diameter of rod (mm) D h (mm) Number of rods 37 1 Inlet area (mm^2) x 10 2 Operating conditions P (atm) T sat ( C) ΔT sat ( C) Mass flux, (kg m -2 s -1 ) Heat flux, (kw m -2 ) Water Scaled-down facility The experimental set up has three sub-assemblies: (a) Tank assembly (water source) (b) Chamber (test section) (c) Visualization system

71 Figure 4-3: Overall view of the experimental setup 55

72 56 (a) The tank assembly includes isolated heated tank, an immersion heater, a pump and a temperature control device. The tank is filled with filtered tab water and then, the heater raises the water temperature to the required temperature. The rise in temperature is monitored by K- type thermocouple which is attached to the outlet of the pump. The pump is used to circulate the water inside the tank to achieve a uniform temperature. Thermocouple is attached to data acquisition system to track the temperature inside the tank. After reaching desire temperature, the outlet valve is opened allowing the water to flow into the chamber assembly through stainless steel metal pipes. Figure 4-4: Schematics of the Tank Assembly Figure 4-5: Tank assembly setup

73 57 (b) This is the part of the assembly where nucleation happens. The assembly consists of a combination of instruments, such as a chamber with a window and a cartridge heater. The chamber assembly was designed so as to be able to easily monitor and vary the pressure, temperature and the flow properties of the system. Its main aim was to create an environment conducive for the bubble nucleation. The chamber is equipped with one window on each side which is resistance to high pressure and temperature. Right at the inlet of the chamber, flow meter is located to control the inlet flow. One K-type thermocouple was placed there as well in order to record the inlet flow temperatures. This temperature is one of the control variables used to study the bubble nucleation. To study the nucleation properly, the flow rate, the temperature and the pressure were all recorded and their relationships to the properties of the nucleation were analyzed. Pressure also directly affects the saturation point of water; therefore, varying the pressure would vary the number of nucleation sites, the nucleation frequency and whether or not the nucleation happens. The key objective of this chamber is to raise the temperature of the water from some subcooled temperature to just under saturation at given the pressure, flow and temperature conditions. Another notable point is the use of zirconium tube. Heater rod is of stainless steel and in order to have the same surface conditions and roughness as the CANDU rods, the heater was placed in a zirconium tube, identical to that of CANDU reactors. Zirconium has unique properties such as excellent corrosion resistance, good mechanical properties and very low thermal neutron cross section which make it ideal cladding material for nuclear reactors. The American Society for Testing and Materials (ASTM) offers various grades of zirconium alloys such as Zircloy-2 (Grade R60802) and Zircloy-4 (Grade R60804). The recent one is currently being used in CANDU and its composition is Zr-1.5%Sn-0.2%Fe-0.1%Cr [65]. More details for the zirconium tubes are presented in Appix D. The requirements of the project were as follows: atm pressure, 32-1 C subcooling temperature, low turbulence, m/s inlet water velocity, 124 kw/m 2 heat flux. A custom made cartridge heater including an output power and temperature controller was purchased from BlueWater Heaters Company. The specifications were as follows:

74 58 Dimensions: 0.493" OD ±.002" x 23.22" ± 2% Voltage: 240 VAC. 1ph Power: 2500 watts (+5%, - 10%) Sheath: Termination: Thermocouple: Others: 321 stainless steel and polished CMR termination, stainless single threaded 3/8-18 NPT fitting silver soldered to sheath Built-in Type K ungrounded thermocouple - 30 mm unheated at disk, 60 mm unheated at lead center 500 mm is heated length - Junction centered in heated length and in center of diameter. - 48" fiberglass insulated power and thermocouple leads. The specifications of the zirconium tube from the manufacturer are as follows: Outer Diameter mm ± 0.025mm Inner Diameter mm ± 0.050mm Length 490mm ± 0.075mm The space between the inner wall of the tube and the electrical heater is filled with stainless steel coating which has the same thermal conductivity as the heater metal sheet and was capable of operating at temperature above 200 o C for high thermal conductivity. The electrical heater has the ability to generate the heat flux of up to 124kW/m 2. The K-type thermocouple embedded between the steel heating rod and the Zr-4 shell is used to measure heater temperature at the stainless steel heater and Zr-4 shell interface and to give a first approximation to the wall temperature. The hydraulic diameter of the chamber was therefore calculated as: ( ) ( )

75 59 Chamber Inlet Dimensions (L x W) Heater Rod Diameter Hydraulic Diameter 1.09'' x 0.735'' mm in or 12.17mm Inlet Area x 10 2 mm 2 Length 0.5m Figure 4-6: The Schematics of the Chamber Assembly Figure 4-7: Chamber assembly setup (c) For the visualization purposes, a high-speed CCD camera was used which is discussed in section 4.3 in more details. 4.3 Digital Photographic Method for Visualization A high-speed CCD camera was used to record the bubble nucleation on the heater surface at subcooled flow conditions. Modified slider mechanism was used to allow for a 2-DOF-system. This allowed the user to make small changes in the x- and y- directions. The lightening issue was

76 60 also important in the camera assembly. It should generate intense light and also the user be able to move it. Also, the camera is adjusted to focus on an active nucleation site and for capturing the very short bubble growth period and departure, the camera frame rate was set as high as 4000 frame per second (fps). Figure 4-8: Camera Setup In this study, for the best result of the flow visualization, a digital high-speed camera was used. This was one of the main improvements of the current study over the previous ones. The available camera has a flash-synchronized shutter speed of 1/8000 s, a total 2.74 million pixels CCD (record pixels 128 x 512), and uses direct connection to a computer for the image recording. After capturing the images, in order to correct the contrast and brightness of the images and also obtaining the necessary data regarding the bubbles, image processing was performed by the use of MatLAB and for assuring the accuracy of the result, it was checked by using Image-J software. Figure 4-9: A sample bubble for image processing The digital image process is performed by the use of MatLAB software. First, the appropriate bubble images were selected as indicated by the figure above. The code allows the user to select and crop the original image such that only the bubble in question is within the field of view.

77 61 Then the image was cropped in order to have the bubble as the main object in the image. A sample of the cropped image is shown below. This cropped image undergoes a manual thresholding process whereby the relative contrast between the bubble and the background is adjusted. This is an important step since sufficient contrast between the edge of the bubble and the background is required for the binarization process. Figure 4-10: A sample of the cropped image Before the thresholding process, the software automatically tags the top right and bottom left corners of the cropped image by setting the values of the pixels of these two corners to be zero, which for a grayscale image means they are the darkest possible colour. Once the cropped image is selected, thresholding is performed where the image contrast is adjusted to enhance the boundaries of the bubble for binarization purposes. A series of filters are used as a first step to filter out noisy pixels and enhance object boundaries within the image. A Gaussian bandpass filter was first used to filter out the noise pixels. Pixels with values greater than 125 (half way between perfectly white and perfectly black) were replaced by white pixel to enhance the ninarization step by removing background disturbance that may interfere with edge detection. Please note that any bubble which is in focus was found to have edge pixel values much lower or darker than 125 and thus, thus step would not alter the experimental data. The method of Sobel was used to detect edges of all objects, which is identified based on the gradient of the pixel values of the grayscale image. After completing the edge detection, the output image would be fully binarized into black and white pixels only, with any objects (bubble and debris/noise) outlined by white pixels as in the figure below. The MatLAB Sobel edge detection method uses the Sobel approximation of the derivative to find he local maximum of the pixel value transition to define edges and thus, highlights the importance of having good contrast

78 62 along the borders of the bubble during the threshold stage. A MatLAB bridge function is used to bridge disconnected pixel by setting a zero valued pixel to 1 (black t white) if the pixel has two neighboring non-zero pixel that are not connected to make sure that there is a complete trace of the bubble boundry. Figure 4-11: Binarized image of the sample bubble Then, a series of steps are performed to further filter out noisy objects and to bridge disconnected pixels at the object boundaries that may have been left out in the edge detection process. The objects, defined as anything that is bound by an edge, is filled to white pixels. Figure 4-12: Schematic of a bubble at the final stage of image processing The size characteristic of every indepent body is bound, and only the largest object (the bubble of interest) is kept. Lastly, any kinks in the bubble boundaries are smoothened out to create the image as Fig Using the above methods, the bubble 3-D diameter, bubble centroid, bubble inclination, advancing, and receding angles amongst other properties are given by the program along with the sequence of images shown above as verification of the quality of the digital image process.

79 63 Figure 4-13: The sample bubble before filtering the noise 4.4 Errors and Uncertainty Analysis There are two sources of errors in the image analysis listed as: 1) In ter of the image processing, the error that would occur is due to the thresholding and edge detection process. Typically the maximum error one can expect may be up to 2 pixels around the circumference of the bubble (one pixel on each side). As a result, in ter of the diameter and as an approximation, there may be a ~30-40micron error based on the size of the each pixel (varies in every experiment). 2) The lift-off diameter is based on the Chu et al's paper. He approximates a 3-D bubble diameter from a 2-D image. Based on sample data, there is a 0.01% to 2.94% error when comparing a 3-D bubble diameter from a 3-D image to the 2-D approximation using the equation he provided [59]. The uncertainties associated with the applied heat and mass fluxes were almost and, respectively. Also the uncertainties for the pressure gauges and the thermocouples were and, respectively. Calibration of the flow meter was performed and its accuracy was given as. The temperature of the fluid and the heater surface was measured by the use of four K-type thermocouples placed on the chamber and underneath the heater surface. The pressure was also measured at the test section by a single scale multi-purpose pressure gauge.

