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Cryogenic Boiling and Two-Phase Chilldown Process under Terrestrial and Microgravity Conditions


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CRYOGENIC BOILING AND TWO-PHAS E CHILLDOWN PROCESS UNDER TERRESTRIAL AND MICROGRAVITY CONDITIONS By KUN YUAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Kun Yuan

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iii ACKNOWLEDGMENTS First, I would like to express my greatest appreciation to my advisor, Dr. Jacob N. Chung, for his continuous support, encouragem ent, motivation, and guidance. Without his direction and support, this work would not have been possible. My sincere thanks are extended to my co mmittee members, Drs. James F. Klausner, Renwei Mei, William E. Lear, Jr., and Gary G. Ihas. Thank you for your time, encouragement, valuable advi ces, and wonderful classes you gave. Special thanks go to Dr. Ihas for the help on design of the experi mental apparatus, and to Dr. Mei for his guidance on numerical computation. I would also like to recognize my fell ow graduate associates Renqiang Xiong, Adam Robinson, and Yun Whan Na for their ki ndly assistance. Speci al appreciation is given to Dr. Jun Liao for the interesting di scussion and his helpful suggestion on code validation. I am deeply indebted to my parents a nd my brother for their never-ending love, dedication, and support through my long journe y of study. Finally, I would like to thank my wife Yan Ji for her continual support, encouragement, and love.

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iv TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iii LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix NOMENCLATURE........................................................................................................xiii ABSTRACT...................................................................................................................xviii CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Research Background.............................................................................................1 1.2 Research Objectives................................................................................................3 1.3 Scope...................................................................................................................... .3 2 BACKGROUND AND LI TERATURE REVIEW......................................................5 2.1 Background.............................................................................................................5 2.1.1 Boiling Curve...............................................................................................5 2.1.2 Two-Phase Flow Regimes and Heat Transfer Regimes...............................6 2.1.3 Gravity Effect...............................................................................................9 2.2 Literature Review.................................................................................................10 2.2.1 Experimental Studies..................................................................................11 2.2.1.1 Terrestrial cryogenic boiling and two-phase flow experiments.......11 2.2.1.2 Terrestrial chilld own experiments....................................................12 2.2.1.3 Reduced gravity boiling and tw o-phase flow experiments..............15 2.2.2 Modeling of Chilldown Process.................................................................16 2.2.2.1 Homogeneous model........................................................................16 2.2.2.2 Two-fluid model...............................................................................18 3 EXPERIMENTAL SYSTEM.....................................................................................23 3.1 Experimental Setup...............................................................................................23 3.1.1 System Overview........................................................................................23 3.1.2 Flow Driven System...................................................................................25 3.1.3 Test Section................................................................................................27

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v 3.1.4 Experimental Rig........................................................................................28 3.2 Data Acquisition System......................................................................................29 3.3 Drop Tower for Providing Microgravity Condition.............................................30 3.3.1 Introduction of Microgravity Facilities......................................................30 3.3.2 Drop Tower Design and Microgravity Condition......................................30 3.3.2.1 Release-retrieve mechanism.............................................................31 3.3.2.2 Guide wires......................................................................................32 3.3.2.3 Drag shield.......................................................................................32 3.3.2.4 Airbag deceleration system..............................................................34 3.3.2.5 External connections........................................................................35 3.3.2.6 Microgravity condition.....................................................................35 3.3.3 Safety Summary.........................................................................................35 3.4 Experimental Condition and Procedure................................................................36 3.4.1 Experimental Condition..............................................................................36 3.4.2 Ground Test Procedure...............................................................................37 3.4.3 Microgravity Test Procedure......................................................................38 3.5 Uncertainty Analysis............................................................................................39 3.5.1 Uncertainties of Temperature Measurement..............................................39 3.5.2 Uncertainty of Mass Flux...........................................................................40 3.5.3 Other Uncertainties.....................................................................................41 4 CRYOGENIC TWO-PHASE CHILLDOWN UNDER TERRESTRIAL CONDITION..............................................................................................................43 4.1 Gravity-Driven Experiment..................................................................................43 4.1.1 Heat Transfer Study....................................................................................43 4.1.1.1 Wall temperature profiles.................................................................44 4.1.1.2 Data reduction..................................................................................45 4.1.1.3 Heat transfer mechanisms................................................................50 4.1.2 Visualization Study....................................................................................55 4.2 Bellows-Driven Experiment.................................................................................59 4.2.1 Introduction................................................................................................59 4.2.2 Visualization Study....................................................................................59 4.2.3 Heat Transfer Study....................................................................................62 4.2.4 Phenomenological Model of the Film Boiling Region...............................66 4.2.4.1 Model description.............................................................................67 4.2.4.2 Film boiling correlation....................................................................71 4.2.4.3 Model evaluation..............................................................................74 4.3 Rewetting Experiment..........................................................................................75 4.3.1 Types of Rewetting.....................................................................................76 4.3.2 Rewetting Temperature and Rewetting Velocity.......................................77 4.3.3 Visualization Study....................................................................................83 5 CRYOGENIC TWO-PHASE CHI LLDOWN UNDER MICROGRAVITY CONDITION..............................................................................................................85 5.1 Introduction...........................................................................................................85

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vi 5.1.1 Film Boiling under Microgravity...............................................................85 5.1.2 Current Experimental Condition................................................................87 5.2 Flow Regime Visualization under Microgravity Condition.................................89 5.3 Heat Transfer Study..............................................................................................90 5.3.1 Wall Temperature Profiles.........................................................................91 5.3.2 Wall Heat Flux...........................................................................................94 6 MODELING CRYOGENIC CHILLDOWN.............................................................96 6.1 Introduction...........................................................................................................96 6.1.1 Flow Regimes and Transition Criteria.......................................................96 6.1.2 Different Modeling Methods and Current Approach...............................100 6.2 Inverted Annular Film Boiling Model................................................................101 6.2.1 Introduction..............................................................................................101 6.2.2 Model Description....................................................................................102 6.2.2.1 Assumptions and conservation equations......................................102 6.2.2.2 Heat transfer in invert ed annular film boiling................................104 6.2.2.3 Constitutive relations......................................................................107 6.2.3 Boundary Condition and Solution Procedure...........................................109 6.2.3.1 Boundary condition........................................................................109 6.2.3.2 Numerical method and solution procedure....................................110 6.2.4 Results and Discussion.............................................................................112 6.3 Dispersed Flow Film Boiling Model..................................................................117 6.3.1 Introduction..............................................................................................117 6.3.2 Model Description....................................................................................120 6.3.2.1 Assumptions and conservation equations......................................120 6.3.2.2 Heat transfer in dispersed fl ow film boiling and constitutive relations...................................................................................................122 6.4 Application of a Two-Fluid Model to Cryogenic Chilldown.............................127 6.4.1 Model Description....................................................................................127 6.4.1.1 Fluid flow.......................................................................................127 6.4.1.2 Heat conduction in tube wall..........................................................130 6.4.1.3 Initial and boundary conditions......................................................130 6.4.2 Numerical method and solution procedure...............................................131 6.4.3 Results and Discussion.............................................................................131 6.4.3.1 Experimental results.......................................................................133 6.4.3.2 Model results and comparisons......................................................135 6.5 Conclusions.........................................................................................................141 7 CONCLUSIONS AND RECOMMENDATIONS...................................................142 7.1 Conclusions.........................................................................................................142 7.2 Recommendations for Future Research..............................................................143 APPENDIX CODE VALIDATION.....................................................................................................144

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vii A.1 Dam-Break Problem..........................................................................................144 A.2 Grid Independence Check..................................................................................148 LIST OF REFERENCES.................................................................................................150 BIOGRAPHICAL SKETCH...........................................................................................160

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viii LIST OF TABLES Table page 3-1. Working condition of the experiments......................................................................37 5-1. Basic findings of flow film boili ng in previous chilldown experiments...................87 6-1. Post-CHF flow regime transition criteria..................................................................99 6-2. Inner wall boundary conditio ns at different regions................................................130 A-1. Analytical solution of dam-break pr oblem for horizontal frictionless channel......145

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ix LIST OF FIGURES Figure page 2-1. Typical boiling curve...................................................................................................6 2-2. Two-phase flow regimes inside a horizontal tube.......................................................7 2-3. Gravity effect on flow regimes....................................................................................9 2-4. Scaling analysis of grav ity effects on two-phase flow..............................................10 2-5. Different conduction controlled models.....................................................................18 3-1. Cryogenic boiling and two-phase flow test apparatus...............................................24 3-2. Photographic view of cryogenic boili ng and two-phase flow test apparatus............24 3-3. Cryogenic flow driven system...................................................................................26 3-4. Test section and thermocouple locations...................................................................28 3-5. Drop tower system.....................................................................................................31 3-6. Release-retrieve mech anism of the drop tower.........................................................32 3-7. Drag shield and the experi mental system before a drop.............................................34 4-1. Sketch of the test se ction and thermocouple locations for gravity-driven test..........44 4-2. Temperature profiles of gravity-dri ven test at different cross-sections.....................45 4-3. Typical curve fit line of the experimental data..........................................................49 4-4. Temperature derivatives calculated by least square fit method and by finite difference method.....................................................................................................49 4-5. Bottom wall heat flux and transient wall te mperature profiles at the outlet crosssection.......................................................................................................................51 4-6. Bottom wall heat flux at the outlet cross section as a function of time......................52 4-7. Bottom wall heat fluxes at different axial locations...................................................54

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x 4-8. Characteristics of horizontal chilldown under low flow rate.....................................56 4-9. Flow visualizations at di fferent stages of chilldown.................................................57 4-10. Propagation of the quenching front.........................................................................58 4-11. Typical flow images under different mass flux.......................................................60 4-12. Thickness of the liquid fila ments at different mass fluxes......................................61 4-13. Length of the liquid filame nts at different mass fluxes...........................................62 4-14. Temperature profiles of the in let section with different mass flux..........................62 4-15. Temperature profiles of the outle t section with different mass flux........................64 4-16. Middle section bottom wall heat fluxes under different mass fluxes......................65 4-17. Middle section local wall h eat fluxes under mass flux of 7.2 kg/m2s.....................66 4-18. Description of the heat transfer mechanism under horizontal dispersed flow condition...................................................................................................................68 4-19. Fractional of liquid filament associat ed area at different wall temperature and mass flux..................................................................................................................69 4-20. Stable film boiling in side a horizontal tube.............................................................72 4-21. Vapor film thickness and vapor velocity along the vapor channel..........................73 4-22. Comparison between experimental a nd model results of the bottom wall heat fluxes at outlet section..............................................................................................75 4-23. A typical chilldown boiling curve and the corresponding transient wall temperature...............................................................................................................78 4-24. Typical temperature prof iles during a rewetting test...............................................79 4-25. Axial variation of the averaged rewe tting temperature at different mass fluxes.....80 4-26. Comparison of rewetting temperatur es between experiments and different correlations...............................................................................................................82 4-27. Average rewetting velocity under different mass fluxes.........................................82 4-28. Visualization result of the rewet process.................................................................83 5-1. Two-phase flow images under both 1-g and microgravity conditions......................89

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xi 5-2. Temperature profiles with differe nt mass fluxes in microgravity test.......................91 5-3. Wall temperature response to microgravity...............................................................93 5-4. Ratio of heat flux under microgravity to 1-g condition with di fferent flow rates and comparison with model prediction....................................................................94 6-1. Post-CHF flow regimes..............................................................................................97 6-2. Heat transfer mechanisms in IAFB..........................................................................106 6-3. Solution procedure of st eady IAFB two-fluid model...............................................111 6-4. Comparison of wall temperatures betw een the IAFB model and the correlation prediction under different heat fluxes....................................................................113 6-5. IAFB model prediction of the liquid ve locity and the vapor velocity along the tube for down-flow, up-flow, and 0-g....................................................................115 6-6. IAFB model prediction of different variables along the tube for down-flow, upflow, and 0-g..........................................................................................................116 6-7. Heat and mass transfer mechanisms in DFFB..........................................................122 6-8. Electrical analog of radia tion heat transfer in DFFB................................................125 6-9. Solution procedure of the cryogenic chilldown model.............................................132 6-10. Comparison between measured and predicted wall temperatures under 1-g condition with flow rate of 40cc/s..........................................................................136 6-11. Comparison between measured and pr edicted wall temperatures under 0-g condition with flow rate of 40cc/s..........................................................................137 6-12. Model prediction of wall temperatures at different axial locations under both 1-g and 0-g conditions..................................................................................................138 6-13. Effects of inlet flow rate and gravity level on chilldown process..........................139 6-14. Wall temperature prof iles at different time............................................................140 6-15. Void fraction along the tube during chilldown.......................................................141 A-1. Dam-break flow model...........................................................................................144 A-2. Comparison between numeri cal results and analytical solutions at 25s after dam break.......................................................................................................................146

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xii A-3. Comparison between numeri cal results and analytical solutions at 50s after dam break.......................................................................................................................147 A-4. Effect of CFL number.............................................................................................148 A-5. Computation results of void fraction with different gr ids at a fixed time step of 0.0001 t ...........................................................................................................149 A-6. Computation results of void fraction with different CF L number at a fixed grid number of 200........................................................................................................149

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xiii NOMENCLATURE a Acceleration [-2ms] A Area [2m] Ca Capillary number D C Drag coefficient CFL Courant number pC Specific heat capacity [-1-1J kgK] d Diameter of liquid droplets [m] D Diameter of the flow channel [m] E Liquid droplet entrainment fraction f Friction factor D F Drag force [N] LF Time averaged fraction of bottom wall surface that is associated with liquid filaments g Gravitational acceleration constant 9.8[-2ms] G Mass flux [-2-1kgms] h Heat transfer coefficient [-2-1WmK]; Enthalpy [-1Jkg]; Water level [m] L h Liquid filament height [m]

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xiv lvh latent heat of evaporation[-1-1JkgK] lvh Latent heat plus vapor sensible heat content [-1-1JkgK] Ja Jacob number k Thermal conductivity [-11WmK ] lm Mass transfer rate per unit area [-21kgms ] lm Mass transfer rate per unit volume [-31kgms ] Nu Nusselt number P Pressure [Pa] ; Perimeter [m] Pr Prandtl number q Heat flux [-2Wm] R Ridius of the flow channel [m] g R Gas constant Ra Rayleigh number Re Reynolds number S Slip velocity; Suppression f actor in flow nucleate boiling 2S Shock speed [-1ms] t Time [s] T Temperature [K] wT wall superheat [K] u Velocity [1ms] V Volume flow rate [31ms ]

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xv We Webber number x Quality ttX Martinelli parameter z Position Greek letters Void fraction; Thermal diffusivity [2-1ms] Vapor film thickness [m] 0 Bottom wall vapor film thickness [m] Emissivity Viscosity [-1-1kgms] Density [-3kg m] Surface tension [-1N m] B Stefen Boltzmann constant 85.6710 [-2-4W mK] Shear stress [-2N m] Subscripts 0 Initial value 2 Two-phase b Bottom wall Ber Berensons correlation CHF Critical heat flux con Convection

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xvi crit Critical d Droplet e Equilibrium evap Evaperation fb Film boiling g Gas i Interfacial; Inner in Inlet j Vacuum jacket l Liquid phase lh Liquid heating max Maximum min Minimum o Outer pool Pool boiling r Radiation rw Rewet s Saturation u Upper wall v Vapor phase vd Vapor to droplet vl Vapor to liquid vs Vapor saturated

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xvii w Wall wd Wall to droplet wv Wall to vapor Superscripts Quantity per unit area ''' Quantity per unit volume Abbreviations CHF Critical heat flux DFFB Dispersed flow film boiling QF Quenching front IAF Inverted annular flow IAFB Inverted annular film boiling IHCP Inverse heat transfer problem LOCA Loss of coolant accident SOU Second order upwind TDMA Tri-diagonal matrix algorithm TVS Thermodynamic vent system

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xviii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CRYOGENIC BOILING AND TWO-PHAS E CHILLDOWN PROCESS UNDER TERRESTRIAL AND MICROGRAVITY CONDITIONS By Kun Yuan August 2006 Chair: Jacob N. Chung Major Department: Mechanic al and Aerospace Engineering Chilldown or quenching is a complicated pro cess that initiates the cryogenic fluids transport, and it involves unsteady two-phase heat and mass transfer. To advance understanding of this process, we co nducted both experimental and modeling investigations. An experimental apparatus was designed a nd fabricated to inve stigate the cryogenic chilldown process under both 1-g and microgr avity conditions. Liquid nitrogen was used as the working fluid. We found that the chil ldown process can be generally divided into three regions: film boiling region, transition boiling regi on and nucleate boiling region, and each region is associated with a different flow regime and heat transfer mechanism. Under low flow conditions, we observed that the two-phase flow regime is dispersed flow in the film boiling region. Th e dispersed liquid phase is in the form of long filaments as the tube is chilled down, a nd the vapor phase is generally superheated. Statistic feature of the liqui d filaments was studied and a phenomenological model, in

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xix which the heat transfer at the bottom is considered as a sum of vapor and liquid components, was developed. Microgravity tests were conducted for chi lldown in the film boiling region. Bottom wall heat flux was found to decrease unde r microgravity condition. Under current experimental conditions, the gravity effect does not show a strong dependence on wall temperature and inlet flow rate. A cryogenic chilldown model was also developed. The model focuses on both vertical tube chilldown and microgravity chilld own. In this model, the chilldown process is characterized as four distin ct regions, which are fully vapo r region, dispersed flow film boiling region, inverted annular film boili ng region, and nucleate boiling region. Twofluid equations were applied to the disperse d flow film boiling region and the inverted annular film boiling region, while the fully vapor region and nucleate boiling region are depicted by single-phase correlations. The model results show a good agreement with previous experimental data.

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1 CHAPTER 1 INTRODUCTION Cryogenic fluids are widely used in indus trial, aerospace, and cryosurgery systems and so on. In these systems, proper transport, handling and storage of cryogenic fluids are of great importance. The chilldown or quenc hing process which ini tiates cryogenic fluids transport is complicated, i nvolving unsteady two-phase heat and mass transfer, and was not fully understood until now. Cryogenic ch illdown shares many common features with other industrial processes such as the refloodi ng process, which is often encountered in Pressurized Water Reactors (PWR) and Bo iling Water Reactors (BWR). Therefore, further knowledge of the cryogenic chilldow n process may be applicable to those processes also. In this study, we experimentally inve stigated the cryogenic two-phase chilldown process under terrestrial and microgravity c onditions, and a numerical model was also developed to predict the chilldown process. 1.1 Research Background One important application of cryogenic fluids is in space exploration. Efficient and safe use of cryogenic fluids in thermal management, power and propulsion, and lifesupport systems of a spacecraft during space mi ssions involves transport, handling, and storage of these fluids unde r both terrestrial and micrograv ity conditions. Uncertainties about the flow regime and heat transfer characteristics pose severe design concerns. Moreover, the thermo-fluid dynamics of twophase systems in microgravity encompass a

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2 wide range of complex phenomena that are not understood sufficiently for engineering design to proceed. Cryogenic fluids are also widely used in industrial systems. Until the early 1970s, liquid hydrogen was mainly used by NASA as a rocket fuel; however, development and growth of commercial markets have since outpaced this use. For example, liquid hydrogen is used in industrial applications such as me tal processing, plate glass production, fat and oil hardening, semic onductor manufacturing, and pharmaceutical and chemical manufacturing. Today, the commercial market is many times larger than the government market. For any process using cryogenic fluids, chil ldown is inevitably the initial stage; therefore, efficiency of the chilldown proce ss is a significant concern since the cryogen used to cool down the system is not utili zed for propulsion, power generation or other applications. In a hydrogen economy, chill down must be accomplished with a minimum consumption of cryogen for the overall energy ef ficiency to be within tolerable limits. Current understanding on chilldown pro cess is, however, very limited. For example, there is considerable disagreement over the chilldown heat fluxes and whether a unique rewetting temperature exists (Dhir et al. 1981; Piggott and Porthouse 1975). For similar experimental observations, quite differe nt explanations were also suggested by different researchers. For example, it was reported that the rewetting velocity increased with increasing inlet flow rate, given the same initial wall temperature (Yamanouchi 1968; Duffey and Porthouse 1973). Duffey and Po rthouse (1973) suggested that this flow rate effect is resulted from increasing the we t side heat transfer coefficient with higher inlet flow. This improves the rate of axial heat conduction and hence leads to a faster

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3 rewetting rate. Thompson (1974), however, ar gued that the inlet flow rate affects precooling on the dry side rather than the heat transfer in the wet side. Another driven force of present investig ation comes from the need for further understanding of the cry ogenic chilldown process under low mass flux in a thermodynamic vent system (TVS) on spacecrafts. A TVS is a system where a small amount of liquid is withdrawn from a cryoge nic propellant tank and vented to remove heat from the bulk liquid cryogen in the tank a nd thus lower the tank pr essure (Lin et al. 1991; Van Dresar et al. 2001, 2002) The mass flux in TVS system is generally very low. Systematic experiments for steady state lo w mass flux cryogenic two-phase flow were conducted by Van Dresar et al. (2001, 2002), th e highly transient chilldown process was, however, not included. 1.2 Research Objectives For liquid hydrogen to be adopted as a rout ine fuel, the chilldown process must be fundamentally understood. The objective of th e experimental invest igations in this research work is to seek a fundamental understanding on the boiling regimes, two-phase flow regimes, and heat transfer charac teristics for chilldown in pipes under both terrestrial and microgravity conditions. Further more, a cryogenic chilldown model is to be developed based on the experimental observa tions and will contribute to the prediction of the chilldown process. 1.3 Scope In Chapter 2, background of boiling heat tr ansfer, two-phase flow pattern and heat transfer regime is briefly introduced. Then previous experimental works for two-phase flow, chilldown and microgravity boiling are reviewed, followed by a short discussion of the two-phase flow modeling.

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4 In Chapter3, the experimental system, e xperimental conditions, and experimental procedure for current study are introduced. Th e uncertainties of the data measurements are evaluated. The design and working conditi ons of the drop tower, which is used to provide the microgravity condi tion, are also given. Chapter 4 presents the ground test resu lts of cryogenic chilldown process. Visualized flow regimes and heat transfer da ta with different mass fluxes are discussed. A phenomenological model is developed ba sed on the experimental observation. Chapter 5 gives the experimental results of cryogenic twophase chilldown under microgravity condition. In Chapter 6, a two-fluid cryogenic chilldown model is developed for both microgravity chilldown and vertical tube ch illdown. Four regions of the chilldown process, namely the fully vapor region, di spersed flow film bo iling region, inverted annular film boiling region, and nuclear boi ling region, are included in this model. Chapter 7 concludes the res earch with a summary of th e overall work and suggests future works.

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5 CHAPTER 2 BACKGROUND AND LITER ATURE REVIEW Cryogenic chilldown involves complex interaction of energy and momentum transfer among the two phases and the solid wall. Understanding of the boiling phenomenon, flow regime and heat transf er regime provides foundation for further insight into this dynamic process. This chap ter gives background information of boiling, two-phase flow regime and heat transfer regime. Previous work s on both experimental and modeling part that related to chilldow n and microgravity boili ng are reviewed and qualitatively assessed. 2.1 Background 2.1.1 Boiling Curve A boiling curve shows the relationship between the heat flux that the heater supplies to the boiling fluid and the heater surface temperatur e. According to the typical boiling curve (Figure 2-1), a ch illdown (quenching) process us ually starts from point E, and then goes towards point D in the film boiling regime as the wall temperature decreases. Point D is called the Leidenfros t point which signifies the minimum heater temperature required for the film boiling. For the film boiling process, the wall is so hot that liquid will vaporize before reaching the he ater surface which causes the heater to be always in contact with vapor. When cooling beyond the Leidenfrost point, if a constant heat flux heater was used, then the boiling would shift from film to nucleate boiling (somewhere between points A and B) direc tly with a substantial decrease in the wall temperature because the transition boiling is an unstable process.

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6 Figure 2-1. Typical boiling curve. 2.1.2 Two-Phase Flow Regimes and Heat Transfer Regimes The flow in cryogenic chilldown process is typically two-phase flow, because the wall temperature usually exceeds the liquid boiling temperature to several hundred Celsius in the beginning. The t opology of two-phase flow has an important effect on heat transfer and pressure drop in the flow channel. Therefore, generally the first step in twophase flow experiment or modeling is to determine the two-phase flow regime. Commonly observed flow regimes in horizon tal tubes are shown in Figure 2-2. General descriptions of the two-phase fl ow regimes can be referred from Carey (1992) and Van Dresar and Si egwarth (2001). Flow regimes of common two-phase flow such as air-water have been extensivel y mapped from experiments. However, the published data for cryogens are limited.

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7 It is also noted that definitions of th e flow regimes are somewhat arbitrary. Qualitative assessment has not been done yet, and transition criteria between different flow regimes are not fully understood. Bubbly flow Plug flow Stratified flow Wavy flow Slug flow Annular flow Figure 2-2. Two-phase flow re gimes inside a horizontal tube. Different flow regimes are often associated with different heat transfer regimes. When phase change occurs as two-phase mixture flows along the channel, as that encountered in chilldown proce ss, the situation is even more complicated (Carey 1992): different flow regimes are generally observed at differe nt positions along the channel length. The sequence of flow regimes will pr imarily depend on the flow rate, channel orientation, fluid propertie s, and wall heat flux.

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8 Some general information could be drawn from the findings of reflooding experiments designed for hypothetical loss-o f-coolant accident (LOCA) in nuclear reactors, for example, Chan and Banerjees re sult for horizontal tube (1981a, b, c) and Cheng et al.s work for vertical tube (1978). When the two-phase flow first enters the hot tube, the liquid pha se evaporates very quickly and forms a vapor film that separa tes the liquid phase from touching the tube wall, and the two-phase flow is in film bo iling state. Depends on the local quality and other thermo-hydraulic parameters, the flow re gime can be dispersed flow or inverted annular flow. The corresponding heat transfer regime will be dispersed flow forced convection, which is also called disperse d flow film boiling (DFFB) in literature (Yadigaroglu et al. 1993; A ndreani and Yadigaroglu 1996; Hammouda et al. 1997; Shah and Siddiqui 2000), or inverted annular film boiling (IAFB). As the wall temperature decreases under cert ain degree, the liquid phase is able to contact the tube wall. The liquid-wall cont acting front, which is often referred as quenching front (QF) or sputte ring region, is characterized by violent boiling associated with significant wall temperature decrease, and propagates downstream with the flow. The heat transfer mechanism at the QF is tr ansition boiling, which is more effective than the film boiling heat transfer. This establishm ent of liquid-wall contact is called rewetting phenomenon and has been a research interest for several decades. After the QF, nucleate boiling heat transfer dominates. For vertic al tube, the flow regime can be annular flow, slug flow or bubbly flow; for horizontal tube, the flow regime is generally stratifie d flow. With further wall temp erature decrease, the nucleate

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9 boiling stage gradually changes to pure conve ction until the wall temperature reaches the steady state, which denotes the e nd of the chilldown process. 2.1.3 Gravity Effect Because of the differences in density a nd inertia, the two phases in two-phase flow are usually non-uniformly distributed acro ss the pipe under terrestrial condition. The absence of gravity has important effects on flow regimes, pressure dr op, and heat transfer of the two-phase flow. Surface-tension-indu ced forces and surface phenomena are likely to be much more important in space than they are on earth. Actually, all flow-regimespecific phenomena will be influenced by gr avity level. As an example, Figure 2-3 compares the flow regime under both terr estrial and microgravity conditions; the difference is obvious. A B Figure 2-3. Gravity effect on fl ow regimes. A) Flow regime in 1-g test. B) Flow regime in microgravity test. Following is a simple scaling analysis that examines the gravity effects. For annular flow film boiling in a horizont al tube, the effect of gravity is assessed based on the ratio of Gr/Re3, where Gr is the Grashof number and Re is the Reynolds number. The gravity effect is measured by the natural convection contribution characterized by the Gr, while the forced convective film boiling is scal ed by the Reynolds number. According to

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10 Gebhart et al. (1988), Re3 is used in the denominator when the flow is perpendicular to gravity for a horizontal tube. Re2 is used when the flow is in the same direction of gravity. All the thermal propert ies are those of vapor because of film boiling. Figure 2-4 shows this ratio with the vapor flow velocity range of 0-0.5 m/s and a T of 100 oC for the Gr estimation. Figure 2-4. Scaling analysis of gravity effects on two-phase flow. Based on Figure 2-4, if the vapor velocity is greater than 10 cm/s, then the Gr/Re3 is less than 0.2. The natural convection is negligible for Gr/Re3 less than 0.225 according to Gebhart et al. (1988). Ther efore, a terrestrial gravity experiment with the vapor velocity greater than 10 cm/s would provi de results that mimic the microgravity phenomenon. 2.2 Literature Review Cryogenic two-phase flow and chilldown process is a complex problem for the scientific community to solve. The following summarizes the previous accomplishments on both experimental and modeling aspect.

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11 2.2.1 Experimental Studies 2.2.1.1 Terrestrial cryogenic boiling and two-phase flow experiments Numerous studies of cryogenic boiling in 1-g environment were conducted in the 1950s and 1960s. Brentari et al. (1965) gave a comprehensive review of the experimental studies and heat transfer co rrelations. For the fluids of oxygen, nitrogen, hydrogen and helium, it was found that for pool boiling, th e Kutateladze (1952) correlation had the greatest reliability for nuclea te boiling, while the Breen a nd Westwater (1962) correlation was best for film boiling. Maximum nucleate flux data were reas onably well predicted by the Kutateladze (1952) correlati on. Although these correlations were selected as the best available, neither has particul arly good agreement with experimental data. For the case of forced convection boiling, Bren tari et al. (1965) reported that no correlation was found to be distinctly better. Some simple predictive methods were found to work as well as more complex schemes. In all boiling cases, it wa s questioned as to whether or not the predictive correlations include all of the significant variables that influence the boiling process. In particular, it was suggested that more detailed and better controlled experiments are needed and that more atte ntion to surface and geometry effects is required. Another comprehensive review of cryoge nic boiling heat transfer addressing hydrogen, nitrogen and oxygen is given by Seader et al. (1965). It was reported that nucleate pool boiling results cannot be correlat ed by a single line but cover a range of temperature difference for a given heat flux. The spread is attributed to surface condition and geometry, and orientation. Maximum h eat flux can be reduced by about 50% when going from 1-g to near 0-g. S eader et al. (1965) re ported a fair amount of data for film pool boiling. Film boiling heat flux is reduced considerably at near 0-g conditions. Only a

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12 very limited amount of data is available fo r subcooled or saturated forced convective boiling and few conclusions were drawn. The lack of data for cryogenic forced convective boiling was also reporte d by Brentari and Smith (1965). Relatively recent correlations have been publ ished for 1-g saturated flow boiling of cryogens (Shah 1984; Gungor and Winterton 1987; Klimenko et al. 1989; Kandlikar 1990; Van Dresar et al. 2002) using the Convection numberCo, Boiling number Boand Froude number Fr as correlating parameters. Klime nko et al. (1989) investigated the effects of tube diameter and orientation on two-phase nitrogen flow and concluded that in vertical channels diameter effect was reve aled in a transition from convective to less intensive nucleate boi ling when the Froude number of a mixture mFrdecreases from 40 to 10. On the contrary, in horizontal nonstratified flow, the reduction of the mFrnumber was accompanied by cross-section averaged heat transfer coefficien t incensement of 2030% in the nucleate boiling region. WithmFr40, the geometry and orientation did not affect the heat transfer coefficient. Van Dr esar et al. (2001) expe rimentally studied the near-horizontal two-phase flow of nitrogen a nd hydrogen. Unlike most of the other works which based on turbulent liquid flow, their wo rk focused on laminar liquid flow and the results for low mass and heat flux flow were correlated with Froude number. 2.2.1.2 Terrestrial chilldown experiments Research on cryogenic chilldown began in the 1960s with the development of rocket launching systems. Burke et al. (1960) studied the chilldown process of stainlesssteel transfer lines of 60, 100 and 175 ft long with a 2.0 in. OD. The transfer lines were quenched by flowing liquid nitr ogen. A sight glass was located near the discharge end for flow phenomena observation. Based on the wall temperature, liquid flow rate, and the

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13 observation, the chilldown process was simply divided into three stages: gas flow, twophase flow and liquid flow. However, the fl ow regime information was lack in the experiments; moreover, the averaged wall te mperature was used in their study. While other researchers (Bronson et al. 1962) point ed out that circumferential temperature gradient could be very large in cryogenic chilldown process. Early visualized study of flow regimes in a horizontal pipe during chi lldown can be retrospect to Bronson et al. (1962). A 50 ft long with 3 1 8 in. ID test section was quenc hed by liquid hydrogen in this work. Results showed that the stratified fl ow is prevalent in the cryogenic chilldown process. Based on their experiments, rudimental models (Burke et al 1960; Bronson et al. 1962) were also suggested to calculate chill down time. Differences in flow regimes were not considered in these models; instead a gr oss effect was used. The work of both Burke et al. (1960) and Bronson et al. (1962) based on extremely long transfer lines, it is doubtful that their results can be applied over a short tube. Chi and Vetere (1964) studied the chill down process of hydrogen flowing through a 2-ft long thin wall copper tube. Thermocoupl es were installed on the outside wall and in the center of the tubing to measure the wall and stream temperatures at both the inlet and the outlet of the test section. The thermocouple beads in the center of the tubing were treated as control volume and their respons es were used to identify different flow regimes. Chi and Vetere (1964) found that the vo id fractions were much larger, more than five times in some cases, than those given by previous investigators (Wright and Walters 1959; Hsu and Graham 1963). They attributed this difference to the effect of nonequilibrium nature of the chilldown pr ocess and concluded that thermodynamic equilibrium cannot exist in film boiling and transition regimes during chilldown. Another

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14 research work by Chi (1965) used seve ral 26-in long aluminum tubes with 316-in ID and ODs from 12 to 2 inch. Unlike the thin wall copper tubing experiments (Chi and Vetere 1964), the temperature responses showed that slug flow was not observed until the aluminum test sections were almost cooled down, and the dominant flow regime was mist flow. As mentioned before, chilldown of a hot surface or tube is of fundamental importance for the re-establishment of normal and safe temperature level following dryout in a LOCA in nuclear reactors. Liquid water or co mmon refrigerant are usually used in this type of experiments. For exam ple, Chan and Banerjee (1981a, b, c) and later Abdul-Razzak et al. (1992) used water to chilldown a preheated horizontal tubes. In their experiments, the chilldown process was divi ded into three regions namely film boiling region, partially quenched region and totally quenched region. Different heat transfer mechanisms were involved in different regions. Kawaji et al. (1985) experimentally inves tigated the chilldow n process inside a vertical tube with different fl ow rates. Their results showed that for high flow rate, the entering liquid will initially boil through film boiling mechanism and then develop into inverted annular flow, dispersed flow and fully vapor flow, for low flow rate, the corresponding sequence was saturated boiling, annular flow, dispersed flow and fully vapor flow. Recently, Velat (2004) experimentally studied the cryogenic chilldown in a horizontal pipe using nitrogen as working fluid. Pyrex glass tube with vacuum jacket was used for visualization. The flow regime s were recorded by hi gh speed camera. Wall

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15 temperature histories and pressu re drop along the pipe were r ecorded and associated with the visualized images. 2.2.1.3 Reduced gravity boiling and two-phase flow experiments Because of the experimental difficulties ther e are very little heat transfer data for cryogenic flow boiling in reduced gravity. We were able to find just one report done by Antar and Collins (1997) investigated the cryogenic flow boiling in low gravity condition. The experimental results of twophase flow under reduced gravity conditions using regular working fluids, such as R113, are also summarized here. Adham-Khodaparast et al. (1995) inves tigated the flow film boiling during quenching of a hot flat surface with R-113. Micro-sensors were used to record instantaneous heat flux and heater surface temp erature. They reported lower heat transfer rates during microgravity as compared to normal gravity and c ontributed that to thickening of the vapor layer. The wall superheat and the surface heat flux at the onset of rewetting and the maximum heat flux were found to increase w ith the inlet liquid subcooling, mass flux and gravity level. The eff ect of gravity was determined to be more important for low flow rates and less releva nt for high flow rates. The two-phase flow regimes were not reported in their work. Another quenching test under microgravit y was done by Westbye et al. (1995). A hot thin-walled stainle ss steel tube was quenched by injec tion of subcooled R113 into the tube under both 1-g and microgravity c onditions. The injection mass flux was 160-850 kg/m2s. It was found that the rewetting temperatures were 150C-250C lower in microgravity than those obtained in 1-g, and the film boiling h eat transfer coefficients in microgravity were less than t hose in 1-g tests. This resu lted in much longer cooling periods in microgravity. It wa s also reported that once the tu be was cooled sufficiently to

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16 allow axial propagation of the QF, the rewe tting velocity was slightly greater in microgravity. The nucleate and transition boiling curves under microgravity were reported to be shifted to lower wall superheats as compared to 1-g results. Antar and Collins (1997) reported cryogeni c chilldown process under 1-g condition and on board a KC-135 aircraft. They observed that a sputtering lead ing core followed by a liquid filament annular flow regime. This flow regime is composed of a long and connected liquid column that is flowing in the center of the tube and is surround by a thick vapor layer. They attributed the filame ntary flow to the lack of difference in the speed of vapor and liquid phases. On the heat transfer side, they reported that the quench process was delayed in low gravity and the tube wall cooling rate was diminished under microgravity conditions. The QF speed was found to be slower under the low gravity conditions. 2.2.2 Modeling of Chilldown Process Mainly two types of flow models were developed for chilldown process modeling. Homogeneous model treats the two-phase mixtur e as homogeneous fluid, while two-fluid model considers the difference of the two phases and solves the equations for the conservation of mass, momentum and energy for each phase. 2.2.2.1 Homogeneous model The primary assumptions of the homogeneous model are: (1) the fluid, either single-phase or two-phase mi xture is homogeneous; (2) in compressible flow; (3) onedimensional flow; (4) thermal equilibr ium exists between the two phases. Burke et al. (1960) developed a crude ch illdown model based on their experiments of quenching large cryogenic piping syst em. The model was one-dimensional and the entire transfer line was treated as a single control volume. This lumped system provided a

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17 simple estimation of chilldown time but lacked accuracy due to its broad assumptions and averaging of fluid properties and flow ra tes over the chilldown time. Bronson et al. (1962) developed a one-dimensional model by assuming constant wall-to-coolant temperature difference along the entire transfer line. This model was used to estimate the chilldown time, however, it did not permit th e estimation of the instantaneous wall and bulk fluid temperature. Chi (1965) developed an analyt ical model for mist-flowdominated chilldown based on the assumptions of constant flow ra te, constant heat transfer coefficient, constant fluid prope rties, homogeneous flow and film-boilingdominated heat transfer. St eward et al. (1970) modeled chilldown numerically using a finite difference formulation of the onedimensional, unsteady mass, momentum and energy equations. Cross et al (2002) used the homogene ous model to solve three chilldown cases with hydrogen as the work ing fluid: the first case got a simplified analytical solution; the sec ond case treated superheated vapor flow and the third case modeled the initially subcooled liquid flow. In LOCA research, a so-called conduc tion controlled model was used by many researchers. By assuming constant wet front speed and introducing coordinate transformation, the main focus in conduction controlled model was shifted to solve the steady state conduction equation of the tube wall within a moving reference frame. The conduction controlled model was fi rst studied by Yamanouchi (1968). The phenomenon was described by one-dimensional quasi-steady heat c onduction in a wall with two distinct regions. The region covere d by the liquid film had a constant heat transfer coefficient, while the bare region was adiabatic. The major flaw of this model is the absence of the sputteri ng region and this leads to unreasonable heat transfer

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18 coefficient. Thompson (1972) suggested th e liquid film can be characterized by a temperature-dependent nucleate boiling heat tr ansfer coefficient, and numerically solved the two-dimensional heat conduction equati on. However, the sputtering region and the film boiling region were still not considered distinctively. S un et al. (1974) was the first one to distinguish and attribut e different heat transfer coe fficient to these two different regions. In their model, the one-dimensi onal heat conduction equation was solved analytically. Figure 2-5 schematically compar es the above three models. Tien and Yao (1975) further developed the conduction co ntrolled model to two-dimensional and analytically solved the limiting cases for both small and large Peclet numbers. Figure 2-5. Different conduc tion controlled models. 2.2.2.2 Two-fluid model Although homogeneous model is simple and has gained success in certain applications, its drawback is obvious: it can not describe the thermal and hydraulic differences between the two phases. In th e homogeneous model, it is assumed that

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19 thermal equilibrium exists between the tw o phases, however, for IAFB and DFFB in chilldown process the vapor phase is generally superheated (C hen et al. 1979; Guo et al. 2002; Tian et al. 2006). The vapor superh eat can up to several hundred Kelvin under some operating conditions. In that situati on, predictions by homogeneous model will inevitably lead to large discrepancy from the experimental results. Moreover, for stratified two-phase flow, the homogeneous assumption is not valid. Therefore, the homogenous model is generally not appli cable to horizontal pipe chilldown. In engineering applications, usually only th e averaged quantities are of engineering interest. Thus one of the main approaches fo r two-phase flow modeling is to average the local instantaneous conservation equations, wh ile the information lost in the averaging process is supplied in the form of auxiliar y relationships. This leads to the two-fluid model or separated flow model (Ishii 1975; Banerjee and Chan 1980; Ardron 1980; Ishii and Mishima 1984). Two-fluid model consists of two sets of conservation equations for the mass, momentum and energy of each phase. Since the averaged fields of one phase are not independent of the other phase, intera ction terms appear in the field equations as source terms. For most practical applicat ions, the model can be simplified to the following forms (Ishii and Mishima 1984): Continuity equation: kk kkkkt v (2.1) Momentum equation: t kkk k kkkkkkkk kkkikikkip t v vv gvM (2.2)

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20 Enthalpy energy equation: t kkk kkkkkk k k kkkikkiskH Hqq t D pHqL D t v (2.3) Here the subscribe k denotes k-phase and i stands for the value at the interface. s L denotes the length scale at the interface. k ikM, i kiq and k are the mass generation, generalized interfacial drag, interf acial shear stress, inte rfacial heat flux and dissipation, respectively. These interfacial transfer terms s hould obey the balance laws at the interface given as: 0 0 0k k ik k kkikis kHqL M (2.4) Chan and Banerjee (1981a, b, c) deve loped a two-fluid model for horizontal chilldown process based on the experimental results of quenching a hot Zircaloy-2 tube, and pointed out that the pr opagation of the QF was larg ely controlled by hydrodynamic mechanisms instead of by conduction mechan ism. The model was one-dimensional and the vapor phase was assumed to be at satura ted temperature. The o ccurrence of rewetting at the bottom of the tube was evaluated based on studying of the Kelvin-Helmholtz instability at the vapor film-liquid interface in the film boiling region. The results agreed reasonably well with experimental data. Late r, a new rewetting cr iterion based on vapor film collapse was added into the horizontal two-fluid chilldown model by Abdul-Razzak et al. (1993).