80 64 In order to have more accurate results, distilled water was used and it was passed through purifier and demineralizer for around 24 hours before each series of tests for removing all the impurities. The dissolved air was also removed by boiling the water in the storage tank for about three to four hours. Once the test was started, and the steady state as well as the desire pressure and the temperature were reached in the test section, the video recording of the bubble nucleation was initiated and it last for about 10 seconds.

81 Chapter 5 Results and Discussion 65

82 66 5 Results and Discussion In this chapter, characteristics of a typical vapour bubble in various subcooled boiling conditions are discussed by using the high-speed imaging results, and the effect of the experimental conditions such as the effect of subcooling, pressure and flow rate on the bubbles will be investigated. Finally, simple correlations for the bubble lift-off diameter are presented and compared with the experimental data. 5.1 Visualization and Image Analysis In subcooled flow boiling process, bubbles nucleate in small cavities and/or pits on the surface of the heater filled with vapour. These cavities are known as nucleation sites. Growth of bubbles is strongly influenced by the temperature and velocity gradients. Typically, bubbles show a similar behavior: bubbles nucleate on the cavities, grow, then slide for a short distance on the heater surface and then detach from the surface to enter the subcooled flow region. After that, they promptly condense. The bubbles sizes and their life-spans strongly dep on the subcooling, surface superheat, mass flow rates and pressure. They are also a function of the cavity size and the local surface temperature variations, as well as the surrounding bubbles (local flow turbulence) [55]. Typical bubble behaviors from the nucleation to lift-off are shown in figures 5-1, 5-4, and 5-6 for three different conditions. Fig. 5-1 shows the process of nucleation and bubble growth at 1atm pressure, mass flux of 350 kg/m 2 s, heat flux of 124 kw/m 2 and subcooling of 4 o C. The nucleation site is shown with a bold arrow at t = 0. Once the bubble is formed, it grows and at some time between t = 0.25 and t = 0.5, the bubble leaves the nucleation site and therefore, departure happens. The vertical solid line on the figure shows the nucleation site on all the pictures. Although the bubble leaves its initial site, it still continues growing almost linearly until about t = 2.5. Note that the time intervals in the consecutive pictures are not the same. After this point, the tip of the bubble gradually enters the subcooled region of the flow. Bubble starts to condensate once it enters the subcooled region. The liquid surrounding a bubble is superheated while the bubble is small. As soon as the bubble reaches a certain size, its tip enters the subcooled region of the bulk liquid and the bubble starts to condense; thus the effective

83 67 superheat surrounding the bubble becomes less than the wall superheat. This effect can be seen as the flatten top of the bubble. During the sliding time, vaporization takes place at the inner surface of the bubble, while there may be condensation at the outer surface of the bubble. This condition is met when the tip of the bubble is out of the superheated layer and enters the boundaries of the subcooled bulk flow. Therefore, growth or condensation of the bubble is governed by the overall effect of these two processes. After sliding for some distance on the heater surface, the bubble reaches its lift-off size. At t = 7.5, the bubble leaves the heater surface and consequently, its diameter at this moment is recorded and identified as the lift-off diameter. After the lift-off, the bubble enters the subcooled flow and therefore, shrinks. This point is shown by the vertical dash line on the figure. The distance between the two vertical lines (i.e. vertical dash and solid lines) shows the sliding distance of the bubble and can be used to obtain the sliding velocity of the bubble. The rate of bubble collapse has a direct relationship with the degree of subcooling of this region. Increasing the degree of subcooling (i.e. cooler flow), results in a faster collapse rate for the bubble. In Fig. 5-1, the degree of subcooling is only 4 o C and thus, the bubble shrinks less compared to the other condition shown in Fig. 5-4 which has the degree of subcooling of 9 o C. Fig. 5-1 has the least pressure and degree of subcooling; subsequently it has the largest lift-off diameter, while conditions in Fig. 5-4 provide the smallest diameter. The experimental test section is horizontal; however, there is a small slope on the images. This slope is due to the camera orientation with respect to the test section.

84 Flow direction from right to left 68 t= 0.0 t= 4.75 Nucleation t= 0.25 t= 5.25 Departure t= 0.5 t= 5.5 t= 0.75 t= 6.0 t= 2 t= 6.75 t= 2.5 t= 7.0 t= 3.25 t= 7.5 Lift- Off t= 4 t= 8.0 Figure 5-1: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1 atm, Mass Flux: 350 kg/m 2 s, Heat Flux: 124 kw/m 2, Subcooling: 4 o C)

85 69 In Fig. 5-2 the temporal variation of the bubble volume and the equivalent spherical bubble diameter, for the above flow conditions is shown. The bubble lifetime is divided into two parts of growth and condensation. The condensation is further divided into two sub-parts: condensation on the wall (while the bubble is still sliding on the heater surface) and condensation after lift-off. As indicated by the figure, bubbles start to condense while they are still on the heater surface and therefore, they reach their maximum size and then condensation happens. As a result, the bubble maximum size and its lift-off size are different. This agrees with Tolubinsky and Kostanchuck [66] and Farajisarir [44]. This is different than that of pool boiling, where the two sizes are the same. The duration of the growth and condensation periods dep on the experimental conditions. According to Akiyama the superheated layer thickness is small and the bubble sps only a small fraction of its growth period in this layer (t <0.10 t m ) [67]. The growth of the bubble is more affected by micro/macro- layer evaporation, than by conduction through the superheated layer [44]. After reaching the maximum size, evaporation from the bubble base is balanced with condensation at the bubble top surface. After this moment, the condensation becomes dominant while the bubble is still sliding on the heater surface and is in contact with it. The surface tension as a result of temperature gradient across the flow is formed along the bubble interface and it is the driving force for the bubble ejection from the wall [68]. Once the bubble detaches from the heater surface, higher rate of condensation occurs since the bubble has lost its contact with the heater surface and become farther from the superheated layer. It was observed that contrary to void growth model assumptions that the OSV point coincided with bubble lift-off, ejection occurred well before the point of OSV.

86 3D Diameter (mm) Volume (mm^3) Volume Lift-off occurs at t = Diamete Growth Region Condensation & Sliding Condensation & Lift-off Time () Figure 5-2: Growth and collapse curve for a typical bubble at Pressure: 1 atm, Mass Flux: 350 kg/m 2 s, Heat Flux: 124 kw/m 2, Subcooling: 4 o C The parallel and normal displacements of the bubble centroid are shown in the figure below. These values are used to calculate the corresponding velocities. Each displacement has been measured with respect to the bubble nucleation site. The parallel bubble velocity is defined as the slope of the parallel displacement curve, while the normal velocity of the bubble is defined as the slope of the normal displacement of the bubble centroid with respect to the heater surface. The parallel velocity is constant throughout the growth and collapse process and has the same order of magnitude of the mean flow velocity. This agrees well with Farajisarir results [44]. Please note that the slip ratio, defined as the ratio of bubble parallel velocity to mean flow velocity, deps only on the local conditions and not on the bubble size as reported by Akiyama and Farajisarir. Farajisarir also found that the slip ratio ranged from in his experiment, while Akiyama reported values of for the slip ratio.

87 Displacement (mm) 71 On the other hand, the bubble centroid has its maximum value of normal velocity at the region after the lift-off. The bubble lift-off velocity is defined as the normal velocity of the bubble at the moment of the lift-off and can be obtained by measuring the slope of the line through the points past the dashed line. The lift-off velocity strongly deps on the subcooling condition. This is more obvious at higher subcooling due to higher temperature gradient, as mentioned by Farajisarir Growth Region Condensation & Sliding Condensation & Lift-off L p L n Time () Figure 5-3: Normal and parallel displacement of the centroid of a typical bubble at Pressure: 1 atm, Mass Flux: 350 kg/m 2 s, Heat Flux: 124 kw/m 2, Subcooling: 4 o C A sample bubble in the pressure of 1.5 atm, mass flux of 300 kg/m 2 s, heat flux of 124 kw/m 2, and subcooling of 9 o C is presented in Fig Again, nucleation takes place at t = 0, but departure happens between t = 0.5 and t = Due to a higher pressure inside the chamber, and a higher degree of subcooling of the inlet flow, size of the bubble in this case, is much smaller than the previous condition. The lift-off occurs at t = 2.75, compared to t = 7.5 which was the lift-off moment for the conditions provided in Fig Sliding distance is again reduced in this condition. All these variations are mainly due to the pressure difference in

88 72 two mentioned cases. Although they are slightly different in their mass fluxes and degrees of subcooling, pressure plays the main role in determining the lift-off instant and diameter. Furthermore, for better understanding of the advancing and receding contact angles (previously shown in Fig. 3-8), the following table is presented to show these two angles at each consecutive image of the bubble shown in Fig. 5-1: Table 5-1: Advancing and Receding contact angles of the bubble shown in the Fig. 5-1 Time () Advancing contact angle Receding contact angle Difference (θ r θ a ) )t= t= t= t= t= t= t= t= t= t= t= t= t= According to the table, the differences range from 80 to 99 degrees and at the moment of the liftoff, the difference is 92 degrees. Additional investigations in this field are required for more accurate results.