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21 For vertical tube, Kawaji and Banerjee (1987, 1988) em ployed the two-fluid model to predict the thermo-hydrauli c criteria for the bottom refl ooding problem in steam-water system. Their model was further developed by Hedayatpour et al. (1993) to model the chilldown mechanism in a vertical tube with f our distinct regimes: fully liquid, inverted annular flow (IAF), dispersed flow and fully vapor flow. The IAF, which comprised of a liquid core surrounded by a vapor film next to the tube wall, was considered as immediately downstream of the quench front. The two-fluid model was used in the IAF and dispersed flow regimes. A one-dimen sional energy equation was formulated for predicting the temperature hist ory of the tube wall. The model was consistent with the experimental results. The major drawback of this approach was the requirement of knowing both the flow pattern as well as the QF speed. Recently, Liao (2005) did a comprehensive study in modeling the cryogenic pipe chilldown and achieved good agreement with th e experimental data. Three models were used for different situations. A simple hom ogeneous model was suggested for simulating vertical pipe chilldown. A pseudo-steady chilldown model, which is similar to conduction-controlled model to some extent was developed to simulate horizontal chilldown. Coordinate transformation was intr oduced to eliminate the transient term and resulted in a two-dimensional parabolic equa tion. By assuming constant wet front speed, the main emphasis was to model the heat transf er coefficients for the stratified flow and the thermal field within the solid pipe. Correlations for film boiling and forced convection boiling were used for different flow regimes. The study showed that the current film boiling correlati ons are not appropriate for th e cryogenic pipe chilldown due to neglecting the information of the flow regime, and a new film boiling correlation was

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22 proposed. The predicted pipe wall temper ature history matched well with the experimental results. To include the predicti on of the flow fields, a more comprehensive two-fluid model was also developed and combined with three-dimensional heat conduction in the solid wall to study the strati fied flow regime in a horizontal pipe. The predicted wall temperature variations show ed good agreement with the experimental measurements.

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23 CHAPTER 3 EXPERIMENTAL SYSTEM To investigate the cryogenic chilldown process, a cryogenic two-phase flow experimental facility has been designed, fa bricated and tested unde r both terrestrial and microgravity conditions. A drop tower is used to provide the microgravity condition. The experimental system, experimental condition an d procedure are introduced in this chapter. 3.1 Experimental Setup 3.1.1 System Overview Most two-phase flow experimental appa ratus are designed as a close loop. The vapor phase is usually cooled back to liquid through the c ondenser and then sent back into the loop. However, the close loop desi gn is not suitable for current cryogenic twophase flow experiment. The reasons are first the boiling temperatures of the cryogens are extremely low, to condense the vapor phase ba ck to liquid phase, sp ecial cryocooler must be used, and this will highly increase th e complicity of the system; secondly no common commercial pump can work at the cryogenic temperature and using cryogenic pump is not economically possible. Considering the above reasons, the experi mental system is designed as a oncethrough flow pass using motor-driven bellows as flow generator. Figure 3-1 shows the schematic of the experimental system, whic h locates in two side-by-side aluminum cubicles and is fabricated for both terre strial and microgravity experiments. The experimental system mainly consists of a nitrogen tank, a motor-driven bellows, test section inlet portion, test s ection, test section outlet por tion, vacuum jacket, vacuum

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24 pump, data acquisition system, lighting and video system. A photographic view of the apparatus is shown in Figure 3-2. Figure 3-1. Cryogenic boiling and two -phase flow test apparatus. Figure 3-2. Photographic view of cryogenic boiling and two-pha se flow test apparatus. Nitrogen flow is generated by a motor-dri ven stainless steel bellows. The test section is transparent. Temperature measur ements are taken at different downstream

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25 locations along the test sec tion when the two-phase nitroge n flow is passing through; video images are also recorded simultaneously. 3.1.2 Flow Driven System Following the traditional method to contro l cryogenic flow (Swanson et al. 2000), nitrogen flow is generated by a motor-drive n stainless steel bellows (Figure 3-3). The basic idea is using a constant speed motor to pull a moving plate which is attached to the bottom of a bellows filled with liquid nitrogen. Therefore, a constant volumetric flow rate can be achieved when the motor is turned on. The bellows used in the experiment is made by thin-wall stainless steel. It has an OD of 4.0 inch and a free length of about 7.5 inch. The bellows is inside of a stainless steel tank, which has an OD of 6.75 inch, ID of 6.35 inch and inner depth of 10.24 inch. A stainless steel flange is fabricated as the tank cap and a copper O -ring is used to seal between the tank and the cap. There are tw o opening on the tank cap, one for feeding liquid nitrogen to the tank and the other fo r feeding the bellows. After assembling, the bellows is at the lower part of the tank, so that the liquid nitrogen in the tank will flow into the bellows when the tank liquid level is high enough, therefore, a full tank will be a sufficient condition for the bellows is also full and immersed in liquid nitrogen. The experimental time is usually only several minutes, during which only a little amount of the liquid nitrogen surrounds the bellows will be boiled off, and it is assumed that the flow from the bellows is pure li quid at saturation temperature. A stainless steel connector welded with a valve is designed and fabricated to assemble the bellows to the tank cap. The valv e is used to fill the bellows and will be closed manually when the bellows is full. Copper O-ring and Teflon gasket seal are adopted at top and bottom of the connector, respectively. The bottom of the bellows is

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26 attached to an aluminum plate. The top of the bellows is stationary while the bottom travels. Figure 3-3. Cryogenic flow driven system. A commercial constant speed motor is m ounted on the tank cap by three brass rods. The shaft of the motor is coupled with a drive screw, which pulls the bottom moving plate by three pull rods and th erefore compresses the bellows with constant speed when the motor is turned on. Totally three moto rs with different speed are used in the experiments. The bellows compression speed is determined by the motor speed and the pitch of the drive screw. Fo am insulation is applied around the outside of the whole tank to reduce the heat loss.

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27 Before using the bellows driven system, an insulated reservoir was also used for ground tests, and the flow is driven by the hydr aulic head of the reservoir. With this configuration the system is easy to control, and the expe rimental time can be extended much longer, however, the major drawback is the larger uncertainty of the flow rate compared with bellows driven system. 3.1.3 Test Section The test section is a Pyrex glass tube of 25.4 cm long. The ID and OD of the test section are 11.1 mm and 15.8 mm, respectivel y. The test section inlet and outlet are stainless steel tubes. At both ends of the test section, stainless steel adaptors and Teflon ferrules are used to connect the test section to the test section inlet and outlet portion. There are 9 drilled holes of approximately 2mm depth in the test section. The diameter of each hole is 1mm. A total of 15 type-T thermoc ouples are placed on the test section, 9 are embedded very close to the inner surface through dr illed holes at three downstream cross-sections. At each cross-section, three thermocouples are located circumferentially at equal separation distan ce. The other 6 thermocouples are used to measure the outside wall temperatures at two cross-sections, also located circumferentially at equal separation distance. The test section can be rotated along its axis before being fastened at two ends. Fi gure 3-4 sketches the test section and the thermocouple locations in one of the tests. The test section inlet, test section and te st section outlet are enclosed in a vacuum jacket built from stainless steel vacuum co mponents. Two transparent quartz windows in the vacuum jacket enable the observation a nd record of the two-phase flow regimes inside the test section. The diameter of each window is 7.62 cm. A ceramic sealed vacuum feed-through flange is used to conne ct the thermocouple wires from the vacuum

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28 side to the air side. The vacuum is main tained by a potable vacuum pump during the experiments. Figure 3-4. Test section and thermocouple locations. A CCD camera (CV-730 from Motion Analys is Inc.) set with 1/1,000 sec shutter speed faces one of the quartz windows to reco rd flow images, while lighting is provided by a fluorescent light at the other widow. 3.1.4 Experimental Rig A rig consists of an aluminum frame that houses the experimental apparatus. The main function of the rig is to secure all th e equipment during the microgravity tests. The important qualities of a rig are: Strong enough to withstand the decelera tion (with all equipm ent attached). Have sufficient room to house the necessary equipment. Minimize weight as much as possible. Two rigs of 16 inch wide, 32 inch long a nd 20 inch high are conn ected and used in the experiments. Bottom of the two rigs is covered by two thin aluminum plates. For ground experiments, the flow driven system a nd the vacuum jacket are fastened to the

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29 bottom aluminum plates. For microgravity ex periments, all the equipment include the light, the CCD camera and the vacuum pump are fastened to the bottom plates and no part of the equipment can stretch out the ri gs. A mirror is used in this situation for adjusting light path so that the camera can be set inside the rig. To ensure smooth drop process the equipment need also to be evenly distributed. 3.2 Data Acquisition System A data acquisition system is built for r ecording temperatures and flow images during experiments. Type T thermocouples (O mega) with Teflon insulation are used for temperature measurement. The gauge size of the thermocouple wires is 30 AWG. The thermocouples are wired to a screw terminal board and then connected to a 16-channel thermocouple board (PCI-DAS-TC from Measur ement Computing) plugged into the PCI slot of a computer. The thermocouple board has built in cold junction compensation and programmable gain ranges. All the thermocouples are tested and calibrated with boiling nitrogen prior to the chilldown experiments. A Labview program is de veloped to read the temperature measurements to the computer. The program has a frie ndly graphical user interface and updates the temperature prof iles simultaneously during the tests. Video images are monitored and record ed by connecting the CCD camera to a frame grabber board (FlashBus MV Lite from Integral) plugged into the PCI slot of the computer. A commercial software records the flow images and also shows the real-time images on the computer screen. For microgravity tests, thermocouple exte nsion wires about 20 m long are used to connect the thermocouples to the temperature acquisition board, so th at temperature data can be collected during the drop with comparable accuracy.

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30 3.3 Drop Tower for Providing Microgravity Condition 3.3.1 Introduction of Microgravity Facilities There are mainly four facilities that can provide microgravity environment: sounding rocket, spacecraft, airc raft flying parabolic trajecto ries and drop tower. With continuing increase in microgravity research, many researchers have found, and will continue to find, the high co st and distant locations associ ated with many of the worlds microgravity facilities limit thei r progress. This is especially true for lower-budget, smallscale research projects. It is also very difficult for many re searchers to quickly develop and perform rough microgravity testing on a ne w concept or idea. However, drop towers can be built on-site, are relatively inexpensiv e to operate, and provide good to excellent microgravity levels. Compared with other faci lities, the available microgravity time from drop tower is relatively short, however, for many research applications especially those in the preliminary testing stages, this is not a limiting factor. 3.3.2 Drop Tower Design and Microgravity Condition An empty elevator shaft located in the Nu clear Science Building at the University of Florida is used as the foundation for the drop tower. The drop towe r is 5-story high and has a maximum drop height of 15.25 m, which a pproximately equals to free fall time of 1.7 seconds. This drop tower is a reconstruc tion of the 2.1 seconds drop tower in the Washington State University. Many parts came from that 2.1 seconds drop tower and most of the designs are similar to the 2.1 s econds drop tower also. For more detail of the drop tower design can refer to the Master Thesis of Snyder (1993). Figure 3-5 gives the sketch and some dimensions of the drop tower. The drop tower mainly consists of a release-retrieve mechan ism, a drag shield, an airbag deceleration system, power and experimental control system.

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31 Winch Retrieve Mechanism Drag Shield Drag Shield Cart Pressure Relief Windows Blower Guide Wires Hatch Door High Density Foam 30" Thick Airbag Access Window Pressure Relief Windows Airbag 144"X79"X83" I-beam 1200lbs. Max load Figure 3-5. Drop tower system. 3.3.2.1 Release-retrieve mechanism The release-retrieve mechanism is compos ed of a steel cro ss member with two arms extending out the sides similar to that of the drag shield (Figur e 3-6). Before a drop, the release-retrieve mechanism can lower the experiment and the drag shield down the shaft to any drop height desired. After a drop, the release-retrieve mechanism can remotely retrieve the experimental system and drag shield with its self-locking hitches. A tapered pin release mechanism is designed that uses frictional forces to hold the

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32 experimental system and the drag shield be fore release. The tapered pin is pounded into place similar to that of a drill chuck. A solenoi d is used to release the frictional forces by simply allowing the chuck to split open as sh own in Figure 3-6. During the release the tapered pin glides along the c huck and provides a symmetrical release which helps avoid any rotation. The connection from the tapered pin to the experimental system is also specially designed to reduce the ad verse effects during the release. Figure 3-6. Release-retrieve mechanism of the drop tower. 3.3.2.2 Guide wires Two guide wires stretch the length of the shaft on both sides of the drag shield. The guide wires are used to keep the drag shield vertical during deceleration and also insure that the release-retrieve mech anism and the drag shield are aligned for remote retrieval after a drop. 3.3.2.3 Drag shield The drag shield is used to isolate the exte rior drags that come from the guide wire, the friction of the air and etc. Bottom section of the drag shield is a semi cylinder filled with sand as ballast. The purpose of this desi gn is to ensure the impact can be evenly

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33 distributed to the airbag deceleration sy stem during the deceleration period. A cart matches the shape of the bottom section is used to slide the drag shield. Top section of the drag shield is rectangular with two arms extending outside to the guide wires. The bottom section of the drag shield is connect ed to the top secti on with the use of 6 enclosed latches, so that the drag shield can be taken apart. When disconnected, the bottom semi cylinder section can stay on the sliding cart a nd be slid out from under the top section. This allows the experimental apparatus to be placed onto the bottom section and then slid back into place under the drag sh ield top again, thus, loading the experiment apparatus. A similar process is followed wh en unloading the experimental apparatus. There are two doors on both side of the drag shield, and can also be used for loading experimental apparatus with light weight. Figure 3-7 gives the sketch and some di mensions of the drag shield and the experimental system. Before each drop, the dr ag shield and the experimental system are held to the release-retrieve mechanism by the tapered pin. The tapered pin is released when the drop button is pushed to trigger the solenoid. During the dr op, the drag shield moves slower than the inside experimental system, because there are some resistant forces on the drag shield from the guide wire s and the exterior air while the only resistant force on the experimental system comes form the inside air, which is also moving with the drag shield. Therefore, high microgravity level can be achieved on the experimental system. To minimize the deceleration impact, it is desirable that the experimental system hits the drag shield at the same time when th e drag shield hits the airbag. However, there

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34 is no effective method to evaluate the drags on the drag shield during the drop. So this is just ensured by trial and error to find the best drop distance of the experimental system. Experimental System Guide Wire Drag Shield Tapered Pin Conneted to the ReleaseRetrive Mechanism Ballast Figure 3-7. Drag shield and the expe rimental system before a drop. 3.3.2.4 Airbag deceleration system Airbag deceleration system built at the bottom of the drop tower is used to decelerate the drag shield at the end of the drop with relatively small impact. The system consists of 1447983 inch wooden box which encloses a vinyl coated po lyester airbag of approximately the same dimension. High de nsity foam of 30 inch thick is laid down between the ground and the airbag. There ar e four pressure relief windows on the box with two on each side. The windows open at the deceleration period to insure smooth deceleration process. Windows at opposite sides of the wooden box are connected together with high tension bungee cord. A one horsepower blower is used to fill the

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35 airbag. The test results show that the airbag deceleration sy stem works efficient and is simple to use. The same air venting settings can cover a large variety of drop weight and drop height with no more than 20-g deceleration. 3.3.2.5 External connections Power, video, data acquisition, and e xperimental control are all connected externally in this design. Thus less equipmen t has to be on the experimental system, and the data acquisition can be accomplished on a standard PC. 3.3.2.6 Microgravity condition The drop tower described here is inexpe nsive to build, easy to operate, has relatively low deceleration, low releas e vibration and rotation, and has a good microgravity level. This drop tower can pr ovide a maximum microgravity time of 1.7 seconds with the microgravity level between 10-5 to 10-4 g. 3.3.3 Safety Summary Safety is the most important issue in the drop tower microgravity tests. A brief summary concerning safety issues is given below. To release the drag shield, a 5V pulse is needed to be sent to the release mechanism by the computer. A control circuit, which cons ists of two switches, is added between the computer and the release mechanism. The firs t switch is controlled by a key that insures no one can operate the drop tower without perm ission. The second is a spring type switch that is activated only when it is pushed down. Thus if the co mputer sends a 5V pulse to the release mechanism on accident the solenoi d will not get power unless this button is also pushed. Four aluminum bars are installed to th e ground floor door to enhance and lock the door while the drop tower is in operation. As mentioned earlier, the two guide wires

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36 insure that the drag shield cannot come of f course during the drop. Safety railing is installed at three sides of the drag shield. Th e other side is secured when the hatch door is open. An expanded wire mesh is installed co mpletely around the guide wires in the drop level in case the wires come loose during a dr op. Four cameras are installed to monitor the drop process, three on the ground level on e on the drop level. The drop process is shown on the computer screen, and a copy is al so recorded in the computer, which could be used for reviewing and improving the design of the drop tower. 3.4 Experimental Condition and Procedure 3.4.1 Experimental Condition In the experiment, liquid nitrogen is chosen as the working fluid because of its nonflammable and non-toxic nature. Liquid nitrogen is also inexpensive to use. Before each test, the tank and the bellows are fed severa l times until the liquid nitrogen inside the tank and the bellows is in a quasi-steady state. Si nce the bellows is totally immersed in liquid nitrogen, it is assumed that the exit state from the bellows is saturated liquid nitrogen at 1atm. The pipes before the test section are also pre-cooled by liquid nitrogen through bypass lines before the test. Efforts have been tried to control the back pressure at the exit of the flow. A tank installed with a check valve is used for this purpose; however, it is found that this method is not applicable for cryogenic fluids: the li quid boils off very quickly inside the tank and causes the check valve to open and close freque ntly, and thus introdu ces large fluctuation to the back pressure. So the flow is vented to the atmosphere directly during the tests. Three constant speed motors are used to drive the bellows. The speed of the motor is 5 rpm, 10rpm and 15 rpm, respectively. The bellows compression speed is determined by the driven motor rotation speed a nd the pitch of the drive screw:

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37 belrotpitVVL (3.1) in which belV is the bellows compression speed, rotVis the motor rotation speed, pitL is the pitch of the drive screw, and the mass flux inside the test section can be expressed as: 2 bel lrotpitD GVL D (3.2) where G is the mass flux, l is the saturation liquid density of the nitrogen, D is the ID of the test section and bel D is ID of the bellows. Table 3-1 shows the working condition of the experiments. The vacuum level during the test is maintained at a bout 0.9 by a portable vacuum pump. Table 3-1. Working condition of the experiments. Motor speed (rpm) Liquid velocity entering the test section (cm/s) Mass flux 2kgms Approximated test duration limit (minute) 5 0.446 3.606 15 10 0.891 7.205 7.5 15 1.337 10.811 5 3.4.2 Ground Test Procedure The ground test procedure is as follows: 1. Install the top moving plane at the bottom position of the drive screw. 2. Turn on the light and the camera. 3. Turn on the vacuum pump; make sure the vacuum level is normal. 4. Close the control valve to the test secti on, open the feeding valve to the bellows and the tank, and open the valve on the bellows. 5. Feed liquid nitrogen to both the bellows a nd the tank. This step is repeated several times until the tank is cooled down. 6. Close the feeding valve and the valve on the bellows. 7. Begin to collect data, run the data acquisition and video record programs. 8. Open the control valve to the test section.

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38 9. Turn on the motor to compress the bellows and liquid nitrogen is introduced to the test section. 10. Finish one test, turn off ever ything and loose the bellows. 3.4.3 Microgravity Test Procedure The microgravity test procedure includes the operation of the drop tower, and is much more complicated compared with the gr ound test. The procedure is summarized as follows: 1. Open the blower to inflate the airbag; check and make sure the air bag and the windows at the 1st floor work properly. This step is ve ry important for the safe operation of the drop tower. The airbag must strong enough to provide proper deceleration for the drag shield and the e xperimental setup, yet it can not be too stiff to bounce the drag shield back and cause damage. The stiffness of the airbag is determined by the tension of the bungee co rds connected the relief windows. The tension of the bungee cords is checked before each drop. 2. Insert and knock in the tapered pin connect or to the release-retrieve mechanism. 3. Open the doors on the drag shield and load the experimental apparatus to the drag shield. 4. Raise the experimental appa ratus until it reach the top of the drag shield. 5. Connect the experimental apparatus to th e threaded head of the tapered pin. 6. Lift the drag shield up a litt le so that the sliding card under the drag shield can be moved out of the space. 7. Lift the drag shield just high e nough to open the hatch door on the 5th floor, and then lower it down for fe eding the liquid nitrogen. 8. Follow the ground test procedure from step 1 to step 10. The only difference is that the feeding pipes are remove d after finish. So there is no equipment stretches out the rigs. 9. Replace the doors on the drag shield; open the two self-locking hitches on the release-retrieve mechanism. Now the drag shield and the experimental apparatus are hung by the tapered pin. 10. Raise the drag shield to the drop position and wait the drag shield to stabilize, recheck every thing on the 5th floor (external wiring video equipment, data acquisition program, etc.).

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39 11. Turn the first switch, the key switch, on the control. Now the release mechanism will work and release the drag shield when ever the second switch, the drop button, is pressed. 12. Turn on the bellows driven motor to genera te the nitrogen flow. The driven motor uses a power cable connects externally to the drag shield. A power outlet with on/off switch connects the power cable to the wall. So the driven motor can be controlled at the drop level. 13. Wait for the desired working condition. The temperatures and the flow images are shown simultaneously on the monitor, so the release can be made at desired working condition. 14. Push the drop button and release the drag shield. 15. Turn off the driven motor to stop the nitrogen flow. 16. Close the two self-locking hitches on the release-retrieve mechanism; retrieve the drag shield and the experiment al apparatus at the ground floor. 17. Stop the data acquisition program. 18. Check the drag shield and the experimental apparatus when they are retrieved back to the drop level, and loose the bellows. 19. Check the airbag deceleration system at the ground level a nd finish one test. 3.5 Uncertainty Analysis For single sampled experiments, the me thod introduced by Klin e and McClintock (1953) has been widely used to determine th e uncertainty. In current experiments, one needs to solve the inverse heat conduction problem (IHCP) to get the surface heat flux from temperature measurements (Ozisik 1993; Ozisik and Orlande, 2000), and simple equation that relates the measured data to th e heat flux does not exist. Therefore, only the uncertainty of the measurement itself and the uncertainty from the experimental apparatus will be given here. 3.5.1 Uncertainties of Temperature Measurement The type T thermocouples used for temper ature measurement have the uncertainty of 00.5C declared by the manufacturer. For highl y transient process like chilldown the

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40 response time of the thermocouples is also im portant. To get quick response, the tip style of the thermocouples is chosen as exposed a nd the wire diameter of the thermocouples is used as smaller as possible. With the wire diameter of 0.25 mm the responding time is less than 0.2 second according to the chart given by the manufacturer. Another uncertainty source of temperat ure measurement comes from the data acquisition (DAQ) system. The DAQ board for temperature measurement has programmable gain ranges and A/D pacing, and accepts all the thermocouple types. The accuracy of the measurement depends on the gain, the sample rate and the thermocouple type. The uncertainty of type T thermocouple is 00.9C for worst case from the product specification. For current experiment, the gain is set at 400 and the sa mple rate is about 60 Hz. It is found that the uncertain ty for current settings is about 00.3C 3.5.2 Uncertainty of Mass Flux The uncertainty of mass fluxG is evaluated as (Kline and McClintock, 1953): sec1 2 22 2 2 2 secbelrotpitGddVL rotpitGGGGG DDVL (3.3) where is the absolute error. The relative error for mass flux measurement is then: sec1 2 222 2 2 2222pit belrotL ddV G belrotpitGDDVL (3.4) The diameter of the test section has an ID of 11.10.2 mm given by the manufacturer. The absolute error of the bellows ID is within 0.2 mm. The error of the motor rotation speed is not given by the manuf acturer. Simple tests have been conducted to calibrate the motor rota tion speed. For each motor used, let the motor run for a

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41 relatively long time and record the time and th e total revolution times, then calculate the motor speed. It is found that th e relative error of the motor rotation speed is with in 5%. The error of the drive screw pitch can be estimated by measuring the length of several screw threads and then divide the number of threads. The relative error of the drive screw pitch is found to be approximately 3%. The error of quoted density data can be formed by comparing values from different sources. In Appendix II of the book written by Carey (1992) gives the saturation liquid density of the nitrogen as 3807.10kg/m, while another book (Flynn 1996) gives the value of 3808.9kg/m. So the relative error of th e saturation liquid nitrogen density is evaluated as 0.22% From Equation 3.4, the relative error for mass flux measurement is 6.88%. Because the diameter of the test section is relatively small and in Equation 3.3 the diameter term is squared, the error of the te st section ID contributes most to the total error. The uncertainty of the mass flux can be greatly reduced by using tubes with higher accuracy. 3.5.3 Other Uncertainties The vacuum level is measured by a vacuum gauge that has the minimum scale of 0.02 bar, so the uncertainty of the va cuum level is approximately 0.01 bar. Thermocouple feed-through is used to connect the thermocouple wires from the vacuum side to the air side. For this situa tion, a third metal othe r than the two metals (copper and constantan) used in the thermocoupl es is introduced in, this will cause error in temperature measurement unless the third metal in both wires are identical, have the same length, and are kept at same temperature. These requirements are satisfied in the experiment, so the error introduced by th e thermocouple feed-through is comparably

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42 negligible. However, attention must be paid to avoid large temperat ure gradient along the feed-through flange during the tests.

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43 CHAPTER 4 CRYOGENIC TWO-PHASE CHILLDOWN UNDER TERRESTRIAL CONDITION Cryogenic two-phase chilldown under terre strial condition are experimentally studied in this chapter. Three different e xperimental methods have been performed. Gravity-driven experiments enhance the basic understanding of the chilldown process, while bellows-driven experiments have more accurate flow control. In rewetting tests, the test section is pre-cooled so that transiti on flow boiling and nuclea r flow boiling stages can also be covered. Based on the experiment al results, a phenomenological model is developed. Good agreement is achieved between the model predictions and the experimental results. 4.1 Gravity-Driven Experiment In gravity-driven experiments, an insulate d reservoir is used to generate the flow with estimated mass flux of 18-232kg/ms by reviewing the recorded flow images. The results show that the cryoge nic chilldown process can be divided into three stages associated with different heat transfer mechanisms. 4.1.1 Heat Transfer Study For horizontal tube orientation, the two-pha se flow is generally stratified because of the gravitational force. Therefore bottom of the tube is chilled down first. The heat transfer mechanism at the bottom of the tube includes film boiling, transition boiling, and nucleate boiling, while the heat transfer mech anism at the top of the tube is mainly convection to superheated vapor.

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44 4.1.1.1 Wall temperature profiles Wall temperatures are measured by 16 th ermocouples, 9 are embedded very close to the inner surface of the t ube wall; the other 7 thermocouples measure the outside wall temperature of the test sec tion. The thermocouple locations are shown in Figure 4-1 and different from that described in Chap ter 3. The unit for dimension is mm. Flow Direction Section 2 13 16 14 12 15Section 1 6 7 11 10 9 8 5 4 3Section 3 1 2 Figure 4-1. Sketch of the te st section and thermocouple loca tions for gravity-driven test. Figure 4-2 gives the temperature profiles at the inlet and middle section. It is found that large temperature difference exists betw een the top and bottom of the test section, which was also reported by Bronson (1962) in the experiments of chilldown heavy-wall transfer line. This temperature difference sugge sts different heat transfer mechanisms are encountered at the top and th e bottom of the test secti on. Since the two phases are separated by gravitational force, the heat tr ansfer mechanism at the bottom is boiling heat transfer, while the heat transfer at the t op is forced convection to the vapor phase.

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45 050100150200250300350 120 140 160 180 200 220 240 260 280 300 Temperature (K)Time (s) TC11 TC14 TC12 TC15 TC13 TC16 A 05010015020025030035 0 120 140 160 180 200 220 240 260 280 300 Temperature (K)Time (s) TC5 TC9 TC7 TC10 TC8 B Figure 4-2. Temperature profile s of gravity-driven test at different cross-sections. A) Inlet section. B) Middle section. 4.1.1.2 Data reduction In boiling heat transfer experiments, surf ace heat flux as a function of wall super heat is often of particular interest, because it denotes different heat transfer mechanisms and is crucial for engineering applicati ons. However, in chilldown or quenching experiments surface heat flux is not controll able. The surface heat flux can be inferred

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46 from the temperature history by solving the IHCP. For quenching of vertical tube, in which axial-symmetrical assumption is genera lly held, the situation is much simpler. Based on exact solution of the IHCP, Burggr af (1964) developed a method to obtain the temperatures and heat fluxes at the inside tu be wall from the temper ature history data of the thermocouple welded on the outside of the test section: 2 2 22422 2 44 2222212ln 4 1 5lnln... 6481616oii i oo oiioioi io oorrr dT TT rrdt rrrrrrr dT rr rrdt (4.1) where ir and ordenote the inner and outer radius, respectively; iT and T are the inside wall temperature and temperature meas ured by thermocouple, respectively; is the thermal diffusivity of the wall. Then the insi de wall heat flux with the first three leading terms can be written as (Iloeje et al. 1975): 2 22342 2 2 3 54236234 3 2 3ln 216164 33 lnln 3841281283843232ioiooii w iio ioioiooiioii iooc rrrrrrr dTdT qc rdtkrrdt c rrrrrrrrrrrr dT krrrdt (4.2) For horizontal chilldown experiments, th e axial-symmetrical assumption is not valid, and the solution of the IH CP surfers from ill-posedness. In order to calculate heat transfer data from the transient temperatur e profiles, an energy balance is performed locally on a control volume of the tube wall at thermocouple location. The change in stored heat in the control volume is equated to the heat transported to the fluid and heat transferred by conduction, minus losses to the environment. This method was used by many researchers in analyzing data from quenching tests (Abdul-Razzak et. al 1992;

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47 Westbye and Kawaji 1995; Chen et al. 1979). The inside wall heat flux is then given as: 2222 2 2222oi oioio w convradcond iiiorr rrrrr dTkdT qcqqq rdtUrdtrrd (4.3) The first term in the right-hand-side (RHS ) of Equation 4.3 comes from the change of the stored heat in the control volume and is the dominant term in chilldown experiments. It is also interesting to note th at this term equals the first term from the IHCP solution given in Equation 4.2. To estimate the axial heat conduction term in rewetting experiments, Chen et al. (1979) assumed a constant rewetting velocity U, and the axial temperature gradient dTdz was represented by 1 UdTdz. Then the effect of the axial conduction on the inside wall heat flux can be evaluated from the second term in the RHS of Equation 4.3. The axial conduction term is generally very small, and it is onl y important at location near the quenching front, where maximum axial temperature gradient exists between the dry side and the wet side of the wall. A comparison between heat fluxes based on a 2-D heat transfer model (Cheng 1978), which consid ers the axial heat c onduction, with those obtained by neglecting axial conduction was given by Cheng et al. (1979). The comparison for the copper test section showed that the two mid-plane boiling curves were approximately the same and the net axial c onduction at the mid-s ection is negligible small. In our experiments, the temperature m easurements show that the axial temperature gradient is relatively small, and additionally the heat conduc tivity of the glass is much smaller than that of the copper used by Cheng et al.(1979), ther efore the axial heat conduction along the test section is neglected in heat flux ca lculation. It is left in Equation 4.3 only for integrity.

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48 The third term in Equation 4.3 accounts for the contribution from the radiation and natural convection inside the vacuum jacket. The details of how they are evaluated will be given later. The last term in Equation 4.3 comes from the circumferential heat transfer. Here, d is the azimuthal angle of the control vol ume and depends on the size of the control volume. In our calculation, the control volume is approximately assumed to be in thermal equilibrium with the embedded thermocouple. Based on this assumption, the control volume size is chosen with an average ar c length of 2.0mm. The circumferential temperature gradient is calculated by lin ear interpolation betw een the thermocouple measuring points. Derivative of the temperature history is needed in calculating the first term in Equation 4.3. Generally, the finite difference method is not suitable to obtain the temperature derivatives, because it is very susceptive to small fluctuations, which are inevitable in measurements. Therefore, a leas t square technique, pr oposed by Iloeje et al. (1975) in similar situation, is used to ge t smooth profiles. To increase accuracy, the temperature data are divided into segments and the order of the curve fit used for each segment is made as high as possible (but less than 6, otherwise will subject to temperature fluctuations) wit hout reintroducing irregularities inherent in the pure data. Figure 4-3 shows a typical result obtained with the least square fit procedure, and Figure 4-4 compares the first term in Equation 4.3 calculated from the least square fit line with that from the finite difference method. It is clear that the finite difference method is not suitable for calculating the derivatives of measured temperature profiles.

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49 051015202530 130 135 140 145 150 155 160 Measured Data Lease Square Fit LineTemperature (K)Time (s) Figure 4-3. Typical curve fit line of the experimental data. 051015202530 0 5000 10000 15000 20000 25000 30000 Least Square Method Finite Difference MethodHeat Flux (W/m2)Time (s) Figure 4-4. Temperature deri vatives calculated by least s quare fit method and by finite difference method. Assume the vacuum jacket and the test section as long concentric cylinders, the radiation contribution to the heat flux, radq is obtained by (Incropera and Dewitt 2002; Liao 2005):

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50 441 1Bjo rad j o tjjTT q r r (4.4) where B is Stefen Boltzmann constant, jT is the temperature of the vacuum jacket, and is assumed to equal room temperature, oT is the outer wall temperature of the test section, j and t are emissivity of the vacuum jacket and the test section, respectively, and or and jr are outer radius of the test section and the inner radius of the vacuum jacket, respectively. To evaluate the natural convection heat tr ansfer due to the residual air inside the vacuum jacket, Raithby and Hollands correl ation (Raithby and Hollands 1975; Liao 2005) is used: lneff convjo ojok qTT rrr (4.5) where effkis the effective thermal conductivit y given by Raithby and Hollands (1975). 4.1.1.3 Heat transfer mechanisms The data reduction method given above is us ed to analyze the tr ansient temperature measurements. Left part of Figure 4-5 shows the calculated bottom wall heat flux as a function of bottom wall temperature at the ou tlet cross-section, while the right part represents the corresponding temperature profiles. The shape of bottom heat flux is similar to the boiling curve from steady-state pool boiling experiments. This suggests that th e chilldown process may share many common features with pool boiling experiments. Fo llowing the method to characterize different heat transfer mechanisms in pool boiling e xperiments, a maximum or critical heat flux

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51 (CHF) CHFq and a minimum heat flux minq are used to divide the chilldown heat transfer into three stages, which are film boiling, tr ansition boiling and nucle ate boiling, as shown in Figure 4-5. 50403020100 0100200300 125 150 175 200 225 250 275 300 Initial Effect Wall Temperature (K)q" min Bottom Wall Heat FluxTime (s) Heat Flux (kW/m2)q" CHF Nucleate Boiling Transition Boiling Upper Thermocouple 1 Upper Thermocouple 2 Bottom Thermocouple Film Boiling Figure 4-5. Bottom wall heat flux and transi ent wall temperature profiles at the outlet cross-section. Initially, the wall temperature is very hi gh, liquid nitrogen evaporates drastically when enters the test section; a vapor film will form and separate the liquid from contacting the wall, the two-phase flow is therefore in film boiling state. At decreased wall temperature, the liquid begins to cont act the wall; the heat transfer mechanism is transition boiling, which is characterized by increasing wall heat flux with decreasing wall superheat that contrary to what in the film boiling region and nucleate boiling region. After passing the CHF point the heat transfer mechanism then changes to nucleate boiling. The calculated bottom wall heat flux as a func tion of time is shown in Figure 4-6. It is obvious that the time of transition boiling is very short compared with the other two boiling stages.

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52 050100150200250300 0 5 10 15 20 25 30 35 40 45 Nucleate Boiling Transition Boiling Bottom Wall Heat FluxHeat Flux (kW/m2)Time (s) Film Boiling Figure 4-6. Bottom wall heat flux at the outlet cross sect ion as a function of time. Similarity between the chilldown boiling cu rve and the pool boiling curve naturally leads one to compare the chilldown data w ith pool boiling correlations. The comparisons between the two turning points, namely the minimum heat flux and the CHF, are given below. For steady state film boiling, the correlat ion developed by Zuber (1959) is widely used to predict the minimum heat flux: 1 4min 2 lv lvv lvg qCh (4.6) here, is surface tension; gis gravitational acceleration; lvh is the latent heat of vaporization, while C was variously given as 0.177 (Zuber 1959), 0.13 (Zuber 1958), or 0.09 (Berenson 1961). The resulting minq is then 13.02kW/m, 9.62kW/m, and 6.62kW/m, respectively. In Figure 4-5, the minq for chilldown is calculated as 13.32kW/m, which is a slightly larger th an steady state prediction with C0.177.