89 73 t= 0.0 t= 1.75 t= 0.25 Nucleation t= 2.0 t= 0.5 t= 2.25 Departure t= 0.75 t= 2.5 Lift-Off t= 1.0 t= 2.75 t= 1.25 t= 3.0 t= 1.5 t= 3.5 Figure 5-4: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1.5 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 9 o C) Fig. 5-5 shows the growth of the bubble in the flow conditions of the Fig In this figure, a rough estimate of the superheated layer close to the heater surface and the subcooled liquid flow on top of that, are presented with red and blue colors, respectively. The gradient change in the colors shows the temperature profile in a normal direction to the flow and the heater orientation.

90 74 In this figure, the consecutive images from Fig. 5-4 are placed in a row to visually show the growth of the bubble in the superheated layer. The calculated heater surface temperature as well as the water temperature is shown at the bottom and the top of the figure. In this work, only the subcooled temperature was measured and the surface temperature was calculated using the Liu and Winterton correlation [21]. The subcooled flow near the heater surface induces a quasisteady drag force on the bubble. Therefore, bubble centre line does not stay vertical to the surface while the bubble slides and the bubble is inclined in the flow direction with some angle. According to the figure shown below, the bubble attempts to straighten itself such that this angle, i.e. the inclination angle, becomes zero. This occurs at the moment of lift-off, where the angle approaches zero. One good explanation for this event is that the quasi-steady drag force becomes negligible as a result of almost zero difference between the bubble and the surrounding liquid velocities. Liquid Temp.: 102 degree C Surface Temp.: 124 degree C Figure 5-5: Bubble growth in superheat layer (same flow conditions as those of the Fig. 5-4) The flow conditions of the third case which is shown in Fig. 5-6 are as follows: pressure: 1 atm, mass flux: 300 kg/m 2 s, Heat Flux: 124 kw/m 2, Subcooling: 9 o C. Its main difference with the first condition shown in Fig. 5-1 is their degrees of subcooling, i.e. 9 degrees versus 4 degrees (there is a slight difference in their mass fluxes as well). Also, comparing this case with the second case shows that the pressure is at 1 atm instead of 1.5 atm. Departure was seen at 0.5 < t < 0.75, while the lift-off occurs at t = 5.5. By comparing all these three cases, one can find that if a bubble is attached to the wall for a longer time, it becomes larger. This is mainly a function of the pressure and the degree of subcooling. To investigate how all these features affect the bubble, we need to analyze the applied forces on a bubble, which will be discussed in more detail later.

91 75 t= 0.0 t= 3.5 t= 0.25 Nucleation t= 4.0 t= 0.5 t= 0.75 Departure t= 4.5 t= 4.75 t= 1.25 t= 5.0 t= 1.5 t= 5.25 t= 2.0 t= 5.5 Lift-off t= 2.5 t= 3.0 t= 5.75 t= 6.0 Figure 5-6: Consecutive images of the nucleation to lift-off process of representative bubbles (Pressure: 1.0 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 9 o C).

92 76 The experimental results have revealed that the nucleation, departure, and liftoff steps dep on the operating conditions. In some cases, the bubble does not depart and the nucleated bubble grows at the nucleation site until it lifts off. In addition, a bubble may only depart from the nucleation site and slide on the surface without lift-off. We will discuss these phenomena more by providing some graphic examples. In Figures 5-1 to 5-6, we had shown and discussed the normal behavior of a bubble in subcooled liquid flow. In these cases, according to the experimental conditions, such as the inlet temperature of the water, pressure, and mass flux, the bubble can have various sizes and departure/ lift-off times. Furthermore, the experimental conditions influence the rate of bubble condensation after its lift-off. In another scenario, which is shown in Fig. 5-7, a bubble remains close to the wall after its liftoff and in some cases bounces back and reattaches to the wall. A good explanation for that is the existence of boundary layers close to the heated wall and velocity profile of the flow in the chamber. This makes a lower pressure region close to the wall and forces the bubble to reattach to the wall. In the presented case, the bubble lifts off at t= 2.0 after the first shown image and then, comes back to the heater surface at t= During this time, i.e = 2.25, during which the bubble has no contact with the heater, it shrinks due to the existence of the subcooled liquid around it. The bubble again leaves the surface at t= 6.75, and will repeat this process for a few times before it exits the test chamber. This figure corresponds to the following condition: inside pressure of 2 atm, mass flux of 350 kg/m 2 s, heat flux of 124 kw/m 2, and bulk water temperature of 104 o C, i.e. subcooling of 16 o C.

93 77 t= 0.0 t= 4.75 t= 1.0 t= 5.0 t= 1.5 t= 5.5 t= 2.0 Lift-off t= 6.0 t= 2.5 t= 6.5 t= 3.0 t= 6.75 Lift-off t= 3.5 t= 4.25 Reattachment t= 7.25 t= 8.0 Figure 5-7: Consecutive images of the Bouncing phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass Flux: 350 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 16 o C) Fig. 5-8 shows a high subcooling case at high pressure conditions. In this case, bubbles never reach the required lift-off size and therefore, just slide along the wall and maintain a relatively constant size. One reason for this phenomenon can be the asymmetrical expansion of the bubble due to the wall existence. This induces an unsteady drag force (also called the growth force) in

94 78 the direction normal to the wall and retards the detachment of the bubble and thus, a bubble has difficulties to detach from the wall due to the significant effect of the growth force. t= 0.0 t= 3.0 t= 0.5 t= 3.5 t= 1.0 t= 4.0 t= 1.5 t= 4.5 t= 2.0 t= 5.0 t= 2.5 t= 5.5 Figure 5-8: Consecutive images of the Sliding phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass Flux: 300 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 26 o C) Coalescence One of the main phenomena in subcooled boiling is the bubble coalescence, which plays an essential role in forming the noticeable void fraction in a channel and causes large vapor clot formation and sometimes, small dry area formation. The bubble coalescence occurs in two ways [69]: 1) coalescence among the discrete bubbles located at neighboring nucleate sites; 2) growing bubbles merge at their nucleation sites into larger flowing bubbles. Both of these were observed in the current work. Bonjour et al. summarized the coalescence phenomena in two-phase flow

95 79 into three types [70]: 1) Coalescence far away from the heated wall, 2) Coalescence between consecutive bubbles near the wall, and 3) Coalescence between adjacent bubbles near the wall. In Bang s work, the coalescence between adjacent bubbles mostly causes the agglomeration of vapor remnants associated with the vaporization of interleaved liquid layer and then the coalesced bubbles act and separate from the surface similar to the discrete bubbles. In Fig. 5-9, Bang showed this phenomenon in more details for both pool and subcooled flow boiling: Figure 5-9: Schematic of the bubble Coalescence in Pool and Flow Boiling [69]

96 80 Video recordings were made of the two-phase flow field in the channel by the use of high-speedcamera. For more understanding of the phenomenon some sample cases are shown below: t= 0.0 t= 2.5 t= 0.25 t= 2.75 t= 0.5 t= 3.0 t= 0.75 Coalescence t= 3.25 t= 1.0 t= 3.75 t= 1.25 t= 4.25 t= 1.5 t= 4.5 t= 2.0 Lift-off Figure 5-10: Consecutive images of the Coalescence phenomenon in subcooled flow boiling (Pressure: 2.5 atm, Mass Flux: 400 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 15 o C)

97 81 t= 0.0 t= 2.75 t= 0.5 t= 3.0 t= 1.0 t= 3.25 t= 1.25 t= 3.5 t= 1.5 t= 3.75 t= 2.0 t= 4.25 Lift-off t= 2.25 t= 4.5 t= 2.5 Coalescence t= 5.0 Figure 5-11: Consecutive images of the Coalescence phenomenon in subcooled flow boiling (Pressure: 2 atm, Mass Flux: 350 kg/m2s, Heat Flux: 124 kw/m2, Subcooling: 16 o C)

98 82 As indicated by the figures above, bubbles grew on the heater surface and coalesced right before detaching the surface. After detaching, due to the lower bulk temperature than the saturated temperature, bubbles shrink and disappeared. The experimental data were analyzed to determine the bubble growth rates, bubble departure diameter, bubble lift-off diameter, and bubble departure velocities. These results will be discussed in more details in the following sections. 5.2 Experimental Analysis Balance of forces acting on a bubble at the departure A bubble will leave its nucleation site once the sum of the forces parallel to the flow direction is equal to zero: where, is the net force acting on a bubble along the x-direction, is the surface tension force along the x-direction, is the unsteady drag force, and is the quasi-steady force in the flow direction. These forces are written as follows [39]: [ ( ) ( ) ( ) ( )] [ ( ) ] where, is the bubble radius and and are its first and second derivatives with respect to time. The bubble radius is a function of time and the Jakob number, and thus, can be written in ter of: where, b is a constant and it is suggested to be 1.73 by Zeng et al. (1993); α f is the thermal diffusivity defined as with Cp f being the specific heat of liquid at constant pressure (J/kg.K),