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53 Based on the similarity between th e CHF condition and column flooding, Kutateladze (1948) derived the followi ng relation for the pool boiling CHF: 1 420.131lv CHFlvv vg qh (4.7) Zuber (1959) got the identical correlation base d on the analysis of Taylor and Helmholtz instability. For liquid nitroge n under atmospheric pressure Equation 4.7 gives a CHF value of 160.72kW/m. The chilldown measurement in Figure 4-6 is only about 27% of this value. This big discrepancy is believe d to come from the different experimental condition between the chilldown and the pool bo iling tests. In pool boiling experiments, the heat supplied to the fluid is maintained by a heater, while in chilldown tests it comes from the stored heat in the tube wall. In th e film boiling region, the heat flux is generally small, therefore the tube wall can maintain a near constant he at flux condition and function like the heater used in the pool boili ng tests. However, in the transition boiling region, the stored energy in the tube wall is depleted so quickly that the experimental condition is very different form that of the pool boiling tests. The limited energy stored in the tube wall put a restriction on the value of CHF, which, therefore, is much less than the pool boiling data. Previous work by Bergles and Thompson (1970) also concluded that quantitively the differences between chilldow n and steady-state boiling curves can be very large. In Equation 4.6 and Equation 4.7 the minimum heat flux and CHF are not correlated with the thermal prope rties of the wall for pool boili ng tests. However, as seen from above, the available heat flux to the flow is closely related to the energy stored in the wall. Therefore, the thermal properties, e.g. thermal conductivity, heat capacity, of the

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54 wall are expected to play a role in the chil ldown process. For example, for a wall with higher thermal conductivity, the energy transferred to the fl ow can be more quickly supplied by the surroundings, and therefor e will result a higher value of CHF. Figure 4-7 shows the calculated heat flux in different axial lo cations. It is found that both the CHF and the minimum heat flux decrease with increasing axial distance from the inlet. This is also associated with an increase in the rewetting temperature. 100120140160180200220240260280300 0 10 20 30 40 50 Heat Flux (kW/m2)Temperature (K) inlet section middle section outlet section Figure 4-7. Bottom wall heat fluxe s at different axial locations. In most of the previous quenching expe riments, the film boiling heat flux was reported as either keeps a re latively constant value (Wes tbye et al. 1995; Cheng and Ragheb 1979) or decreases as the test section is chilled down (Gani and Rohsenow 1977; Bergles and Thompson 1970). In our experime nts, however, the local heat flux first increases in a short period then decreases grad ually. This is consistent with the transient nature of the experiments. Generally the incr easing period is expected to be shorter at higher mass flux if the other c onditions are kept the same. The mass fluxes in previous investigations were much larger than that in current experime nts, and therefore associated

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55 with very short increasing time of the heat flux in the film boiling regime. This might be the reason that the increa ses of the heat flux were not recorded before. 4.1.2 Visualization Study Heat transfer analysis shows the chilldown process can be divided into three stages with each stage associated with different he at transfer mechanisms. The visualization study casts more light on the characteristic of flow regimes during the chilldown process. Figure 4-8 illustrates the overall chill down sequence in our experiments, while some selected flow images in different regi on of chilldown are shown in Figure 4-9. In the beginning of the f ilm boiling region, the flow pattern is basically dispersed flow, in which the liquid phase is dispersed as near spherical drops with in a continuous vapor phase. The void fraction of the two-phase flow decreases as the tube is chilled down, and long liquid filaments, separated from wall by a thin vapor film, are observed to flow along the tube bottom. The length of the li quid filaments generally increases with decreasing wall temperature. For short liquid filaments, the flow regime is close to dispersed flow, while for very long filaments, th e flow regime can be classified as highly skewed inverted annular flow. In the film boiling region, heat is primarily transferred from the wall by conduction through the vapor film and thus evaporate the liquid filaments, and by convection to the vapor phase. Once the bottom wall temperature has been reduced low enough, transient boiling, characterized by intermittent liquid-wall contact and violent bubble generation, is observed. Shortly after the transient boili ng, a continuous liquid-wall contact is established and the liquid nitrogen begins to pile up on the bottom wall. Many nucleation sites are observed to be suppressed as th e wall temperature keeps decreasing. The

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56 prevailing boiling regime is nucleate boiling a nd the flow pattern is stratified flow or wavy flow. Previous horizontal quenching tests (Chan and Banerjee1981a; Abdul-Razzak et al. 1992) showed the same sequence as our expe riments, however, with different flow regimes mainly in the film boiling region. In their experiments, the flow regime in film boiling was inverted annular flow. The thic kness of the liquid core increases with decreasing wall temperature, and then follows the stratified flow regime. While in our experiments, the thickness of th e liquid filament is generally a constant, instead the liquid thickness increases in the nucleate boili ng region as shown in Figure 4-8. Quenching Front Film Boiling Transition Boiling Nucleate Boiling Liquid Droplets Liquid Filaments Stratified Flow Figure 4-8. Characteristics of horiz ontal chilldown under low flow rate. The difference in flow regimes is believed mainly due to different flow rates. The flow rate in the test of Chan and Banerjee (1981a) was about 150~4502kg/ms, while it was even higher (400~13002kg/ms) in the experiments by Abdul-Razzak et al. (1992). In current chilldown test, the flow rate is mu ch lower. The heat stored in the tube wall causes dry-out of the liquid phase in the film boiling region and thus leads to the dispersed flow. The visualization study also gives the deta il of propagation th e quenching front and how the liquid rewets the tube wall (Figure 410). The arrow in Figur e 4-10 indicates the limit between the quenching front and the nucleate boiling region.

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57 A B C D Figure 4-9. Flow visualizations at different stages of chilldown. A) Initial stage. B) Film boiling stage. C) Transition boi ling stage. D) Nucleate boiling stage.

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58 Quenching Front Figure 4-10. Propagation of the quenching front. As shown in Figure 4-10, the quenching fr ont is characterized by vehement bubble generation and intermittent liquid-wall contact. Following the quenching front, a continuous liquid-wall contact is established, the flow regime changes to stratified flow, and many nucleation sites are suppressed.

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59 4.2 Bellows-Driven Experiment 4.2.1 Introduction The flow rates in current bellows-dri ven experiments are very low. As a comparison, previous quenching experiments were generally conducted with flow rates higher than 402kg/ms. For example, the liquid nitrogen flow rate was in the range of 550-19402kg/msin the experiments of Antar and Collins (1997) and was 40.7271.32kg/msin the experiments of Iloeje et al. ( 1982), while the flow rate of R-113 used by Westbye et al. (1995) was from 160 to 8502kg/ms. No experimental work has been reported for cryogenic chilldown proce ss under relatively low flow rate. On the other hand, further understanding of the cryogenic chilldown process at low flow rate is of crucial importance for some applications, for example the cooling process in the TVS on a spacecraft. The mass flux in a TVS system is generally very low, in steady state test by Van Dresar et al. (2001, 2002) the nitr ogen mass flux ranged from3.3 to 332kg/ms. The highly transient chilldown pro cess under low flow condition has not been fully studied. In present study a horizontal test secti on is quenched by the liquid nitrogen flow with mass flux form 3.6 to 10.82kg/ms, the flow regimes and heat transfer behavior are studied experimentally, and a phenomenol ogical model is developed based on the experimental observations. 4.2.2 Visualization Study The test section is initially at room temp erature. The visualization study shows that in the film boiling region the flow regimes ar e similar to that illustrated in Figure 4-8. When the chilldown is initiated the liquid phase is in the form of droplets that bounce

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60 back and forth on the bottom wall while trav eling downstream. As the wall temperature decreases, the liquid droplets tend to form filaments and settle down on the bottom wall. Images of typical liquid fila ment at different mass fluxes are shown in Figure 4-11. A B C Figure 4-11. Typical flow images under diffe rent mass flux. A) Mass flux of 3.6kg/m2s. B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8 kg/m2s.

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61 Generally, the thickness of the liquid fila ments does not change much as the test section is chilled down; howev er, the length of the filaments increases with increasing mass flux and decreasing wall temperature. The drop-wall interaction from several experiments was summarized by Gani and Rohsenow (1977). They listed the most frequently observed states of drop-wall interaction and the interaction sequence, as the wall is cooled down. Current observations ge nerally agree with their summarization. The statistic feature of the liquid filament s is shown in Figure 4-12 and Figure 4-13. It is clear that the thickness of the filame nts shows very limited increase with increasing mass flux and does not present a strong correlati on with the wall temperature; the length of the filaments, however, is more scatte red at higher mass fluxes and lower wall temperatures. In other wards, the probabil ity of observing a longer liquid filament is larger under higher mass flux and lower wall temperature. 180200220240260280300 0 2 4 6 Liquid Filament Thickness (mm)Bottom Wall Temperature (K) 3.6kg/m2s 7.2kg/m2s 10.8kg/m2s Figure 4-12. Thickness of the liquid filaments at different mass fluxes.

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62 180200220240260280300 0 5 10 15 20 25 30 Liquid Filament Length (mm)Bottom Wall Temperature (K) 3.6kg/m2s 7.2kg/m2s 10.8kg/m2s Figure 4-13. Length of the liquid f ilaments at different mass fluxes. 4.2.3 Heat Transfer Study The temperature profiles measured from the embedded thermocouples at the inlet and the outlet cross-sections with differe nt mass fluxes are shown in Figure 4-14 and Figure 4-15, respectively. 0100200300400500600 180 200 220 240 260 280 300 Temperature(K)Time(s) TC 1 TC 2 TC 3 A Figure 4-14. Temperature profiles of the inle t section with different mass flux. A) Mass flux of 3.6 kg/m2s. B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8 kg/m2s.

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63 050100150200250300 160 180 200 220 240 260 280 300 TC 1 TC 2 TC 3Temperature (K)Time (s) B 0255075100125150175 180 200 220 240 260 280 300 TC 1 TC 2 TC 3 Temperature (K)Time (s) C Figure 4-14. Continued. It is obvious that the bottom wall of the test section is chilled down more quickly, because most of the liquid phase is confined at the bottom. The temperature difference between the bottom and the top of the test section is found to in crease with increasing mass flux at each cross section.

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64 The quality of the two-phase flow and va por superheat generally increase along the test section, consequently, the temperature difference between the top and bottom wall is expected to be smaller at further downstream locations. This is confirmed by comparing Figure 4-14 with Figure 4-15. 0100200300400500600 200 220 240 260 280 300 Temperature(K)Time(s) ch14 ch15 ch16A 050100150200250300 180 200 220 240 260 280 300 TC 14 TC 15 TC 16 Temperature (K)Time (s)B Figure 4-15. Temperature profiles of the ou tlet section with different mass flux. A) Mass flux of 3.6 kg/m2s. B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8 kg/m2s.

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65 0255075100125150175 200 220 240 260 280 300 TC 14 TC 15 TC 16Temperature (K)Time (s) C Figure 4-15. Continued. The calculated middle section bottom wall heat fluxes under different mass fluxes are shown in Figure 4-16 as a function of the local wall temperature. The bottom wall heat fluxes first increase during the initial stage, and then decreases gradually with decreasing wall temperature. 180200220240260280300 0 2000 4000 6000 8000 10000 12000 Heat Flux (W/m2)Wall Temperature (K) 3.6kg/m2s 7.2kg/m2s 10.8kg/m2s Figure 4-16. Middle section bottom wall he at fluxes under different mass fluxes.

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66 Figure 4-17 shows the local heat fluxes at three circumferential locations at the middle cross-section as a function of lo cal wall temperature under a mass flux of 7.22kg/ms. It is found that the two heat fluxes at the upper portion of the test section increase at the beginning dur ing the chilldown process, a nd then maintain at almost constant values. The heat fluxes at the upper portion of the test sec tion are much smaller than the bottom wall heat flux in a wide wall temperature range. Because the upper wall losses heat mainly by convection to the superheated vapor, while the main heat transfer mechanism at the bottom wall is film boiling, and is more efficient than convection. 180200220240260280300 0 2000 4000 6000 8000 Heat Flux (W/m2)Wall Temperature (K) TC4 TC5 TC6 Figure 4-17. Middle section local wall heat fluxes under mass flux of 7.2 kg/m2s. 4.2.4 Phenomenological Model of the Film Boiling Region For dispersed flow film bo iling (DFFB), it is widely acc epted that a significant thermodynamic non-equilibrium condition exists between the vapor phase and the liquid phase (Laverty and Rohsenow 1967; Koizumi et al. 1978; Chen et al. 1979; Chung and Olafsson 1984; Tian et al. 2006). A model for vertical dispersed flow boiling suggested by Koizumi et al. (1978) assumed that heat transfer takes place in steps: from the wall to

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67 the vapor and then from the va por to the droplets suspended in the stream; and from the wall to the droplets in contact with the wa ll. Chen et al. (1979) proposed a model for post-CHF region that considered the total h eat transfer as a sum of vapor and liquid components and ignored radiation heat transfer to the two-phase mixture. During the chilldown process, the inlet quality and vapor superheat are not constants but change with time and mass flux, and are hard to identify from the experiments. Therefore, a phenomenological model, which also includes information form visualization results, is developed to analyze the dispersed flow boiling heat transfer. 4.2.4.1 Model description As mentioned before, the visualization s hows that except in the very beginning stage, most of the liquid filaments are flow ing along the bottom of the tube. Consequently, in this model the heat transfer mechanism at the bottom of the test section is considered as the sum of vapor and liquid components, while the heat transf er mechanism at the upper portion of the test section is forced c onvection to superheated vapor. It has been shown (Guo and Mishima 2002; Tian et al. 2006 ) that for wall superheat up to several hundreds Kelvin the radiation he at transfer in post-dryout di spersed flow is generally negligibly small. It is also judged that ther mal radiation is minor in our case; therefore radiation heat transfer is ignored in this model. The heat transfer mechanisms in this m odel are illustrated in Figure 4-18. As an idealization, the liquid filament s are modeled as half cylinders in a film boiling state and move along the bottom of the tube. The filame nts are at the saturation temperature and separated from the tube wall by a thin vapor film. The bottom wall heat flux is a sum of vapor and liquid components, and can be written as:

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68 12, 11bbLbLfbLbconLqqFqFqFqF (4.8) where bq is the effective bottom wall heat flux, and f bq is the heat flux from the portion of the bottom surface where a liquid filament is in the vicinity and separated from the wall by a thin vapor film, therefore, f bq is a film boiling heat flux. bconq is the heat flux from the bottom surface where there is no liquid filament around, so it is due to pure forced convection to the superheated vapor. L F is defined as the time averaged fraction of bottom wall surface that is asso ciated with liquid filaments. Figure 4-18. Description of the heat transfer mechanism under horizontal dispersed flow condition. The upper wall of the test section is fully in contact with the vapor phase, and the upper wall heat flux is described as: 12, 1, 2(1)(1)uuLuLuconLuconLqqFqFqFqF (4.9) where uq is the effective upper wall heat flux, and 1 uconq is the convective heat flux to

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69 the superheated vapor for the por tion that is directly opposite to the bottom portion that is associated with liquid filaments as shown in Figure 4-18. 2 uconq is for the portion that is directly opposite to the bottom portion that is not associated with liquid filaments. 1 uconq and 2 uconq are different due to differe nt bulk vapor velocities in their respective sections. The fractional of liquid filament associated area L F is expected to increase with increasing mass flux and decreasing wall temper ature. The transient liquid fractions in recorded frames are widely scattered. Therefore L F is calculated by averaging over a certain time period, the result is shown in Fi gure 4-19. The fitted linear curves in Figure 4-19 are used in the model calculation. 180200220240260280300 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 FLWall Temperature (K) Experiments Model 3.6kg/m2s 7.2kg/m2s 10.86kg/m2s Figure 4-19. Fractional of li quid filament associated area at different wall temperature and mass flux. Another information referred from the reco rded images is the local void fraction Generally, the vapor film between the liquid filament and the tube wall is very thin, therefore at a cross-section that contains liquid filament, the local void fraction can be approximately expressed as:

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70 2arccos112 1LLLLhRhRhRhR (4.10) here, L h is the measured thickness of the liquid filament, and R is tube inner radius. The forced convective heat transfer to the vapor phase is evaluated by DittusBoelter equation as: 0.80.40.023v conDwvk qRePrTT D (4.11) in which vk is the vapor phase thermal conductivity; D is the hydraulic diameter of the vapor flow; DRe is Reynolds number; P r is the vapor Prandtl number; wTand vT are the wall temperature and balk vapor phase temper ature, respectively. It is noted that both 1uconq and 2uconq are evaluated using Equation 4.10 the difference is that each is evaluated based on the respective bulk vapor velo city in its section as shown in Figure 418. For the cross-section contains only va por phase, the vapor velocity is simply evaluated by: vvuG (4.12) in which G is the mass flux, while for the cross s ection contains both liquid filament and vapor phase, the vapor velocity is calculated by: 1vvluGS (4.13) where S is two phase slip velocity, it is defined as vluu, and can be evaluated as (Zivi 1964): 132.5lvS (4.14)

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71 In current model, upper wall heat flux is described as containing only convective heat transfer; the vapor phase temperature can be calculated by matching the measured upper wall heat flux. Then the bottom heat flux can be calculated from Equation 4.8 if the film boiling heat flux to the liquid filament f bq is known. The correlation used to evaluate this heat flux is given below. 4.2.4.2 Film boiling correlation Film boiling, in which a thin vapor film blankets the heating surface due to the high wall superheat, is often encountered in th e handling of cryogenic fluids. Many studies have been conducted on stable film boiling on external geometries, such as vertical surface, (Bromley 1950; Chang 1959) horiz ontal surface (Bromley 1950; Chang 1959; Berenson 1961), outer surface of horizontal cylinders (Bromley 1950; Breen and Westwater 1962), and spheres (Merte and Clar k 1964; Frederking et al. 1964). However, not enough effort has been paid to film bo iling inside of a horizontal tube, which is common in engineering systems, the known i nvestigations include research work by Chan (1995) and Liao (2005). In both of these two works, it was assumed that the vapor phase flows in a thin channel as shown in Figure 4-20, and a linear temperature profile exists in the vapor layer, then an analytic al solution of the local vapor film thickness and vapor velocity in the vapor channel in the circumferentia l direction were derived, and the local film boiling heat transf er coefficient was obtained as: g fbk h (4.15) here, to differ from the vapor phase that is not inside of the vapor film, subscript g is used to denote the gas in the vapor film.

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72 In Liaos study (2005), the va por flow was simplified to boundary-layer type flow, and by neglecting the vapor thrust pressure and surface tension, the film boiling heat transfer coefficient was given as: 1 4Ra 0.6389 Jagg fbkk h DF (4.16) in which 3RalggggD is the Raleigh number, lgJapgwsCTTh is the Jacob number, and F is a geometry influence factor needs numerical integration. Figure 4-20. Stable film bo iling inside a horizontal tube. As a comparison, in deriving the analyt ical solution for film boiling inside a horizontal tube, Chan (1995) in cluded the vapor thrust eff ect but assumed a constant vapor velocity in the cro ss section of the vapor cha nnel, and obtained a simpler expression for the heat transfer coefficient at the bottom of the tube. In this derivation the interfacial velocity is assumed to be half of the vapor velocity, however, in most of the research works, the interfacial velocity is assumed to equal the liquid phase velocity,

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73 which is often much smaller than the vapor velocity. Therefore, in current study, the interfacial velocity is assumed to be zero. The vapor film thickness and the vapor velocity are then calculated based on this modified boundary condition. For stable film boiling of liquid nitrogen inside a horizontal tube, Fi gure 4-21 shows typical results for different liquid level hL. One can find that approximately in the firs t half of the vapor channel, the vapor film thickness remains almost a constant value, and the vapor velocity increases linearly; while in the second half of the channel, th e vapor film thickness increases very fast accompanied with a fast decrease of the vapor velocity, and the vapor velocity drops to zero at the top of the liquid filament. 0.00.10.20.30.40.5 0.0 0.5 1.0 1.5 2.0 0 2 4 6 8 Tw=2000C Fluid: LN2 Vapor Velocity ug (m/s) Vapor Film Thickness (mm)Location Along Vapor Channel, hL/R=1.0 hL/R=0.75 ug ug Figure 4-21. Vapor film thickness and va por velocity along the vapor channel. Calculation of the local vapor film thic kness and vapor velocity requires numerical solution as finite difference method (Chan 1995) however, a simple expression exists for the vapor film thickness at the bottom of the tube as:

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74 1 2 4 01.189gw lglgkT R gh (4.17) in which wT is the wall superheat, and lgh is defined as the latent heat plus vapor sensible heat content: 0.5lglgpgwhhCT (4.18) It should be noted that in the above equati ons, all the thermodynamic properties of the gas in the vapor film are evaluated at an average film temperature given by: 0.5() g wsatTTT (4.19) Because the vapor film remains essentially constant over a relatively long distance from the bottom of the tube as shown in Fi gure 4-21, the heat transfer to the liquid filament at the bottom of th e tube can be evaluated by: 0 w fbgT qk (4.20) 4.2.4.3 Model evaluation The phenomenological model described a bove permits calculation of bottom wall heat flux with known upper wall heat flux. Figur e 4-22 compares the experimental results with the model prediction of the bottom wall heat fluxes at the outlet section under different mass fluxes. It is seen that the model over predicts the heat fluxes in the beginning stage of chilldown, after that the model is reasonably accurate. The flow visualization shows that in the beginning stage the liquid droplets bounce back and forth on the wall rather than settle down on the bottom wall, therefore th e above film boiling model with a stable liquid filament in the wall vicinity is not adequate for the beginni ng period. Because of

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75 the much higher heat flux for a stable film boiling condition than that of bouncing liquid droplets, the current model over-predicts th e heat transfer in the beginning stage. 200220240260280300 2000 4000 6000 8000 10000 12000 14000 Experimental Model 3.6kg/m2s 7.2kg/m2s 10.8kg/m2s Heat Flux (W/m2)Wall Temperature (K) Figure 4-22. Comparison between experiment al and model results of the bottom wall heat fluxes at outlet section. 4.3 Rewetting Experiment Rewetting is the establishment of liqui d-wall contact and characterizes the transition from film boiling to transition boiling. Earl y researchers tend to believe that the liquid will contact the hot surface at a fixe d temperature usually called Leidenfrost temperature, however, more and more results show that there is no unique temperature at which a hot surface will rewet, instead, the rewetting temperature is a function of many thermal, hydrodynamic and geometric paramete rs pertinent to th e system (Chan and Banerjee 1981a, Abdul-Razzak et al. 1992, Barn ea et al. 1994). In this section, the rewetting phenomenon is experimentally inve stigated by pre-cooling and then quenching the test section with different mass fluxes.