99 83 ρ f being the liquid density (kg/m 3 ), and Jakob number defined as: being the thermal conductivity (W/m.K). Ja is the ( ) ( ) where, ΔT sat is the wall superheat (K), h fg is the latent heat at measured at the operating pressure (kj/kg), T w is the wall temperature (K), and T sat is the saturation temperature (K). σ is the surface tension coefficient (N/m); is the bubble contact diameter and is given as, by Cho et al (2011), where is the contact angle. The advancing and receding contact angles, i.e. θ a and θ r, are obtained from: and, or. where, is reported by Klausner as =4.5 o, while Bibeau [71], and Winterton [72] evaluated as 2.5 o and 10 o, respectively. In literature, the value reported by Klausner was mostly used [37]; thus, in this report, is assumed to be 4.5 o, as well. Rewrite the force balance as: [ ( ) ( )] [ ] ( ) By defining: ( ) ( ) [ ( )] [ ] [ ( ) ( )( )] [ ] Zeng et al. (1993) provided the following relations for the forces:

100 84 (1) (2) The contact angle and the departure diameter can be determined from the above equations. The solution to the above equations is provided in Appix-A Balance of forces acting on a bubble at the lift-off At the instant of the bubble lift-off from the heater surface, the net forces normal to the flow direction acting on the growing bubble are just balanced. The instant of the bubble lift-off was determined as the moment that the bubble had the least contact with the heated surface. It should be noted that in the subcooled boiling cases, the center of the bubble continuously moves away from the nucleation site. In the pool boiling syste, a bubble departure generally means the instant that a bubble is detached from a heated surface, and the bubble grows from the time of nucleation to the time of departure due to the evaporation. Therefore, the total heat transfer to the bubble can be determined based on knowing the local heat flux and the time of lift-off. On the other hand, a departure in forced convective boiling corresponds to the instant that the bubble leaves the nucleation site, according to Klausner et al. s definition [37]. However, in many cases, a bubble can slide continuously away from the nucleation site while it is actively growing due to the evaporation heat transfer. Therefore, it is more difficult to determine the total heat transfer to the bubble in the forced convective boiling syste. Fig shows the force balance in the y-direction and at the moment of the bubble s lift-off. Due to the insignificant contact area between the bubble and the heater surface, the bubble surface tension, contact pressure force and hydrodynamic force are almost zero and can be neglected. In addition to these assumptions, the bubble inclination angle is almost zero, and therefore, the growth force has only one component in y-direction. Thus the only forces acting on the bubble are the growth, buoyancy and shear lift forces. The force balance in y-direction:

101 Y 85 X Y F b F sl X F du F b F h, F cp = 0 F sl F sy = 0 Figure 5-12: Force balance F du of a vapour bubble at lift-off F h, F cp = 0 By Substituting the expressions of the growth force, shear lift and buoyancy forces into the above equation: F sy = 0 ( ) ( ) ( ) Zeng observed that for predicting the bubble lift-off diameter, the shear lift force can be omitted, since the bubble sliding velocity at the moment of the lift-off is almost the same as the surrounding liquid and its shape is almost spherical (having close to zero contact angle) [39]. According to these assumptions, the following correlation for the bubble lift-off diameter was obtained: ( ) ( ( ) ) eq. 5-1 The growth rate constant, b, was obtained from the Zuber s model [15]: eq. 5-2

102 86 One can see the depence of the bubble growth on the temperature of the surrounding liquid in that model. Various values have been offered for b for different conditions and assemblies. As an example Zeng suggested using a value of 1.73 comparing to other values ranging from 0.24 to 3.5. In the current work different values for each pressure were tried to get the minimum error and thus, a model for b as a function of pressure is suggested. This model was obtained by curve fitting the experimental data. Moreover, some more experimental cases were carried out without curve fitting in order to check the model s prediction ability for the new data set. Generally, bubbles have high rates of growth at the early stages of their nucleation, but this reduces in time. This shows that b does not remain constant as the pressure changes: eq. 5-3 where, b o is found to be constant value of , and p is the experimental pressure in atm. As the model shows, the bubble lift-off diameter was evaluated in ter of heat flux, mass flux, and degree of subcooling. According to the model, depence of the bubble lift-off diameter on the Jakob number is obvious. In this model Ja e is the effective Jakob number which is: ( ) eq. 5-4 where, ( ), and is the suppression factor and equals to (by Situ et al. (2005)): where Re TP is the two-phase Reynolds number calculated by setting vapor quality as zero, ( ). According to the short length of the test section and its small heater power, the estimation of the point of net vapor generation does not considerably affect the calculation of the wall temperature.

103 87 where, ( ) To calculate the Jakob number, we need to either measure the heater surface temperature or estimate it. Since in this work, the surface temperature was not measured, Liu and Winterton method was used to estimate the surface temperature [21]: [ ( ( )( ))] eq. 5-5 With ( ) is the bulk liquid temperature, is the heater surface temperature, and is the water saturated temperature. The other parameters are: [ ( )] ( ) ( ) ( ) Upon analyzing the recorded images for the bubble behaviors, it was found that there are significant differences in bubble sizes and lifetimes for bubbles in the same experimental conditions. There are two main causes for such variations: (1) existing cavities on the surface have different sizes, which result in various bubble sizes, and/or (2) bubbles are experiencing varying local temporal and velocity fields. Prodanovic mentioned the later effects as the dominant in creating scatter in experimental data [55]. In this study, bubbles whose detachment

104 Bubble Diameter, mm 88 diameters and initial growth rates are closest to averages for a given set of experimental conditions are chosen. Also surface roughness plays an important role in initiating the nucleation and bubble diameter. In this study, the average surface roughness was around 0.12, since the maximum roughness was around 0.6. In each experimental case, different values for the bubble lift-off diameter have been measured. Therefore, in order to report one lift-off diameter for each case, an average and a standard deviations over the entire measured lift-off diameter in each case have been calculated. In the figure below, all the case for 1 atm along with their corresponding standard deviations are shown. According to the figure, the maximum standard deviation was seen in Case 9 which was mm, while the least standard deviation was mm for the Case Mass Flux= 300 kg/s.m2 Mass Flux= 350 kg/s.m2 Mass Flux= 400 kg/s.m Subcooling, Deg. C Figure 5-13: Bubble lift-off diameters vs. Subcooling for all the cases at 1 atm and their corresponding standard deviations Generally, experiments have revealed that bubble behavior within a given range of experimental conditions, such as mass and heat fluxes, cannot be represented by a single model; although they behave in a similar manner within a region bounded by the ONB and OSV [55]. One weakness of the methods adopted by the method above is the assumption of the rigidity of the bubble from the force balance approach, which neglects changes in surface tension forces in directions along

105 89 and normal to the flow. Kandlikar and Stumm alleviated this issue by using a control volume approach on two halves of a bubble [73]. However, their model neglected inertial forces and thus only accurate for low flow rate conditions. Bubble lift-off diameter was measured from all the experimental tests. The lift-off diameter was averaged over all the nucleation sites. In this study, it was found that our experimental conditions covered the late stage of the partial boiling (PB) region and the early stage of the fully developed boiling (FDB) region as well as a few cases close to the FDB- OSV border deping on the flow and heat flux conditions. In this study, the wall superheat at the onset of nucleate boiling (ONB) was calculated using Hsu correlation [31]. Also, the wall superheat at the FDB was obtained by the use of Thom et al. method [34]. Saha and Zuber correlation was used in order to determine the subcooling at the point of onset of significant void (OSV) [36]. One reason for using an average lift-off diameter among all the nucleation sites in each experimental condition is that the bubble data such as lift-off diameter and frequency might be different from one cavity to another because of the differences in the microscopic structure of each cavity. Using the proposed model for the lift-off diameter and the suggested correlation by Liu and Winterton for calculating the wall superheat, the predicted bubble lift-off diameters were calculated and are presented in table 5-1.