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76 4.3.1 Types of Rewetting Rewetting phenomenon is rather complex and involves the interaction among the liquid phase, vapor phase, and th e solid wall. Iloeje et al. (1975) was the first one who successfully isolated three di fferent controlling mechanisms for forced convective rewet. These are: impulse cooling collapse, axial conduction controlled rewet and dispersed flow rewet. The impulse cooling collapse was proposed as the controllin g mechanism for the IAFB region, in which the liquid-vapor interface is wavy and fluctuates about a mean position. If the wall temperature or heat fl ux is lowered, the vapor thickness decreases and eventually the liquid may contact the wall. Depending on the temperature and the wall heat flux, permanent liquid-wall contact is either maintained or the liquid will be pushed away from the surface with the forma tion of vapor. In the second case, each liquid-wall contact is equivalent to an impul sive cooling of the surface. For a chilldown process, repeated contacts will lower th e surface temperature enough to permit rewet. Recent experiments (Cokmez-Tuzla et al. 2000 ) employed a special rapid-response probe validate this impulsive liquid-wa ll contact in film boiling re gion. Some researchers (Chan and Banerjee 1981b, Adham-Khodaparast et al. 1995) used the Kelvin-Helmhlotz instability to explain the growth of the interfacial wave. Based on this controlling mechanism, Kalinin et al. (1969) proposed that the wall temperature corresponding to the minimum heat flux can be obtained from their empirical correlation: 0.25 min1.650.162.4sl critl wkc TT TTkc (4.21) in which, critT is the thermodynamic critical temperature, subscript l is for liquid and w is

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77 for wall. The hydrodynamic parameter of the flow rate is, however, completely absent in this model. In a system with an already wetted upst ream surface, Simon and Simoneau (1969) suggested that the transition from the film boiling to nucleate boiling is governed by axial conduction. They assumed that the rewet temp erature is a thermodynamic property of the fluid, and is determined by using the Van de r Waals equation of state (Spiegler et al. 1963): 0.130.84rw critcritT p Tp (4.22) here, rwT denotes the rewet temperature, critp is the critical pressure. In dispersed flow regime, Iloeje et al. (1975) postulated that rewetting was controlled by the limiting effects of two pro cesses, namely, heat transfer to the vapor assuming no effect of the existence of droplets, and heat transfer due to the presence of the droplets, which may or may not be touc hing the surface. The su m of the two heat transfer components gives the total heat flux and indicates the location of the minimum heat flux and minT. 4.3.2 Rewetting Temperature and Rewetting Velocity The local wall temperature at the onse t of rewetting is very important for theoretical modeling and engine ering applications. Many defin itions have been used in the literature, such as rewetting temperat ure, apparent quenching or rewetting temperature, minimum film boiling temperat ure, Leidenfrost temperature, etc. In different investigations, usually one of the above definitions was selected according to

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78 the experimental configuration. This pa rtly reflects the limited understanding on rewetting phenomenon. Figure 4-23 shows a typical chilld own boiling curve and the corresponding transient wall temperature. Since the liquidwall contact indicates the end of the film boiling, the rewetting temperature should be defined as the minimum film boiling temperature minT, which corresponds with the minimum film boiling heat flux, as shown in Figure 4-23. Figure 4-23. A typical ch illdown boiling curve and the corresponding transient wall temperature. However, the apparent rewetting temperatur e, which is the intersection of tangent lines to the knee of the meas ured temperature-time trajector ies, was also used by many researchers (Chen et al. 1979, Abdul-Razzak et al. 1992, Barnea et al. 1994, Westbye et al. 1995). Other definitions of rewetting temp erature include the temperature at the knee of the temperature-time trajectory (Iloeje et al. 1982) and complete rewetting

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79 temperature defined at the CHF point (Adha m-Khodaparast et al 1995). The rewetting temperatures from those above definitions are generally not equal. In current test, it is shown that the wall temperature has an abrupt decrease at the rewetting point; therefore the temperature at the knee of the temperatur e-time trajectory is used to define the rewetting temperature. Typical temperature profiles of a rewetting test are shown in Figure 4-24. The test section is pre-cooled to certain temper ature and then quenched by injecting liquid nitrogen from the bellows with constant mass flux. The wall temperatures decrease very slowly at the beginning and then drop abruptly at the rewetting point. 50060070080090010001100 120 150 180 210 240 TC1 TC2 TC3 TC4 TC5 TC6Temperature (K)Time (s) Mass flux=3.6kg/m2s Figure 4-24. Typical temperature profiles during a rewetting test. The axial variation of the averaged rewetti ng temperature at the bottom of the tube under different mass fluxes is illustrated in Figure 4-25. The rewetting temperature increases with increasing mass flux; this has also been reported in high mass flux experiments (Chan and Banerjee 1981a, Abdul -Razzak et al. 1992, Westbye et al. 1995, Xu 1998). It was proposed by Xu (1998) that the vapor film thickness would decrease at

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80 higher mass flux, and therefore lead to rewett ing at a higher wall temperature. No clear trend of axial variation is shown in Figure 4-25. 6080100120140160180 160 170 180 190 200 210 Rewetting Temperature (K)Axial Location (mm) 3.6kg/m2s 7.2kg/m2s 10.8kg/m2s Figure 4-25. Axial variation of the averag ed rewetting temperature at different mass fluxes. Although it is quite complicated and diffi cult to fully analyze the rewetting phenomenon, many researchers have tried to pr edict rewetting temperature by theoretical models and experimental correlations. Bere nson (1961) extended Zuber's vapor escape mode1 to analyze the minimum heat flux c ondition in steady film boiling over a flat horizontal surface. The heat transfer through th e vapor film was described as a pure heat conduction problem, and the following correlati on was obtained to predict the minimum film boiling temperature for pool boiling: 211 323 min0.127lv vlvv vlvlvlvg h T kg (4.23) The minimum film boiling temperature ca lculated from Equation 4.23 is 142.3K. The impulse cooling collapse model (Kalinin et al. 1969), which is given in Equation 4.21, considers the properties of the so lid wall and gives a minimum film boiling

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81 temperature of 189.97K, which is close to th e experimental values. Predicted rewetting temperature from the axial conduction model is only 106.4K, which is much less than the present data. Under current experimental cond ition, long liquid filaments are observed to flow at the tube bottom, the impulse cooli ng collapse model was proposed for IAFB and therefore gives a better result over the axial conduction model. The flow rate effect has not been show n in the above correlations; however, as mentioned before all the previous experime nts indicated the rewetting temperature also depends on hydrodynamic parameters. Iloeje et al. (1975) conducted vertical flow boiling experiments with water in an inconel tube and observed minimum film boiling superheats asymptotically approaching certain values. Th ey suggested that this asymptote would be close or equal to a pool boiling value and correlated their data in the following empirical form: min,11nm mBerTTAxBG (4.24) where mBerT is Berensons minimum film bo iling temperature for pool boiling (Equation 4.23), x is quality, G is mass flux, A B m and n are constants. Xu (1998) used R113 to quench a hot surface and suggested a similar form as Equation 4.24 to correlate his experimental data as: min,1m mBerTTBG (4.25) A correlation similar in the form of Equation 4.25 is used in cu rrent study, with the same exponent as Iloeje et al. ( 1975), the best fit is obtained as: 0.49 min,10.242mBerTTG (4.26)

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82 The prediction results from all the above corr elations and the experimental data are compared in Figure 4-26. 34567891011 100 120 140 160 180 200 Foam limit (Spiegler) Minimum film boiling temperature (Berenson) Impulse cooling collapse (Kalinin) Experimental FitRewetting Temperature (K)Mass Flux (kg/m2s) Figure 4-26. Comparison of rewetting temperatures between experiments and different correlations. The propagation speed of the QF or the rewe tting velocity can be determined as the axial distance between the thermocouple lo cations divided by time difference of the rewetting time (Chan and Banerjee 1981a). Figure 4-27 shows the average rewetting velocity under different mass fluxes. 34567891011 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Rewetting Inlet flow velocityRewetting Velocity (cm/s)Inlet Mass Flux (kg/m2s) Figure 4-27. Average rewetting velo city under different mass fluxes.

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83 The rewetting velocity is larger than the inlet velocity and increases with increasing mass flux. The difference between the rewetting velocity and the inlet velocity is larger under higher mass flux. 4.3.3 Visualization Study According to impulse cooling collapse model, the liquid-wall contact is not the sufficient condition that leads to the surface rewet. For rewet phenomenon to occur, the surface temperature must be lower enough to allow the liquid-wall contact to spread. Chan and Banerjee (1981c) also suggested that the rewetting was due to not only the breakup of the liquid-vapor interface but al so the growth and sp read of the rewet spots. The visualized images for the rewet process, which are s hown in Figure 4-28 in time sequence, tend to support this hypothesis. The flow direc tion is from left to right with a mass flux of 3.62kg/ms. Figure 4-28. Visualization re sult of the rewet process.

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84 Figure 4-28. Continued. The rewet spots, which are foam-like c hunks consists by many small bubbles, first appear at some local points. After generation, they grow and spread in both direction while being drifted downstream at the same tim e. Liquid droplets or liquid filaments are observed to coalesce with the rewet spots. The tube wall is then covered by a foamy mixture of bubbles with wavy interface, wh ich is known as quenching front. The nucleate boiling beneath the quenching front is hi ghly transient, as the wall temperature decreasing rapidly the liquid nitrogen begins to contact the wall and many nucleation sites are suppresses.

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85 CHAPTER 5 CRYOGENIC TWO-PHASE CHILLDOWN UNDER MICROGRAVITY CONDITION Efficient and safe utilization of cryo genic fluids in a spacecraft during space missions demands thorough study of cryogenic tw o-phase flow and heat transfer under microgravity condition. However, researches on this field are very limited due to the experimental difficulties. In present study, experimental study of cryogenic chilldown under microgravity condition is conducted. The investigation focuses on the film boiling region. 5.1 Introduction 5.1.1 Film Boiling under Microgravity Among the various film boiling correlations for pool boiling, it is very interesting to note that the surface heat flux or heat tran sfer coefficient is usually correlated with 14g, in which g is the gravitational acceleration. Fo r example, the highly cited Bromleys correlation (Bromley 1950) for horizontal tubes is: 14 30.62vlvvlv fb vwkhg h DT (5.1) For horizontal surface, the mostly us ed correlation gives (Berenson 1961): 14 12 30.425vlvvlvlv fb vwkhgg h T (5.2) in which the 12 lvg term is actually a geometrical factor as pointed out by Berenson (1961), and has the dimension of [-1m], thus in Equation 5.2 the film boiling

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86 heat transfer coefficient is still proportional to 14g. Liao (2005) and Chan (1995) also got the same relation, as shown in Chapter 4. Th e list also includes th e correlations given by Noyes (1963), Chang and Snyder (1960), etc. The only exception, to the authors knowledge, is the correlation proposed by Cha ng (1959), in which the film boiling heat transfer coefficient is sugg ested to be proportional to 13g. It is also noted that some of the above correlations were derived based on quite different approaches, such as analytical so lution of flow in vapor film channel (Chan 1995; Liao 2005) and vapor escape model based on Taylor -Helmholtz instability (Berenson 1961). Therefore, it is natural for one to think that the heat transfer characteristic in film boiling is related to 14g and extend the above correlations to different g-level. For example, the Brom leys correlation can be modified as: 14 30.62vlvvlv fb vwkhg a h DTg (5.3) in which, a is the local acceleration. However, experiments by Merte and Clark ( 1964) showed that the heat flux and the Nusselt number were proportional to 13ag in the examined gravity range of 0.011ag; on the other hand, the maximum and minimum heat flux were found to depend on gravity according to 14ag. Unlike most the other microgravity pool boiling researches, which were perfor med under steady or quasi-stea dy conditions with constant wall heat flux or constant wall temperature, the experiments by Me rte and Clark (1964) were highly transient. In their experiments, a small ball was quenched inside the saturated liquid nitrogen under different g-level, the te mperature of the ball keeps decreasing, to

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87 this extent, their experiment al condition is close to cryoge nic chilldown process. The drop tower used in their experiments can pr ovide a free fall time of about 1.4 second. For flow boiling experiments, the flow w ill play a role in both bulk convection and vapor removal mechanism; therefore the heat transfer coefficient will not have a simple relation with local acceleration as that in pool boiling. Chilldown investigations in reduced gravit y is very limited, all of the previous experiments in open literature have been re viewed in Chapter 2. The basic findings for flow film boiling are summa rized in Table 5-1. Table 5-1. Basic findings of flow film boiling in previous chilldown experiments. Adham-Khodaparast et al. (1995) Westbye et al. (1995) Antar and Collins (1997) Experimental apparatus horizontal surface horizontal tube vertical tube Working fluid R113 R113 LN2 Flow pattern NA inverted annular flow liquid filament annular flow Heat transfer rate under microgravity lower lower lower Rewetting temperature under microgravity lower lower lower Rewetting speed under microgravity NA higher lower All previous researches reported lower he at transfer rate in reduced gravity, Adham-Khodaparast et al. (1995) attributed this reduction to the thickening of the vapor film. 5.1.2 Current Experimental Condition Since the microgravity duration is relativel y short, the experiment is designed to drop the apparatus at different wall temperat ures with different mass fluxes. The wall temperature is classified as three groups that are high wall te mperature (about 270K),

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88 medium wall temperature (about 240K) and low wall temperature (about 210K). Different motors are used to ge nerate different mass fluxes. The gravity level and the deceleration impact have been measured by an accelerometer (Omega ACC104A) mounted on an aluminum piece that attached to the drag shield. The accelerometer has a calibra tion coefficient of 10mV/g and needs an excitation current range of 2-20mA. A current source (Ome ga ACC-PS1) powered by 9V batteries is used to provide the constant ex citation current of 2mA. The signal is send out from the current source through BNC coax ial connector to a screw terminal (Measurement Computing SCB-50). A data acquisition board (Measurement Computing PCI-DAS 6036) plugged into the PCI slot is us ed for data acquisition and is connected to the screw terminal. The method of measuring gravity level a nd the deceleration le vel follows Snyders experiments (Snyder 1993). By taking certain time of data at each drop before the release, an average voltage level at 1g is obtained. Using this information, combined with the calibration constant of the accelerometer, the following equation gives the g-level: 11readgVV a C (5.4) where readV is the voltage read from the accelerometer, 1 g V is the averaged voltage at 1-g, and C is the calibration constant of the accelerome ter. The 1 is added to account for the fact that the reference ac celeration level is 1g. The drag shield is dropped without lo ading the experimental apparatus. The deceleration level is averaged about 7g with a maximum of about 18g. The current accelerometer is designed for high g-level m easurement and the output uncertainty is

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89 larger than the microgravity level. As an accelerometer capable of measuring 10-5g and can still survive high deceleration is not avai lable, the performance of the low-gravity level is not measured directly. 5.2 Flow Regime Visualization und er Microgravity Condition The flow regimes before and during drop ar e compared in Figure 5-1. The images on the left are taken before drop, while the microgravity images are on the right. In the experimental wall temperature range, the two-phase flow is in the DFFB state and the liquid phase is either in the form of small droplets or connected as long filaments before drop. The characteristics of the 1-g flow regime are summarized in Chapter 4. Different flow behaviors have been record ed during the microgravity period. If the liquid phase before drop is dispersed droplets, these droplets will enter the central region still as droplets during the drop period (F igure 5-1B). For long liquid filaments, sometimes the filaments are lifted up and still maintain original shape during the drop (Figure 5-1D); in some other cases, the liqui d filaments are broken and dispersed into the central region (Figure 5-1F) or has a liquid-vapor core in th e center and smaller chunks at both top and bottom (Figure 5-1H). A B Figure 5-1. Two-phase flow images under bot h 1-g and microgravity conditions. A) 1-g case 1. B) Microgravity case 1. C) 1-g case 2. D) Microgravity case 2. E) 1g case 3. F) Microgravity case 3. G) 1g case 4. H) Microgravity case 4.

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90 C D E F G H Figure 5-1. Continued. 5.3 Heat Transfer Study Due to the thickening of the vapor film, the heat transfer in film boiling is generally lower under microgravity condition. However, this effect is expected to be relatively less important with increasing inertial term. In this section, the heat transfer in film boiling region under microgravity is to be discussed.

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91 5.3.1 Wall Temperature Profiles To get more data points during the microgr avity period, the wall temperatures are measured only at one cross-section. Figure 5-2 gives the typical temperature profiles with different mass fluxes. 0255075100125150 245 250 255 260 265 270 275 280 Mass Flux: 3.6kg/m2s Temperature(K)Time(s) TC14 TC15 TC16A 050100150200250300 200 210 220 230 240 250 260 270 280 290 Mass Flux: 7.2kg/m2s TC14 TC15 TC16 Temperature(K)Time(s)B Figure 5-2. Temperature prof iles with different mass fluxes in microgravity test. A) Mass flux of 3.6 kg/m2s. B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8 kg/m2s.

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92 020406080100120140 190 200 210 220 230 240 250 260 270 Mass Flux: 10.8kg/m2s Temperature(K) Time(s) TC14 TC15 TC16C Figure 5-2. Continued. The circled temperatures in Figure 5-2 a pproximately indicate the time period of one drop, which includes release of the drag shield, microgravity time, impact on the air bag, and deceleration period. To exam the detail of the wall temperat ure response to sudden removal of the gravity force, the temperature profiles are zoomed in. Figure 5-3 il lustrates the typical results. It is observed that the temperature decreasing rate at the bottom wall is generally slower during the microgravity period, because the removal of the gravitational force will thicken the vapor film and re duce the film boiling heat flux. Since the top wall transfers heat mainly by convection, the gravity field is expected to have less effect on the heat transfer at the top wall. However, as shown in Figure 5-1, it is possible for the liquid phase to contact the top wall during the micr ogravity period and results in higher heat removal rate. For current transient experiment al condition, the best way to represent the data is to calculate the averaged heat flux wh ich is to be given in the following section.