106 90 Table 5-2: Data bank Label Pressure (atm) Mass flux (kg/m^2.s) Heat flux (kw/m^2) Local Subcooling (deg. C) No. of sites Mean lift-off Dia (mm) No. of bubbles Subcooling Regime Jakob No. Predicted Dia. (mm) Case PB Case PB Case FDB Case FDB Case FDB-OSV Case PB Case FDB Case FDB-OSV Case OSV Case PB Case FDB Case FDB Case PB Case PB Case FDB Case FDB-OSV Case PB Case PB Case PB Case FDB

107 91 Label Pressure (atm) Mass flux (kg/m^2.s) Heat flux (kw/m^2) Local Subcooling (deg. C) No. of sites Mean lift-off Dia (mm) No. of bubbles Subcooling Regime Jakob No. Predicted Dia. (mm) Case PB Case PB Case FDB-OSV Case OSV Case PB Case PB Case OSV Case PB Case PB Case PB Case OSV Case PB Case PB Case FDB Case FDB-OSV Case PB Case PB Case PB Case FDB Case FDB Case PB Case FDB Case FDB

108 92 Label Pressure (atm) Mass flux (kg/m^2.s) Heat flux (kw/m^2) Local Subcooling (deg. C) No. of sites Mean lift-off Dia (mm) No. of bubbles Subcooling Regime Jakob No. Predicted Dia. (mm) Case FDB

109 Bubble Diameter, mm 93 The experimentally determined bubble lift-off diameters are plotted versus the mass flux, the operating pressure and the degree of subcooling. Fig shows the effect of the liquid pressure on the bubble lift-off diameter. The lift-off diameter reduces by increasing the fluid pressure at all the mass fluxes and the subcooling temperatures. The same result was obtained by previous researchers (e.g. Tolubinsky and Kostanchuk [66]; Prodanovic [55]). However, the present study in contrary to that of Tolubinsky s work, shows that the bubble lifetime and sliding time decrease with an increase in pressure (similar to Prodanovic work). The bubble sizes are smaller at higher pressures, and bubbles collapse faster at higher subcooling temperatures. Furthermore, Yuan et al. [74] reported that the bubble growth rate at 0.1 MPa was about 10 times of that at 1.0 MPa in their experiments Pressure, atm "G=300 kg/s.m2, Subcooling=8-11 deg. C" "G=300 kg/s.m2, Subcooling=17-24 deg. C" G=400 kg/s.m2, Subcooling=8-9 deg. C Figure 5-14: Effect of the liquid pressure on the bubble lift-off diameter (heat flux: 124 kw/m2). Next, the effect of the liquid mass flux on the bubble lift-off diameter was investigated in various conditions. The results show that the bubble lift-off diameter decreases with increasing the mass fluxes. This is shown in Fig Effect of the liquid mass flux on the bubble sizes and lifetimes is more evident in lower heat fluxes. Since in this study, the available heat flux was relatively low, the effect of the mass flux is more pronounced. This effect becomes less important as the OSV is neared, which is in agreement with Prodanovic s study [55]. It is also observed that the bubble population increases with decreasing the mass flux, particularly at low heat fluxes where the single-phase forced convection plays an

110 Bubble Diameter, mm 94 important role. Lower liquid mass flux means lower convection heat flux coefficients. This causes less heat removal from the surface and thus, causes higher local surface temperatures that increases the number of active nucleation sites (i.e. more bubbles can nucleate on the surface). On the other hand, by increasing the mass flux in the chamber, the wall superheat is lowered due to more efficient heat transfer, which results in decreasing the bubble population. Also, the higher mass flux, which means a higher flow velocity, causes more bubbles to separate from the wall Mass Flux, kg/s.m 2 p=1 atm, subcooling=17-20 Deg. C p=1.5 atm, subcooling=24 Deg. C p=2 atm, subcooling=16-20 Deg. C p=2.5 atm, subcooling=14-15 Deg. C p=3 atm, subcooling=16-17 Deg. C Figure 5-15: Effect of the mass flux on the bubble lift-off diameter (heat flux: 124 kw/m2). Fig shows the effect of the liquid subcooling on the bubble lift-off diameter. The bubble lift-off diameter decreases by increasing the subcooling and the mass flux. Our results are in agreement with those of Okawa et al. who reported that bubbles slid a longer distances for lower subcooling temperatures and higher mass fluxes [56]. Generally, the bubble sizes increase with decreasing the subcooling temperature at a fixed flow rate, heat flux and pressure. At low subcooling temperatures, the lower temperature gradients in the liquid surrounding a bubble lowers the condensation rates and allows the bubble to grow more (Zeitoun and Shoukri [75]; Tolubinsky and Kostanchuk [66]; Farajisarir [44]; Kandlikar [73]). In addition to the bubble size, lower subcooling temperature reduces the bubble lifetimes.

111 Bubble Diameter, mm 95 The results also show that there are substantial variations in the bubble lift-off diameter. This was the case even for the neighboring sites considering that the heat flux was almost the same for all such nucleation sites, and even for cases in which the liquid subcooling between the inlet and outlet was 3-4 o C. This implies that although most of the models and correlations assume that the bubble lift-off diameter and nucleation frequency are only a function of external mass flow and the heat flux, bubble characteristics, such as bubble diameter and frequency, dep on the microstructure of the nucleation cavities. Therefore, an adequate number of nucleation sites should be considered to obtain reliable results. Also the bubble lift-off diameter and the frequency compete with each other in removing the heat from the heater wall which results in higher than average value for the bubble lift-off diameter and lower the average value for the nucleation frequency, and vice versa. The heat flux for all test cases was kept constant at 124 kw/m 2. The results have also shown that the contact angle of the bubble with the heater surface increased with increasing flow velocities. This happens because at higher velocities, the quasi-steady drag force increases and results in an increase in the advancing contact angle p=1 atm p=1.5 atm p=2 atm p=2.5 atm p=3 atm Subcooling, Deg. C Figure 5-16: Effect of the fluid subcooling on the bubble lift-off diameter (heat flux: 124 kw/m2, mass flux: 300 kg/m2.s).

112 Comparison between the experimental and predicted results In this section, the experimentally obtained bubble lift-off diameters are compared with those predicted by the developed model. Fig compares the experimental and predicted bubble lift-off diameters at two different conditions versus the chamber pressure. The predictions are in good agreements with the experimentally determined values. The conditions for the data presented in this figure correspond to the conditions selected from Fig (only two conditions were selected). Fig compares the experimental and predicted bubble lift off diameters for various mass fluxes. Two of the conditions provided in Fig are selected for this comparison. The predicted results match the experimental data with good accuracy. In Fig. 5-19, tr in subcooling was investigated for both the experimental and predicted bubble lift-off diameters. It is evident that they both decrease with higher subcoolings but the values of the diameters as well as the rate of decreasing are different.

113 Bubble Diameter, mm Bubble Diameter, mm Experimental data for G=300 kg/s.m2, Subcooling=8-11 deg. C Predicted data for G=300 kg/s.m2, Subcooling=8-11 deg. C Pressure, atm a) Mass flux= 300 kg/m 2.s, and Subcooling= 8-11 o C Experimental data for G=300 kg/s.m2, Subcooling=17-24 deg. C Predicted data for G=300 kg/s.m2, Subcooling=17-24 deg. C Pressure, atm b) Mass flux= 300 kg/m 2.s, Subcooling= o C Figure 5-17: Comparison of the experimental data with the predicted data at different pressures and for different flow conditions.

114 Bubble Diameter, mm Bubble Diameter, mm Experimental data for p=1 atm, subcooling=17-20 Deg. C Predicted data for p=1 atm, subcooling=17-20 Deg. C Mass Flux, kg/s.m 2 a) Data for pressure= 1 atm, subcooling= o C Experimental data for p=2 atm, subcooling=16-20 Deg. C Predicted data for p=2 atm, subcooling=16-20 Deg. C Mass Flux, kg/s.m 2 b) Data for pressure= 2 atm, subcooling= o C Figure 5-18: Comparison of the experimental data versus the predicted data in different conditions (mass flux)

115 Bubble Diameter, mm Bubble Diameter, mm Experimental data for p=1 atm Predicted data for p=1.0 atm Subcooling, Deg. C a) Data for pressure= 1 atm, mass flux= 300 kg/m 2.s Experimental data for p=2.5 atm Predicted data for p=2.5 atm Subcooling, Deg. C b) Data for pressure= 2.5 atm, mass flux= 300 kg/m 2.s Figure 5-19: Comparison of the experimental data versus the predicted data in different conditions (subcooling) The general tr of the predicted and experimental data appears similar although the error does increase as discussed above with increasing the pressure. With an increase in subcooling

116 100 margin, the bubble lift-off diameter decreases for a constant pressure. This is likely due to the fact that at higher subcooling, the effective wall superheat decreases due to the higher forced convection effect with lower bulk liquid temperature. In addition, both experimental and predicted trs show that increasing the pressure will decrease the bubble lift-off diameter for the same subcooling. In this work, the effect of heat flux on the bubble diameter was not investigated. To give some idea regarding the heat flux effect, Prodanovic finding is presented [55]. He has reported that increasing the mass flux will decrease the bubble diameter; however, when OSV was neared, the effect of mass flux became less pronounced. He also concluded that increasing the heat flux would decrease the maximum bubble diameter. This was observed in low heat fluxes while in higher heat fluxes, the bubble diameter remained almost constant. In the present study, a database for the bubble lift-off diameter was built by integrating our experimental data. Then, the predictive capability of the proposed model was evaluated against the database. As mentioned before, two series of experiments have been conducted in this research work. By completion the first set, all the bubble lift-off diameters were measured and a model by curve fitting method was proposed. Fig shows the errors associated with this set. Then, the second set of experiments has been carried out in order to compare the experimental results with the predicted bubble diameters from the proposed model. The errors for data points of this set are also shown in Fig Finally, for the purpose of error analysis over the whole work, the proposed model is compared with all the data points and it is presented in Fig The proposed model provides reasonable agreement with our experimental work by having average errors of 21.07%, 16.81% and 19.91% for each figure, respectively. The cases in the first set of experiments are as follows: 1-6, 8-11, 13-20, 22-26, total of 32 cases Rest of the cases has been done for the second set of experiment.

117 101 The absolute error for each experiment is defined as: eq. 5-6 Also, the weighted error for a specific case based on the experimental data available is: eq. 5-7 where, n is the number of the bubbles used to find the experimental lift off diameter, and i is the number of the experiments (from the first to the N th experiment). The weighted average error becomes: ( ) eq. 5-8

118 Predicted Lift-off Diameter, mm Predicted Lift-off Diameter, mm % % Measured Lift-off Diameter, mm Figure 5-20: Prediction results of the proposed model against the first set of the experimental lift-off diameter (average error: 21.07%) % % Measured Lift-off Diameter, mm Figure 5-21: Prediction results of the proposed model against the second set of the experimental lift-off diameter (average error: 16.81%)

119 Predicted Lift-off Diameter, mm % % Measured Lift-off Diameter, mm Figure 5-22: Prediction results of the proposed model against the entire experimental lift-off diameter (average error: 19.91%) There are several sources of error in our experiments. These are errors associated with the measurement methods and apparatus, and image processing. In addition, the model has not considered all the physical process. For instance, the shear forces are neglected and the contact angle at the time of lift off is assumed to be zero. Although the relative velocities of each bubble in the direction of the flow were measured, the standard deviation was high. Therefore, the shear lift-coefficient could not be accurately determined. In addition, the definition of the relative bubble velocity with respect to the bubble centroid may cause errors when bubbles deform at the lift-off. Future works can include accurately characterizing the bubble relative velocity. In the current model, b as a function of pressure was used to provide the lowest average error of %19.91 (average weighted error of %21.53). The present model is also compared with several commonly reported used models, as shown in Fig The present model can be considered to be one of the better models for the prediction of the bubble lift off diameter. Five models in addition to our current model are shown in this figure. The average errors associated with Prodanovic model [55], Unal model

120 104 [53], Zeng model [39], Situ model [18], and Basu model [50] are 27.8%, 44.1%, 78.2%, 53.6%, and 48.9%, respectively. Zeng model shows the highest average error and generally overpredicts the experimental result. This is mainly due to the use of constant value for b. He did not propose an explicit model but the results shown are based on his proposed force balance and growth rate constant. This model was developed for horizontal flows but does not seem to be reliable. The second highest error was for the Situ s model. This model was developed for vertical chambers and the main reason for this error has come from their assumption that the bubble sliding velocity is half of the local liquid velocity. This assumption did not coincide with other researchers observations. Basu and Unal models also show high errors which is due to the fact that their models were developed for vertical and not horizontal flows. In addition, Unal s model predicts the maximum bubble diameter and not the lift-off diameter. The best result was seen in Prodanovic with only 27.8% of error which is still almost 8% higher than our error. These comparisons clearly prove that vertical models should not be used for horizontal flows and in order to achieve better results, more works have to be performed for horizontal flow conditions.

121 Predicted Lift-off Diameter, mm % -50% Current Model Prodanovic Model Unal Model Zeng Model Situ Model Basu Model Measured Lift-off Diameter, mm Figure 5-23: Prediction results of five model against the present lift-off diameter data

122 Chapter 6 Summary and Conclusions 106

123 107 6 Summary and Conclusions An experimental study is performed on the bubble nucleation on a heated zirconia rod horizontally located in a subcooled flow channel. The project investigates two-phase subcooled flow boiling inside a rectangular horizontal channel with heat supplied by an electrically heated rod while vapour bubbles were created on a horizontal wall in a uniform flow. The purpose of this investigation was to find a preliminary empirical relationship for bubble lift-off diameter, and growth rate constant under different experimental conditions. These experiments have been designed in order to validate the predictions, and to ext the predictive capacity for the conditions that actually occur in practice. Image recordings were analyzed and used to get the bubble geometrical parameters, which were needed to calculate forces acting on the bubble. Force analysis is performed to estimate force magnitude and to apply it to the suggested model in order to compare predicted and estimated lift-off diameters. Agreement between these two is necessary for the model validation. A dedicated experimental set-up has been designed so that the flow that approaches the bubble is practically uniform. A high-speed camera has been used for filming the bubble growth and detachment from its side view. The MatLAB image processing code was developed for data analysis of images acquired during the experiments. Parametric studies, such as effects of pressure, bulk liquid velocity, and inlet subcooling level were also performed. The comparison between the current study and those of other researches shows good agreement. Bubble growth constant before the lift-off and the bubble lift-off diameters at various flow conditions were measured, and a bubble lift-off diameter model was developed and correlated with experimental data. Qualitative observations were made for bubble sliding, lift-off velocities, and contact angles at lift-off after observing significant standard deviation in the experimental data for velocities and contact angle. Experiments were performed for inlet water subcooling of 32 o C to 1 o C, pressure of 1atm - 3atm, and flow rates of kg/m 2 s at a constant heat flux of 124kW/m 2. Based on the analysis of high-speed photography the following were concluded: A bubble begins from an embryo and grows from its active nucleation site. After reaching a certain size, it departs and then may slide from its original site, and finally

124 108 lifts-off. A sliding bubble can also coalesce with a bubble downstream and then liftoff into the bulk flow. If heat fluxes are low, sliding bubbles may not have a chance to coalesce before they lift-off. On the contrary, coalescence can happen before a bubble starts to slide, due to high bubble number densities. There are also intense interactions between bubbles and nucleation sites. A nucleation site can be activated or deactivated by an adjacent bubble or a bubble sliding from upstream, which occasionally happens. The bubble lifetime was divided into two distinct regions of growth and condensation. The growth is partitioned into two stages with growing at the nucleation site and growing with bubble sliding on the heater surface. The condensation region also is further subdivided into condensation with bubble sliding on the wall and condensation after bubble ejected into the flow. On a heating surface, bubbles serve as a heat sink with a high heat transfer coefficient due to phase change. The temperature beneath a bubble, therefore, is expected to be low and close to the saturation temperature. The heating surface without bubbles covering it, is then controlled by two heat transfer mechanis, forced convection to the bulk flow and lateral heat conduction to the bubble-covered region. Compared to phase change during bubble growth, the forced convection is relatively inefficient in transferring energy. If the thermal conductivity is sufficiently high, lateral heat conduction can be even more important than forced convection in transferring energy from the heating surface into the bulk flow. The results predicted by the model show that the thermal conductivity plays an important role through lateral heat conduction inside the heater block and, therefore, has a significant impact on boiling heat transfer performance. At high bulk liquid subcooling most of the condensation occurred while bubbles were sliding on the wall, though ejection was still present. At lower subcoolings, the bubble radius, bubble growth time and condensation time increased. The density of the nucleation sites and frequency of bubble formation were also increased with a decrease in the subcooling. Bubbles slide parallel to the wall with a constant velocity approximately equal to the mean flow velocity during both the growth and condensation periods. Also, the effect

125 109 of flow velocity on bubble parameters was found to be negligible in the range of this study. Only three main forces, i.e. buoyancy force, growth force and shear lift force, are counted for analyzing the bubble at the lift-off instant in the direction normal to the wall. In this direction three other non-negligible forces are active: the bubble surface tension, contact pressure force and hydrodynamic force. The latter is composed of several contributions, related to the bubble growth and to the uniform approaching flow. Bubble growth rate and maximum bubble radii obtained in this study were obtained by the use of the bubble growth model of Zuber. Lift-off bubble radius was correlated with wall superheat (Ja), pressure and indirectly to liquid bulk subcooling: ( ) ( ( ) ) The bubble growth rate constant, b, is assumed to be b = 1.73 in most applications. The present study showed that the growth rate constant cannot be assumed as a constant and it is a strong function of flow pressure. The constant value of b significantly over predicted the measured bubble diameters. Although more experiments should be performed at higher pressures to validate this model, by using this new model, the prediction error of the bubble lift-off diameter was significantly reduced. Therefore, a new empirical correlation for b as a function of experimental pressure is found which better predicts the data. The new correlation for b is: where. It was found that predicted diameters had an on average 19.91% error and 21.53% weighted error using a preliminary correlation of the bubble growth constant which assumed to vary with pressure only (comparing to the average error of 31.1% using a constant value for b at different pressures).

126 110 There are a few recommations for future works, which can improve the experimental setup, to enable more accurate results for the model and its validation: Simulate the bubble growth numerically by the use of different boundary conditions matching the bubble shape observed experimentally. This simulation for different boundary conditions will promote better understanding of the important parameters in bubble growth. Also performing numeric modeling of the temperature field around a bubble in the center of the test chamber, in uniform approaching flow would be beneficial. Perform additional experiments with higher flow velocities and different hydraulic diameters to investigate the effect of flow and geometry on the bubble parameters. Measure the temperature profile across the flow to obtain the local subcooling and the thickness of the superheated layer. The temperature measurements would determine the effect of true liquid subcooling and superheating on the bubble growth and collapse. Validate the physical models at various scales by using more advanced instrumentation techniques such as x-rays, liquid crystal thermography, high speed infrared thermography, and laser induced fluorescence. Use more advance high-speed camera to help saving time in image analyzing as well as capturing high-resolution images at much higher speeds. Install Micro Motion flowmeter (ELITE Sensor CMF025) in the test pipeline to gather and save data into LabView software.