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93 146148150152 246 248 250 252 254 -g Impact Temperature (K)Time (s) TC14 TC15 TC16 1-g Mass Flux:3.6kg/m2sA 236237238239240 208 212 216 220 TC14 TC15 TC16Temperature (K) Time(s) -g Impact 1-g Mass Flux: 7.2kg/m2sB 75767778798081828384 204 208 212 216 220 Mass Flux: 10.8kg/m2s TC14 TC15 TC16Temperature (K)Time (s)1-g -g Impact C Figure 5-3. Wall temperature response to microgravity. A) Mass flux of 3.6 kg/m2s. B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8 kg/m2s.

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94 5.3.2 Wall Heat Flux The gravity effect is shown in Figure 5-4, in which the ratio of bottom heat flux before drop and during drop is pl otted for different flow rates. The heat flux at the bottom of the tube decreases under microgravity c ondition and the ratio varies from a minimum of about 0.66 to about 0.90. The result does not show a strong dependence on wall temperature and inlet flow rate. Two runs of the quenching test performed by Xu (1998) reported similar ratio of 0.7 and 0.8, however, in Westbye et al.'s ( 1995) work, this ratio was found to be much less and ranged from 0.15 to 0.6. 200210220230240250260270280 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Experimental Model prediction 3.6kg/m2s 3.6kg/m2s 7.2kg/m2s 7.2kg/m2s 10.8kg/m2s 10.8kg/m2sHeat Transfer Ratio q"g/q"1g Wall Temperature (K) Figure 5-4. Ratio of heat flux under microgravity to 1-g condition with different flow rates and comparison with model prediction. The bottom wall is subjected to film boiling of the liquid filaments and the convection to the super heated vapor phase. For the film boiling part, the heat flux and the heat transfer coefficient are proportional to 13ag as suggested by Merte and Clark (1964). Assuming that the convection is not affected by the microgravity condition, the resulted heat flux ratio is shown in the dash line in Figure 5-4; the gravity level in this

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95 calculation is 10-4g. The calculation results are much scattered and significantly less than the experimental values. This suggests that under microgravity condi tion, the effect of convection part may raise the heat flux, and th erefore the total effect of the microgravity is less prominent than that in the pool boiling experiments.

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96 CHAPTER 6 MODELING CRYOGENIC CHILLDOWN Numerical modeling is a power ful tool to help reveal the physics behind the experimental phenomenon, and to make predic tion when systematic experiments are not attainable. For many complicated phenomena such as the chilldown process, on which the experimental investiga tions are relatively limited, modeling has become an indispensable part to adva nce our understanding. In this chapter, a so-calle d two-fluid model is de veloped and applied to the cryogenic chilldown process. The model focu ses on predicting chilldown heat and mass transfer under the microgravity condition, for which the experiments are difficult and costly; this model is also applicable to the vertical tube chilldown process. 6.1 Introduction 6.1.1 Flow Regimes and Transition Criteria From experimental investigations, we know that several flow regimes exist in quenching or chilldown proce ss. Since different flow regimes are associated with different heat transfer mechanisms, therefor e the first step in modeling the chilldown process should be a correct description of the flow regimes and the corresponding transition criteria. Particularly, the flow behavior after the onset of the CHF or the socalled Post-CHF flow shows ma ny varieties and is more ch allenging to model. As a comparison, the flow before the CHF point is in the nucleate boiling state and can generally be well predicted by nucleate boili ng correlations or a homogeneous model.

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97 For a steady state boiling system or a c onstant wall heat flux experiment in a vertical tube, it is generally accepted that the sequence of the Post-CHF flow regimes mainly depends on the thermodynamic quality at the CHF location, and can be classified into two types (Chen et al. 1979; Nelson and Unal 1992; Yadigaroglu 1978; Andreani and Yadigaroglu 1996). Figure 61 illustrates the Post-CHF flow regimes. If the CHF occurs at low or negative (subcool ed) flow qualities, the flow re gime is expected to be an inverted annular flow (IAF), followed by a dispersed flow. At high qualities, the CHF occurs due to the liquid film dryout and the fl ow pattern is generally a dispersed flow. A boiling regime map (Collier 1981) is often used to predict the flow regimes under a constant heat flux condition. Nucleate Boiling Transition Boiling Inverted Annular Film Boiling Dispersed Flow Film Boiling CHF LocationA Nucleate Boiling Dispersed Flow Film Boiling Dryout CHF Location B Figure 6-1. Post-CHF flow regimes. A) Low-quality CHF. B) High quality CHF.

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98 The boiling regime map is, however, not appl icable to chilldown experiments. The reason is that neither the wa ll heat flux nor the CHF location is fixed during chilldown. As shown in previous chapters, the CHF location moves downstream as the tube is chilled down and the wall heat transfer expe riences the film boiling, transition boiling and nucleate boiling sequential stages. Moreover, the detailed structures of the flow regimes are highly dependent on the flow regime from which it originates. In a chilldown process, initially the wall temperature is often several hundred degrees above the Leidenfrost temperature. When the liquid ente rs the hot tube, a vapor film is formed immediately and it separates the liquid from touc hing the wall. In a vertical tube or under microgravity environment, the liquid phase ge nerally flows in the middle of the tube. Therefore, for vertical tube chilldown or mi crogravity chilldown, th e general sequence of the flow regime after the rewett ing point is expected to be IA F, dispersed flow, and single phase vapor flow. The above discussion on flow regimes de scribes a general classification, more detailed flow regimes have been reported from experiments. For example, the IAF was further divided into different flow regime s such as smooth IAF, rough-wavy IAF, and agitated IAF as summarized by Is hii and Dejarlais (1986, 1987). The flow regime transition criterion is another important fact or required for a successful modeling of the twophase flow system. For Post-CHF flows, the void fraction or quality x is usually used as the transition crite rion. Obot and Ishii (1988) developed a set of flow regime transition criteria in terms of the capillary number and the downstream distance from the CHF location (Table 6-1), and th eir criteria were

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99 implemented into a nuclear reactor safety code. Here, Z is the downstream distance from the CHF location, D is the tube diameter, and Ca is the capillary number. Table 6-1. Post-CHF flow regime transition criteria. Regime Ishiis Correlation Void Frraction Smooth IAF 1/2/60CaZD 0.050.3 Rough-Wavy IAF 1/2/295Ca ZD 0.30.4 Agitated IAF 1/2/595CaZD 0.40.75 Dispersed IAF (post-agitated IAF) 0.750.98 Highly dispersed IAF 0.98 If only IAF and dispersed flow are modele d in the Post-CHF region as shown in Figure 6-1A, then the only transition encount ered is form IAF to dispersed flow. A widely accepted criterion given by Groeneveld (1975) suggests that the dispersed flow develops at the void fraction high than 0.8. However, lower values were also used. Hammouda et al. (1997) used 0.5 in their IAFB model. The physics behind this transition is believed to be related to the instabilities that develop at the liquid-vapor interface, which c onsequently lead to necking and detachment of the liquid column (Kawaji and Banerjee 1987). The detached liquid column breaks up further into droplets thro ugh different mechanisms (Andreani and Yadigaroglu 1994). The transition criterion used by Ka waji and Banerjee (1988) is given as: 0.5lj or 10.15ljljZ and 10.6lj Here, l is the volume fraction of the liquid, and j denotes the node point. Analy tis and Yadigaroglu (1987) pr oposed to use the Weber number as the criterion, the Weber number in their study is defined as: 2We2vvluuR (6.1) where v is vapor density; vu and lu are vapor and liquid phase velocity, respectively; R is tube radius; is vapor film thickness; is the surface tension.

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100 Upstream of the CHF point, the two-phase flow is in the transition or nucleate boiling state. The rewetting temperature is ofte n used as the transiti on criterion to discern Pre-CHF and Post-CHF region. The rewetting temperature is affected by flow rate, wall surface condition, axial temperature gradient and many other factors, and therefore is usually extracted from the experimental results. 6.1.2 Different Modeling Methods and Current Approach Different methods have been used in two-phase flow modeling, ranging from the homogenous model (Cross et al. 2002) to the two-fluid model (Ishii 1975; Ardron 1980; Ishii and Mishima 1984), then to the thr ee fluid model (Alipchenkov et al. 2004), in which the entrained phase is described by an additional set of cons ervation equations, and further to more detailed models that inco rporate both microand macro-scale models (Ben David et al. 2001 a, b). A review of diff erent levels in chilldown models is given in Chapter 2. During a chilldown process, the velocity difference between the two phases are considerably large, moreover, downstream of the rewetting point, the flow is essentially in thermodynamic non-equilibrium. In the twofluid model, each phase is described with a set of conservation equations; therefore this model is more applicable to discern the differences between phases, and is adopted in the current inves tigation. The general conservation equations are given in Equations 2.1-2.4. In this study, four distinct flow regions, namely, fully vapor region, DFFB region, IAFB region, and nucleate boiling region, are modeled. The two-fluid model is used to describe the DFFB and IAFB region, while fully vapor region a nd nucleate boiling region are treated as single phases.

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101 6.2 Inverted Annular Film Boiling Model In chilldown experiments, IAFB is expect ed to immediately follow the QF and then change to DFFB downstream at a high void fr action. A two-fluid IAFB model is to be discussed in this section; the model will be implanted into cryogenic chilldown model later. 6.2.1 Introduction IAFB is characterized by high surface te mperatures and consists of a continuous liquid core at the center of the channel, surrounded by a vapor blanket covering the heated surface. The study of the IAFB is of considerable practical interest in many applications, such as cryogenic system, nuclear reactor safety, steam generators, evaporators, and metallurgical pr ocessing (Hammouda et al. 1997). The two-phase flow and heat transfer phe nomena in IAFB are rather complicated. For example, in IAFB, for highly subcooled liquid and high flooding rates, momentary local transition to nucleate boili ng near the QF is also thought to be possible (Edelman et al. 1983). Incorporation of such detailed eff ects in a mechanistic IAFB model would be an almost impossible task (Analytis and Yadigaroglu 1987). Theref ore, the two-fluid model has been used as a balance between simplicity and inclusion of important phenomena. The conservation equations of all the tw o-fluid IAFB models come from the fundamental work of Ishii and other re searchers (Ishii 1975; Ardron 1980; Ishii and Mishima 1984). The steady state form of tw o-fluid IAFB model was suggested by Analytis and Yadigaroglu ( 1987) and by Hammouda et al. (1997), while the transient form was developed by Kawaji and Banerj ee (1987, 1988). Having almost the same

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102 conservation equations, these models differ from one another in how the constitutive relations are formed. 6.2.2 Model Description 6.2.2.1 Assumptions and conservation equations Conservation equations for the IAFB m odel are derived based on the assumptions listed below: 1. Liquid flows in the center of the flow channe l and is separated from the heated wall by a vapor layer. 2. The vapor layer thickness is uni form around the tube periphery. 3. The vapor layer contains no entrained liquid. 4. The liquid core contai ns no vapor bubbles. 5. The pressure is uniform in the radial direction. 6. The two phases are in thermodynamic non-e quilibrium, and the vapor phase is treated as an ideal gas. 7. The interface is smooth and the interfacial velocity iu is equal to the liquid phase velocity lu. 8. The interface is saturated. 9. The vapor flow changes from laminar to turbulent at a vapor Reynolds number, Rev, large than 100. The above turbulent transition criterion was suggested by Hsu and Westwater (1959). Later, Kao et al. (1972) argued that there was transiti on to turbulence in the vapor film almost immediately downstr eam from the origin of the film boiling region. However, current study shows that the vapor Reynolds number increases very fast in the film boiling region, therefore, use either of the above transition criteria will have an insignificant difference. In this study the first transition criterion is used.

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103 For a vertical tube, the transient one-dim ensional two-fluid equations for the IAFB region are given as below: Continuity equations: i l llP um tzA (6.2) i l vvP um tzA (6.3) Momentum equations: lii ii llll lluuP P dP uuugm tzdzAA (6.4) vii iiwvw vl vvuuP PP dP uuugm tzdzAAA (6.5) Enthalpy energy equations: lsli lhi l llhhP qP huhm tzAA (6.6) vsvi vi l vvhhP qP huhm tzAA (6.7) State equation of the vapor phase: v g vP RT (6.8) In the above equations, subscript l is for liquid phase, v is for vapor phase, w is for wall, s is for saturation, and i denotes the liquid-vapor interface; is void fraction, while 1l is the liquid volume fraction; lm denotes the vaporization mass flux at the interface; lhq and vq are the heat fluxes used to heat up the liquid and vapor, respectively;

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104 iP and wP are interfacial and wall perimeter, respectively; A is the cross section area of the flow channel; is the shear stress; g is the gravitational acceleration constant and g R is the gas constant. For the body force in the momentum equations, plus sign is for downward flow, and minus sign is for upward flow. The above equations are derived for subc ooled flow film boiling case, which is more general. The liquid heating term, lhq is used to account for the heat distributed to heat up the subcooled liquid. For saturated flow boiling, 0lhq and the entire liquid core is at saturation temperature, theref ore the enthalpy of th e liquid phase is only depends on the local pressure, which is not unknown after solving the momentum equation, thus Equation 6.6 need not to be solved. As stated in assumption 6, the interfacial velocity is equal to the liquid phase velocity; therefore the third term in th e RHS of Equation 6.4 will disappear. The momentum equations for saturated IAFB are written as: ii lll llP dP uuug tzdzA (6.9) vli iiwvw vl vvuuP PP dP uuugm tzdzAAA (6.10) 6.2.2.2 Heat transfer in inverted annular film boiling Proper selection of the constitutive relations to close the above equations requires clear understanding of the physical mechanisms in IAFB region. Therefore, before given the constitutive relations, the heat transfer mechanism is to be discussed here.

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105 A typical flow section in IAFB is sketch ed in Figure 6-2. The liquid core is separated from the hot wall with a vapor film of thickness in a hot tube with radius of R From previous assumption, it is readily to get: 1lR (6.11) The interfacial perimeter and inside wall perimeter are then given as: 2iPR (6.12) 2wPR (6.13) The heat transfer in IAFB is proposed as a three-step process: heat transfer from wall to vapor, wvq ; from vapor to liquid, vlq ; and from the interface to liquid core, lhq which is used to heat the subcooled liquid and vanishes for satura ted boiling. Radiation heat transfer from wall to the liquid, rq is also considered. From energy balance, the total heat flux received by the liquid column is: lvlrqqq (6.14) while the energy balance for the vapor phase gives: ivwvwvliPqqPqP (6.15) The interfacial and wall perime ter appear in the above equa tion due to the difference in heat transfer area. The total he at flux to the liquid phase is us ed to evaporate the liquid at interface as well as heat up the liquid core (f or subcooled flow boiling only). Therefore: evllhvlrlhqqqqqq (6.16) For saturated flow boiling, the independent variables in the above analysis are wvq vlq and rq The vapor phase flows between the a nnulus of the wall and the liquid core.

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106 Kays (1993) tabulated the Nusselt number for annulus flow. However, the Nusselt number depends on the ratio of the inner a nd outer radius, which is changing in IAFB region, as shown in Figure 6-2. Therefore, th e vapor flow is treated as flow between two parallel plates for R while Colburn equation (Incr opera and Dewitt 2002) is used for ~ R Figure 6-2. Heat transfer mechanisms in IAFB. Considering the vapor flow as flow betw een two parallel plates and liquid at saturation temperature, the wall to vapor and vapor to liquid heat fl uxes can be given as (Kays 1993): w *2Nu 21-v wvwvvsk qTTTT (6.17) i *2Nu 21-v vlvswvk qTTTT (6.18)

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107 where is the influence coefficient. Kays (1993) gave that for laminar flow Nu=5.385 and *0.346; for turbulent flow with Re10000 Nu=27.8 and *0.220 (for Pr0.7 ). The Nuseelt number Nu and can be interpolate between the laminar values and turbulent values for R For ~ R the Colburn equation (Incrop era and Dewitt 2002) gives: 0.80.330.023RePr 2v wvwvwvk qTT (6.19) 0.80.330.023RePr 2v vlivvlk qTT (6.20) while the Reynolds number is defined as: Re2wvvvu (6.21) Re2ivvlvuu (6.22) in which, v is the vapor viscosity. Assume that the vapor film is transparen t and the wall is gray, the radiation heat flux to the liquid core is writt en as (Hammouda et al. 1997): 4411 1Bws r w llTT q (6.23) where 8245.6710WmKB is the Stefan-Boltzman constant; w and l are emissivity of the wall and the liquid, respectively. 6.2.2.3 Constitutive relations For saturated flow boiling, constitutive relations for lm vq ,i wv should be specified to close the model equations. Di fferent constitutive relations, which are

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108 generally come from single-phase or adiabatic annular two-pha se flow experiments, have been proposed in the literature In present approach, attention has been paid to provide the constitutive relations in the same form at similar boundary conditions. For example, the wall shear stress and inte rfacial shear stress are give n in the same form. The constitutive relations will be summarized below. Vapor generation term. In the model equations, the vapor generation term, lm has the unit of [2kg/ms]. It denotes the vapor genera tion rate per unit area at the interface. Given the latent heat for phase change, lvh, the vapor generation term is expressed as: levlvmqh (6.24) where the evaporation heat flux evq is given in Equation 6.16. Vapor heating term. As described previously, vapor heating term can be calculated from Equation 6.15. Shear stress terms. For turbulent flow in the vapor film, correlations for wall shear stress and interfacial shear stress ar e given by (Kawaji and Banerjee 1988): 20.5wvwvv f u (6.25) 20.5iivvl f uu (6.26) where w f and i f are friction factor, and given by: 0.250.085Rewwf (6.27) 0.250.085Reiif (6.28) in which Rew and Rei are defined in Equation 6.21 a nd Equation 6.22, respectively.

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109 6.2.3 Boundary Condition and Solution Procedure For the transient form of th e IAFB model, a semi-implicit, finite-difference scheme is adopted, and a Second Order Upwind (SOU) scheme is used for convection term. IAFB model can also be applied to steady state problem as in a vertical channel heated with constant heat flux, and the insi de two-phase flow is in steady film boiling state with low to moderate void fraction. This is a common process in many industrial systems. On the other hand, the solving pro cedure and results of the steady IAFB model are beneficial to adopt its transient form in chilldown model as well as assess the validity of the model. In this section, the bounda ry condition and solution procedure for the steady IAFB model will be given. 6.2.3.1 Boundary condition The steady IAFB model is appl ied to a stainless steel vertical tube heated with constant heat flux wq The tube has 0.635cm OD, 0.432cm ID, and 70 cm length. Small initial void fraction and slip velocity are assi gned at the inlet (Xu et al. 2006). An initial void fraction1 of 0.01 and a slip velocity 2 at the order of 10-3 are used in the computation. The two-phase nitrogen flow is in jected from top or bottom of the tube with a volume flow rate of V. The pressure at the inlet is given and both phases are in saturated temperature s T at the inlet. The boundary conditi ons of the two-phase flow at the tube inlet are summarized as: 01 0 ,0 ,0,02 ,0 specified specifiedinin l vl vvsPPP uVAV uu hh (6.29)

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110 For the tube wall temperature calculation, adiabatic boundary condition is set at the inlet and outlet of the tube wall; the outer surface of the tube is subjected to constant heat flux, while the inner surface lose s heat to the two-phase flow. 6.2.3.2 Numerical method and solution procedure Different numerical methods have been used to solve the two-fluid governing equations in the literature SIMPLE method was used by I ssa and Kempf (2003) and by Liao (2005), while Runge-Kutta (Hammouda et al. 1997) and Euler method (Yang and Zhang 2005; Xu et al. 2006), which are much easier, were also often used. In current study the Euler method is used. For saturated flow boiling, the dependent variables are P, lu, vu, vh. The continuity and momentum equa tions can be expressed as: 2 1 2 2 3 420 1021 00 001vvvv v llll l vvv lllB Pz uu B uz uu B uz u B z u (6.30) Here, 2 1 2 3 41lvli iiwvwv vv ii l liv v limuuP PP Bug AAAz P Bg A mP Bu Az mP B A (6.31) Introduce the vapor momentum equation into vapor enthalpy equation, one can get:

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111 vilvsvilv v vvqPAmhhPAmh h zu (6.32) To obtain the wall temperature, the 1-D heat conduction equation is used, and gives: 2 20wwwvr wwTqqq zk (6.33) where, wk is the thermal conduc tivity of the wall and w is the wall thickness. The discretized equation is solved by Tri-diagonal Matrix Algorithm (TDMA) method. The solution procedure is illustrated in Figure 6-3. Figure 6-3. Solution procedure of steady IAFB two-fluid model.