127 111 7 Bibliography [1] "CANDU," May [Online]. Available: ssfullycompl.aspx. [2] "Canadian Nuclear FAQ," CANDU Technology, [Online]. Available: [Accessed Aug 2013]. [3] C. Bames, C. Anderson, T. Mali, D. Mcdemic and V. Zmic, "A CANDU Channel Thermohydraulics Model," [4] H. Chung, "A Review of CANDU Feeder Wall Thinning," Nuclear Engineering and Technology, vol. 42, no. 5, pp , [5] "CANDU Reactor," June [Online]. Available: [6] "Natural Uranium," May [Online]. Available: [7] "Cameco-CANDU," May [Online]. Available: [8] X. Cheng and U. Muller, "Review on Critical Heat Flux in Water Cooled reactors," Institut fur kem-und Energietechnik, Forschungszentum Karlsruhe, [9] R. Porter, "Reactor Mechanical Design," October [Online]. Available: [Accessed June 2013]. [10] S. Nukiyama, "The maximum and minimum values of heat, q, trasmitted from metal surface to boiling water under atmospheric pressure," Journal of Society od Mechanical Engineers, pp , [11] "Nucleate Boiling," September [Online]. Available: [Accessed November 2011]. [12] S. Chang and W. Beak, "Critical Heat Flux-Fundamental and Applications," Chungmoongak, Seoul, [13] J. LeCorre, "Flow regimes and mechanistic modeling of critical heat flux under subcooled flow boiling conditions," Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, USA, [14] G. Celta, M. Cumo and A. Mariani, "Assessment of correlations and models for the prediction of CHF in water subcooled flow boiling," International Journal of Heat Mass Transfer, vol. 37, no. 237, 1994.

128 112 [15] N. Zuber, "The dynamics of vapor bubbles in non-uniform temperature fields," International Journal of Heat Mass Trasnfer, pp , [16] S. Fazel and S. Shafaee, "Bubble dynamics for nucleate pool boiling of electrolyte solutions," Journal of Heat Transfer, vol. 132, no. 8, [17] P. Guan, L. Jia, L. Yin and S. Wang, "Experimental investigation of bubble behaviour in subcooled flow boiling," Journal of Thermal Science, vol. 21, no. 2, pp , [18] R. Situ, T. Hibiki, M. Ishii and M. Mori, "Bubble lift-off size in forced convective subcooled boiling flow," International Hournal of Mass Transfer, vol. 48, pp , [19] S. Kandlikar, "Heat transfer characteristics in partial boiling, fully developed boiling, and significant void flow regions of subcooled flow boiling," Journal of Heat Transfer, vol. 120, pp , [20] G. Warrier and V. Dhir, "Heat transfer and wall heat flux partitioning during subcooled flow nucleate boiling-a review," Journal Heat Transfer, pp , [21] Z. Liu and R. H. S. Winterton, "A General Correlation for Saturated and Subcooled Flow Boiling in Tubes and Annuli, Based on a Nucleate Pool Boiling Equation," Int. J. Heat Mass Transter, no. 34, pp , [22] J. Chen, "Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow," Ind. & Eng. Chem. Process Design and Dev., vol. 5, no. 3, pp , [23] R. Bowring, "Physical Model Based on Bubble Detachment and Calculation of Steam Voidage in the Subcooled Region of a Heated Channel," Institutt for Atomenergi, Halden, Norway, [24] K. Engelberg-Forster and R. Greif, "Heat Transfer to a Boiling Liquid-Mechanism and Correlation," Trans. ASME, Ser. C: J. Heat Transfer, vol. 81, pp , [25] A. Colburn, "A method of correlating forced convection heat transfer data and a comparision with fluid friction data," Trans. Am. Inst. Chem. Eng., vol. 29, p. 174, [26] W. Rohsenow, "Heat transfer with evporation," in Proceedings of Heat Transfer- A Symposium Held at University of Michigan During the Summer of 1952, University of Michigan Press, Ann Arbor, pp , [27] A. Bergles and W. Rohsenow, "The Determination of Forced Convection, Surface Boiling Heat Transfer," ASME Journal of Heat Transfer, vol. 86, pp , [28] R. Bjorge, G. Hall and W. Rohsenow, "Correlation of Forced Convection Boiling Heat Transfer Data," International Journal of Heat Mass Transfer, vol. 25, pp , 1982.

129 113 [29] S. Kutateladze, "Boiling Heat Transfer," International Journal of Heat Mass Transfer, vol. 4, pp , [30] M. Cooper, "Saturation Nucleation Boiling-A Simple Correlation," IChemE Symp. Ser., vol. 86, pp , [31] Y. Hsu, "On the Size Range of Active Nucleation Cavities on a Heating Surface," Journal of Heat Transfer, Trans. of the ASME, vol. 84, pp , [32] T. Sato and H. Matsumura, "On the Conditions of Incipient Subcooled Boiling with Forced Convection," Bulletin of JSME, vol. 7, no. 26, pp , [33] L. Tong and Y. Tang, Boiling Heat Transfer and Two-Phase Flow, Second Edition, Taylor & Francis. [34] J. Thom, W. Walker, T. Fallon and G. Reising, "Boiling in Subcooled Water During Flow up Heated Tubes or Annuli," in paper presented at Symposium on Boiling Heat Transfer in Steam Generating Units and Heat Exchangers, Manchester, Institute of Mech. Eng., London, [35] Y. Ahmad, "Axial Distribution of Bulk Temperature and void Fraction in a Heated Channel With Inlet Subcooling," Journal of Heat Transfer, vol. 92, no. 4, pp , [36] P. Saha and N. Zuber, "Point of Net Vapour Generation and Vapour Void Fraction in Subcooled Boiling," in Proc. 5th International Heat Transfer Conference, Tokyo, [37] J. Klausner, R. Mei, D. Bernhard and L. Zeng, "Vapor bubble departure in forced convection boiling," International Journal of Heat Mass Transfer, pp , [38] G. Thorncroft, J. Klausner and R. Mei, "An experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling," Int. J. Heat Mass Transfer, vol. 41, pp , [39] L. Zeng, J. Klausner, D. Bernhard and R. Mei, "A unified model for the prediction of bubble detachment diameters in boiling syste-ii. Flow boiling," International Journal of Heat Mass Transfer, pp , [40] N. Zuber, "Hydrodynamics aspects of boiling heat transfer," US AEC Rep. AECU 4439, Tech. Inf. Serv. Oak Ridge, Tenn., [41] R. Cole and H. Shulman, "Bubble departure diameters at subatmospheric pressures," in Chem. Eng. Progress Symp. Ser. 62, 6-16, [42] R. Cole and W. Rohsenow, "Correlation of bubble departure diameters for boiling of saturated liquids," Chem. Eng. Prog. Symp. Ser., vol. 65, no. 92, pp , 1969.

130 114 [43] G. Kocamustafaogullari and M. Ishii, "Interfacial area and nucleation site density in boiling syste," Int. J. Heat Mass Transfer, vol. 26, no. 9, pp , [44] D. Farajisarir, "Growth and collapse of vapour bubbles in convective subcooled boiling of water," Master Thesis, University of British Columbia, Vancouver, Canada, [45] G. Thorncroft, J. Klausner and R. Mei, "Bubble forces and detachment models," Multiphase Sci. Technol. 13, 35-76, [46] N. Basu, G. Warrier and V. Dhir, "Wall heat flux partitioning during subcooled flow boiling: Part 1-Model development," J. Heat Transfer, vol. 48, pp , [47] G. Sateesh, S. Das and A. Balakrshan, "Analysis of pool boiling heat transfer: effect of bubbles sliding on the heating surface," International Journal of Heat and Mass Transfer, vol. 48, pp , [48] G. Duhar and C. Colin, "Vapor Bubble Growth and detachment at the wall of a shear flow," in ECI international Conerence on Boiling Heat Transfer, Spoleto, Italy, [49] J. Magnaudet, S. Takagi and D. Legre, "Drag, deformation and laterak migration of a buoyant drop moving near a wall," J. Fluid Mech., vol. 476, [50] N. Basu, G. Warrier and V. Dhir, "Onset of Nucleate Boiling and Active Nucleation Site Density during Subcooled Flow Boiling," Journal of Heat Transfer, vol. 124, pp , [51] Y. Cho, S. Yum, J. Lee and G. Park, "Development of bubble departure and lift-off diameters models in low heat flux and low flow velocity conditions," International Journal of Heat and Mass Transfer, vol. 54, no , pp , [52] F. Staub, "The void fraction in subcooled boiling- prediction of the initial point of net vapor generation," Journal of Heat Transfer, pp , [53] H. Unal, "Maximum bubble diameter, maximum bubble-growth time and bubble-growth rate during the subcooled nucleate flow boiling of water up to 17.7 MPa," International Journal of Heat Mass Transfer, vol. 49, pp , [54] S. Chang, I. Bang and W. Beak, "A photogrphic study on the near-wall bubble behavior in subcooled flow boiling," Korea Advanced Institute of Science and Technology, [55] V. Prodanovic, D. Fraser and M. Salcudean, "Bubble behavior in sub-cooled flow boiling of water at low pressures and low flow rates," International Journal of Multiphase Flow, pp. 1-19, 2002.

131 115 [56] T. Okawa, I. Ishida, I. Kataoka and M. Mori, "Bubble rise characteristics after the departure from a nucleation site in vertical upflow boiling of subcooled water," Journal of Nuclear Engineering, vol. 235, no , pp , [57] R. Mei and J. Klausner, "Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free-streamvelocity," Phys. Fluids, vol. A4, pp , [58] B. Bae, B. Yun, H. Yoon, C. Song and G. Park, "Analysis of subcooled boiling flow with onegroup interfacial area transport equation and bubble lift-off model," Journal of Nuclear Engineering and Design, vol. 240, no. 9, pp , [59] I. Chu, H. No and C. Song, "Bubble Lift-off Diameter and Nucleation Frequency in Vertical Subcooled Boiling Flow," Journal of Nuclear Science and Technology, pp , [60] Y. Chen, M. Groll, R. Mertz and R. Kulenovic, "Force analysis for isolated bubbles growing from smooth and evaporator tubes," Trans. Inst. Fluid-Flow, vol. 112, pp , [61] P. Saffman, "The lift on a small sphere in a slow shear flow," J. Fluid Mech., vol. 22, pp , [62] T. Auton, "The lift force on a spherical body in a rotational flow," J. Fluid Mech, vol. 183, pp , [63] S. Levy, "Forced Convection subcooling boiling-prediction of Vapor Volumetric Fraction," General Electric Company, GEAP-5157, [64] F. Farhadi and N. Ashgriz, "A CFD Modeling of 37-element Fuel String in a 5.1% Crept Channel," CANDU Canada, Toronto, Canada, [65] A. W. Chang, "Reactor Grade Zirconium Alloys for Nuclear Waste Disposal," [Online]. Available: [Accessed September 2013]. [66] V. Tolubinsky and D. Kostanchuk, "Vapour bubble Growth Rate and Heat Transfer Intensity at Subcooled Water Boiling," in International Heat Transfer Conference, Paris, [67] M. Akiyama and F. Tachibana, "Motion of vapor bubbles in subcooled heated channel," Bulletin of JSME, pp , [68] E. Bibeau, "Void growth in subcooled flow boiling for circular and finned geometries for low values of pressure and velocity," Ph.D. Thesis, University of British Columbia, Vancouver, Canada, 1993.

132 116 [69] I. Bang, S. Chang and W. Beak, "Visualization of the subcooled flow boiling of R-134a in a vertical rectangular channel with an electrically heated wall," International Journal of Heat and Mass Transfer, pp , [70] J. Bonjour, M. Clausse and M. Lallemand, "Experimental study of the coalescence phenomenon during nucleate pool boiling," Journal of Thermal Fluid Science, pp , [71] E. Bibeau and M. Salcudean, "A study of bubble ebullition in forced-convective sub-cooled nucleate boiling at low pressure," International Journal of Heat Mass Transfer, pp , [72] R. Winterton, "Flow boiling: prediction of bubble departure," International Journal of Heat Mass Transfer, pp , [73] S. Kandlikar and B. Stumm, "A control colume approach for investigating forces on a departing bubble under subcooled flow boiling," International Journal of Heat Mass Transfer, pp , [74] D. Yuan, D. M. Pan, D. Chen, H. Zhang, J. Wei and Y. P. Huang, "Bubble behavior of high subcooling fow boiling at different system pressure in vertical narrow channel," Journal of Applied Thermal Engineering, vol. 31, pp , [75] O. Zeitoun and M. Shoukri, "Bubble behavior and mean diameter in subcooled flow boiling," ASME Journal of Heat Transfer, vol. 118, pp , 1996.

133 117 Appix A: Force Balance in x-direction (departure moment) The force balance approach proposed by Klausner et al. [37] (and the subsequent work by Zeng et al. [39]) has appeared most commonly in literature. The departure diameter is important because the bubble departure frequency is expressed as a dimensionless quantity in ter of the bubble departure diameter. Based on developments in Chapter 5, the force balance in the x-direction of the bubble at departure is as follows: ( ) ( ) ( ) ( ) [ [( ) ] ] ( ) ( ) ( ) [ [( ) ] ] ( ) ( ) [ [( ) ] ] ( ) ( ) ( ) Zeng et al. [39] argues that surface tension forces may be neglected at the point of departure because the contact diameter approaches zero at departure, that surface tension force is generally less than that of the growth force, and that empirically measured contact diameter

134 118 is normally over-estimated. Thus an approximation would be to ignore the surface tension term, which would yield: ( ) [ [( ) ] ]

135 119 Appix B: Bubble size measurement technique Upon completion the image processing, the image can be analyzed to extract experimental data for each bubble. The following sections describe how data relevant to the bubble lift-off diameter, the lift-off velocity, the growth, the angles of inclination, the upstream angle, and the downstream angle were extracted from the images. B.1. 3-D Bubble Lift-off Diameter Approximation using 2-D Image Image analysis of a bubble departure from the heater surface involves the conversion of the bubble diameter found from the image analysis into an actual bubble diameter. First of all, this process involves the conversion of a 2-D bubble image to find an approximate 3-D bubble diameter. The total number of pixels inside an area projected by the bubble is found by MatLAB using the methods described before. The software outputs both a normalized 2-D diameter and an approximated 3-D diameter (although the approximated 3-D diameter will be used as the final data). The normalized 2-D diameter is simply reformatting the 2-D area encompassed by the bubble to the diameter of a circle occupying the same area. This can be found by: To approximate the 3-D diameter, the method developed by Chu et al. [59] will be used. They calculated the bubble volume at lift-off based on the 2-D image using: The summation is taken from the first pixel (or bottom) to the n th pixel which describes the lowest and highest points the projected area of the bubble takes within the image. is the lift-off volume, is the height of one pixel which can be taken as unity or be converted at

136 120 this step based on an experimental scaling factor from a reference object, and is the cordial length of the bubble parallel to the heater surface at the k th pixel above the heater surface. Note that if is converted via scaling factor at this step then must also be converted. This volume is essentially assuming that at each k th pixel, the height of the pixel represents the height of a cylinder of diameter and the volume of this cylinder is found and summed from the bottom to the top of the bubble. This process is automated within the MatLAB program after the image is binarized and filtered. Chu et al. assumed that a bubble is circular when viewed from the top (or looking into the heater surface) based on the experimental observations of Basu et al. [50]. As a result we can use the following: ( ) This formula can be used for finding the 3-D diameter using the bubble volume. Chu et al. reported an error of 0.01% to 2.94% with an average of 1.39% when compared with bubble diameter found from the 3-D image, which can be considered as the actual bubble diameter. This shows that bubble diameter found using the method above from a 2-D image is a fairly good representation of that found from a 3-D image. As a result, this approach will be used to approximate the 3-D diameter of the bubbles taken due to the lack of 3-D imaging and image process software. B.2. Bubble Lift-off Velocity Bubble instantaneous lift-off velocity will be calculated using centroid data taken from two successive images and defined as the component of bubble velocity perpicular to the heater surface when it loses contact with the heater. The change in the distance of the y- component of bubble centroid is taken over the time interval between the two images to be the instantaneous lift-off velocity. The reference of the centroid location is the base of the image and will cancel when velocity is calculated. The velocity vector found is perpicular to the base of the image and not necessarily the heater surface. Thus, if the image taken is slightly tilted as in Fig. B-1, the absolute x-component (relative to the left of the image) of

137 121 bubble centroid will also be calculated to find the x-component bubble velocity at lift-off and a vector sum of the components of each of the velocities perpicular to the heater surface will be found and added to find the lift-off velocity perpicular to the heater surface. a) b) Figure B-1: Images taken 0.25 apart at inlet conditions of 100 o C, 1.5atm, 2gpm. The indicated bubble detached from the heater during this period B.3. Bubble Upstream, Downstream, and Inclination Angles at Lift-off Bubble contact angles and inclination angles are measured at the moment before lift-off or the image in which bubble lift-off diameter is extracted. Three angles are of interest, the inclination angle, the upstream contact angle, and the downstream contact angle as defined in earlier sections. The inclination angle will be measured by finding the middle of the base of the bubble or middle of the line of in which the bubble contacts the heater surface before liftoff. The centroid data of the bubble will then be used, and a virtual line will be drawn from the centroid to the mid-point of the heater-bubble contact line (in the 2-D image) and the angle of this line from a line perpicular to the heater surface will be considered the