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112 After setting the boundary conditions at th e inlet, initial gu esses of the vapor temperature and wall temperature are given. Th e computation first solves the continuity and momentum equations and then the vapor enthalpy equation. After that the wall temperature is updated based on the heat conduction equation. Next, the vapor temperature is updated from state equation. This process is it erated until the wall temperature converges. 6.2.4 Results and Discussion To validate the IAFB model, it would be desirable to compare the modeling results with experimental measurements. However, to our knowledge, the av ailable experimental data are either for transient process (Kaw aji et al. 1985; Lee and Kim 1987) or for subcooled flow boiling (Takenaka et al. 1989) As a compromise, part of the model results is compared with a correlation. For IAFB, the only correlation we can find in the literature is given by Carey (1992), in which the heat transf er coefficient is given as: 14 34vlvlvv CHFvwsghk h zzTT (6.34) where, CHFz is the CHF location, and CHFzz denotes the distance from the CHF location. lvh is defined by: 3 8lvlvpvwshhCTT (6.35) The wall heat flux is calculated by: wwsqhTT (6.36)

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113 Apparently, Equation 6.34 comes from the Bromley type correlation (Bromley 1950) for stable pool boiling, and therefore only applicable for two-phase system with very small interfacial shear stress (Carey 1992). The effects of flow direction and flow rate are not correlate d in Equation 6.34. Figure 6-4 compares the wall temperatur es computed by the IAFB model and by Equation 6.34 under three different wall heat fluxes of 3.52kW/m, 5.02kW/m, and 10.02kW/m. The CHF location in Equation 6.34 is evaluated from the inlet void fraction 0 through: 0001vlvllv CHF whV z qD (6.37) where D is the ID of the tube. The IAFB mode l is carried out for down-flow case. -0.10.00.10.20.30.40.50.60.70.8 90 120 150 180 210 240 270 300 10kW/m2,correlation 10kW/m2,model Wall Temperature (K)Z (m) 3.5kW/m2,correlation 3.5kW/m2,model 5kW/m2,correlation 5kW/m2,model Figure 6-4. Comparison of wall temperat ures between the IA FB model and the correlation prediction under different heat fluxes.

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114 With increasing wall heat flux, more liquid nitrogen is evaporated, and the slip velocity increases according to mass conservatio n. Therefore the interfacial shear stress is larger at higher wall heat flux. For the small and moderate wall heat flux cases, in which the interfacial shear st ress is not very large, the correla tion is valid as motioned before and agrees well with the IAFB model. As more liquid phase is evaporated, the va por velocity and slip velocity increase along the axial direction, associ ated with increasing heat tr ansfer coefficient and vapor film thickness, which are two competing parameters that influence the wall-to-vapor heat transfer. Experimental results (Hammouda et al. 1996) show that the wall temperature approaches a constant value or even decrea ses after certain downstream location. The model result for large wall heat flux, the 10.02kW/m case, shows this trend correctly, on the other hand, the correlation of Equation 6.34 comes from pool boiling experiments and only considers the effect of th e thickening of the vapor film at downstream location, it breaks down and gives unreasona bly high wall temperature, as shown in Figure 6-4. For up-flow, the slip velocity is generally highe r than that of the dow n-flow case, and the correlation is expected to gi ve less accurate prediction. The IAFB model can also be used to study the gravity effect on the two-fluid system. Figure 6-5 shows the liquid velocity lu and vapor velocity vu along the tube for down-flow, up-flow and 0-g case w ith the wall heat flux of 5.02kW/m. The body force term in Equation 6.31 is zero for 0-g case, while plus and minus sign are for down-flow and up-flow case, respectively. It is obvious that the up-flow case has the largest slip velocity, while the down-flow case has the smalle st slip velocity and 0-g case lies in the

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115 middle. The highest liquid phase velocity is achieved in the down-flow case, and the highest vapor velocity corres ponds to the up-flow case. -0.10.00.10.20.30.40.50.60.70.8 2 4 6 8 10 12 14 16 Velocity (m/s)Z (m) Downflow ul Downflow uv 0-g ul 0-g uv Upflow ui Upflow uv Figure 6-5. IAFB model prediction of the liqui d velocity and the vapor velocity along the tube for down-flow, up-flow, and 0-g. Generally, all the velocities increase along the axial direction, how ever, it is noted that the vapor velocity for the down flow case decreases from 2.8m/s to about 2.1m/s at the tube inlet and then increases. For down flow, the liquid velocity has the maximum increase rate and the void fraction is near ze ro at the tube inlet, to satisfy the mass conservation equation, the vapor velocity must decrease at the tube inlet. Until at further downstream location, the void fraction is la rger and the vapor phase begins to be accelerated. The corresponding wall temperature Tw, vapor temperature Tv, and void fraction are shown in Figure 6-6 for down-flow, up-fl ow and 0-g case. The down-flow has the highest wall temperature, vapor temperature, and void fraction. This is because for downflow case the vapor velocity is the lowest (Fi gure 6-5). In IAFB, the heat from the wall is

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116 mainly carried away by the vapor phase, the vapo r phase then distributes part of this heat to evaporate the liquid phase, and the radiation heat transfer is often negligible small. The convective heat transfer betw een the wall and the vapor is characterized by the vapor Reynolds number in Equation 6.19; therefore, lower vapor velocity is associated with higher wall temperature, higher vapor temperature and higher void fraction. -0.10.00.10.20.30.40.50.60.70.8 80 100 120 140 160 180 200 220 Temperature (K)Z (m) Downflow Tw Downflow Tv Upflow Tw Upflow Tv 0-g Tw 0-g Tv A -0.10.00.10.20.30.40.50.60.70.8 0.0 0.1 0.2 0.3 0.4 0.5 Void FractionZ (m) Downflow 0-g UpflowB Figure 6-6. IAFB model predic tion of different variables al ong the tube for down-flow, up-flow, and 0-g. A) Wall temperatur e and vapor temperature. B) Void fraction.

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117 One can also find that the thermal equilibrium only holds for locations close to the CHF point, and the degree of thermal non-equili brium increases along th e flow direction. Therefore, it is generally inapplicable to describe the IAFB with simple empirical correlations which are usually ba sed on saturation properties. 6.3 Dispersed Flow Film Boiling Model In chilldown experiments and in flow channe ls heated with consta nt heat flux, with increasing void fraction and velocity deferen ce between the two phases, dispersed flow is expected to appear downstream of the IAFB region. A two-fluid model for the dispersed flow is developed in this study and used in the cryogenic chil ldown model later. 6.3.1 Introduction Dispersed flow is also called mist or liquid deficient flow in the literature. It is characterized by liquid droplets dispersed in a continuous vapo r phase. Dispersed flow is generally in a non-equili brium state(Carey 1992). The existence of the droplets in the flow channel will inevitably alter both the flow field and the total heat transfer coefficien t. As summarized by Andreani and Yadigaroglu (1996), the dispersed phase can modify the temp erature field and modify the velocity and thermal boundary layers. For example, for fl ow channel with uniformly distributed droplets, a large interfacial heat transfer and va porization rate occurs in the vicinity of the wall where the vapor temperatur e is highest. This will result in a strong reduction of the vapor temperature in the viscous sublayer. Mo reover, the structure of the turbulence is strongly affected by the disperse d phase: the presence of par ticles near the wall promotes turbulence in the boundary layer, increasing heat transfer, while partic les in the core may dampen or increase the turbulence.

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118 The droplets size, distribu tion and revolution are impor tant in dispersed flow prediction. Wide spectrum of droplet size and different distribution functions have been reported in the literature (Gani and Rohsenow 1977). However, detailed description of the droplets during a test is a difficult ta sk, and not enough data have been accumulated to provide satisfactory correlation untill now. Lacking of the proper droplet size distribution, together with currently poor understanding of the interfacial exchange mechanisms, makes the DFFB m odels often end up with too many adjustable parameters. Generally, the prediction methods for DFFB can be classified into the following four groups: empirical correlations, phe nomenological models, look-up table and mechanistic models. These methods will be brie fly reviewed below, for more details the review by Andreani and Yadigar oglu (1994) is a good reference. An often used correlation for DFFB is developed by Dougall and Rohsenow (1963), it is a Dittus-Boe lter type correlation: 0.80.4 20.023RePrv wvwsk qTT D (6.38) with: 2ReRe1v vee l x x (6.39) where e x is the equilibrium quality, and all the properties are evaluated at saturation temperature. The Dougall-Rohsenow correla tion requires only information on local conditions and therefore easy to use, it produ ces rather good prediction of the wall heat flux. However, this correlation does not pred ict the state of non-equilibrium, and has only limited accuracy in some situations.

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119 The phenomenological models are ba sed on a simplified phenomenological description of the physical pro cess, and consider the vapor superheat. One of the highly cited phenomenological models was proposed by Chen et al. (1979), known as the CSO model. For 0.5ex the thermal non-equilibrium is correlated in this model as: 0.650.26 1 1.15vs ewv crTT x x TT pp (6.40) here, x is the actual quality, crp is the critical pressure. Then, based on Reynolds analogy, the convective heat transf er coefficient is inferred as: 23 ,,Pr 2pwfGwf f hGxc (6.41) in which, G is the mass flux, and vapor heat capacity pwfcand the Prandtl number ,PrGwf are calculated at film temperature, 0.170.037Re f is the friction factor. This model has limited success at moderate to high pre ssure; however, it is inadequate under low mass flux and low pressure conditions. Most of the DFFB correlations are app licable only over limited ranges of flow conditions, and most of them do not provide reasonable pred ictions when extrapolated outside this range. Therefore, a totally empirical approach the look-up ta ble based on Post-CHF data and interpolat ing techniques has been proposed (Groeneveld et al. 2003). However, this approach contains no understa nding of the physical mechanisms in film boiling and is still under development. The mechanistic models simulate the basic mass, momentum and energy mechanisms and calculate the evolution of a ll the flow variables. In these models, the empiricism is generally shifted towards the determination of the parameters entering in

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120 the closure laws (Andreani and Yadigarogl u 1994). Examples include the two-fluid model (Kawaji and Banerjee 1988 ) and models accounting for the distributed heat sink effect (Chung and Olafasson 1984). The mechanistic models provide more details of the flow and heat transfer field in the DFFB, however, the success of these models highly dependent on the accuracy of the closure re lations and other adjustable parameters. 6.3.2 Model Description A two-fluid model for DFFB, which includes all the heat transfer mechanisms, will be discussed in this section and then impl anted into cryogenic ch illdown model later. 6.3.2.1 Assumptions and conservation equations Assumptions to derive the conservation e quations for DFFB are listed as follows: 1. The liquid phase is dispersed spherica l droplets, while the vapor phase is continuous. 2. The two phases are in thermodynamic non-e quilibrium, the liquid phase is at saturation temperature, and the vapor phase is treated as ideal gas. 3. The vapor and liquid pressures are unifor m and equal to the tube exit pressure. 4. At any given cross-section of the flow cha nnel, all droplets have a same diameter d The droplet diameter is a function of axial position or vapor quality x 5. At any given cross-section of the flow ch annel, all droplets move with a same velocity du. 6. The interfacial velocity is the same as the droplet velocity. The assumption 3 is based on the fact that the pressure drop in the dispersed region is very small compared with the total pressure drop. Under this assumption, the pressure is not an unknown, and the vapor momentum equation does not need to be solved, therefore the problem is significantly simplified. As stated in assumption 4, single-droplet formulation is used in current study. The reason for this assumption lies in two aspects. First, the work of Kawaji and Banerjee (1988) included both the single-droplet form ulation and multi-field approach, in which the droplet size distribution was modeled by eleven groups of droplets, and the two

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121 methods resulted in fairly good agreement. The multi-field approach did not show discernable advantage over the single-droplet formulation in their work. On the other hand, the droplet size distributi on function used in the model work is often adjustable, this function has not been well correlated to many influencing parameters from the experiments as discussed in previous section. For vertical tube, the transient one-di mensional two-fluid equations for DFFB region are given as below: Continuity equation: lllldlum tz (6.42) vvvlum tz (6.43) Momentum equation: lldllddllduuug tz (6.44) Vapor enthalpy equation: vvvvvvlvsvhuhqmhh tz (6.45) The density of vapor phase is calculated form Equation 6.8. In the above equations, subscript d is for liquid phase, v is for vapor phase and s denotes saturation; lm is the interfacial mass transfer rate per unit volume with unit of [3kg/ms]; vq is the heat flux used to heat up the vapor; for the body force in the momentum equati ons, plus sign is for down-flow, and minus sign is for up-flow.

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122 6.3.2.2 Heat transfer in dispersed flow film boiling and constitutive relations Heat transfer in the DFFB region is rather complex. In Figure 6-7 the heat and mass transfer mechanisms in DFFB are illustr ated as (Andreani and Yadigaroglu 1994; Guo and Mishima 2002): 1. Convective heat transfer fr om the wall to the vapor wvq ; 2. Interfacial heat transfer be tween the vapor and droplets vdq ; 3. Direct contact wall-todroplet heat transfer wdq ; 4. Radiative heat transfer from the wall to the droplets rwdq ; 5. Radiative heat transfer from the wall to the vapor rwvq ; 6. Radiative heat transfer from the vapor to the droplets rvdq ; 7. Evaporation of the droplets lm Figure 6-7. Heat and mass tran sfer mechanisms in DFFB. There might be some confusion by using the term direct contact wall-to-droplet heat transfer. In DFFB, the wall temperature is generally higher than the Leidenfrost temperature, therefore when the droplets are in the vicinity of the wall; a thin vapor film will separate it from in touch with the wall. In this context, the term actually means the

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123 heat transfer through this thin vapor film. Only in very few occasions, the droplets can have enough momentum to penetrate the vapor film and wet the wall. Some literature (Carey 1992) name the former and the later as dry contact and wet contact, respectively. However, the wet contact is generally consider ed negligible, and the direct contact heat transfer has been used in most of the literature, although misleading literally. This tradition is followed in current study. Convective heat transfer fr om the wall to the vapor. This part contributes most to the total heat removal from the wall, and is modeled as: 0.80.330.023RePrv wvvvwvk qTT D (6.46) in which, D is the tube ID and Rev is the vapor Reynolds number. Interfacial heat transfer between vapor and droplets. This part is calculated by the Lee-Ryley model (Lee and Ryley 1968): 0.50.3320.74RePrv vddvvsk qTT d (6.47) here, d is the droplet diameter, Red is the droplet Reynolds number that defined as: Revvd d vuud (6.48) Direct contact wall-to-droplet heat transfer. This part is usually much smaller than the convective heat transfer from the wall to the vapor, and is modeled by (Guo and Mishima 2002): 14 335 5418 1vRvlvd wdws lvwskthm qTT dTT (6.49)

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124 in which lvlvpvshhCTT is the modified latent heat; Rt is the droplet resident time, which characterizes the average time that the droplet in contact with the wall, and is given by Bolle and Moureau (1986) as: 316Rltd (6.50) dm is the deposition rate, which represents the droplet mass impinging rate to the wall per unit area, and given by Ka taoka and Ishii (1983) as: 1dlmK (6.51) where K is the deposition mass transf er coefficient, given as: 0.26 0.740.740.22Relv l lKE D (6.52) here, Edenotes the fraction of liquid droplet entrai nment in the vapor core and equals to unity for dispersed flow. Radiative heat transfer. The radiation heat transfer among the wall, the vapor and the droplet is usually small. When the radi ation is considered, the method proposed by Sun et al. (1976) is highly c ited. The wall, the vapor, and the droplets are characterized by an electrical network as shown in Figure 6-8. The radiation heat fluxes can then be expressed as: 1 44 rwvwvwvdBwvqRRRRRTT (6.53) 1 44 rwdwdwddBwsqRRRRRTT (6.54) 1 44 rvdvdvdwBvsqRRRRRTT (6.55) where

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125 11vvvvdR (6.56) 11dddvdR (6.57) 111wvdwwR (6.58) In the above equations, w v and d are emissivity of the wall, the vapor and the droplets, respectively. 1ww 11dv 11vd 1dv Figure 6-8. Electrical analog of ra diation heat transfer in DFFB. Interfacial mass transfer rate. All the heat absorbed by the liquid phase is assumed to be used to evaporate the liquid dr oplets. From energy balance, the heat used to evaporate the droplets per unit volume is given by: ,,4evapivdrvdwdrwdqAqqqq D (6.59) The interfacial mass transfer rate per unit volume in the model equations is, therefore: levaplvmqh (6.60)

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126 here, because of the difference in the heat transfer area for different heat transfer mechanisms, i A and 4 D appear in Equation 6.59. For a flow channel with length l and contains n droplets with diameter of d the interfacial area is: 2i A nd (6.61) while, the sum of the total volume of the droplets over the flow channel volume is the liquid fraction, this gives: 231 2i D l A d (6.62) and the interfacial area per unit volume of the flow channel is: 61iA d (6.63) The vapor to droplet convective heat transfer area equals the interf acial area, while the other heat transfer mechanisms are c onsidered to take place at the wall. Vapor heating term. The vapor phase is heated by th e wall and passes part of this heat to evaporate the liquid droplets. The va por heating term in Equation 6.45 is given as: ,,4vwvrwvrvdivdqqqqAq D (6.64) Interfacial drag term. The interfacial drag on th e droplets per unit volume is calculated by: 361D d F d (6.65) where D F is the drag force on one droplets, which was suggested by Rowe (1961) as:

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127 224D DvvdvdC F uuuud (6.66) in which, the drag coefficient is given as: 0.68724 10.15Re ReDd dC (6.67) Droplet diameter. The droplet diameter is an important parameter, and is evaluated by the model of Kataoka et al. (1983): 1323 323 27.9610Revv v ll vvd u (6.68) 6.4 Application of a Two-Fluid Model to Cryogenic Chilldown In this section, a cryogenic chilldown m odel is developed with four regions. Previously discussed IAFB and DFFB m odel are introduced into this cryogenic chilldown model. The code validation of the cryogenic chilldown model is given in the Appendix. 6.4.1 Model Description Chilldown process inside of a vertical stai nless steel tube is modeled. The tube, which is inside of a vacuum jacket, has 0.635cm OD, 0.432cm ID, and 70 cm length. Saturated liquid nitrogen is injected from the bottom of the tube at certain fixed inlet flow rate. The computation has been carried out for both normal gravity case and microgravity case. 6.4.1.1 Fluid flow When saturated liquid nitrogen with a sma ll initial void fraction as in Equation 6.29 enters from the bottom of the tube, the two-pha se flow is in IAFB state. The two-fluid

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128 IAFB model discussed in previously is used to describe the two-phase flow behavior in this region. The void fraction keeps increasing as th e two-phase flow propagating downstream. In current study, the transition criteri on from IAFB to DFFB is set as 0.90 The governing equations for DFFB are given in E quation 6.42-6.45, and the pressure drop is neglected in DFFB region. The boundary condi tions at the transition interface are given from the upstream IAFB region. If the flow channel is enough long, all the liquid droplets in the DFFB front will be evaporated eventually and the flow becomes fully vapor. In this study, when the void fraction reaches 0.99, the effect of the liquid phase is neglected and the flow is modeled as fully vapor, in which the only heat transf er mechanism is due to the forced convection to the vapor: 0.80.330.023RePrv wvvvwvk qTT D (6.69) When the tube wall has been chilled down to rewetting temperature, intermittent liquid-wall contact is established and tran sition boiling begins. The transition boiling, characterized by rapid bubble ge neration, is highly unstabl e and immediately replaced by the nucleate boiling. Model th e transition boiling region in chilldown is generally a difficult task, because the understanding and e xperimental data of the transition boiling are still very limited at current stage. On the other hand, the transition boiling period in chilldown process is so short a nd the heat flux of transition bo iling is in the same order as that of the nucleate boiling, therefore nucle ate boiling correlations are used to model both the transition boiling region and the nuclear boiling region in th is work, this approach is also adopted by other researches (Kawaji and Banerjee 1988; Hedayatpour et al. 1993).

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129 The Chens correlation (Chen 1966) for nucleate boiling is used, in which the total heat transfer coefficient equals to the sum of a microscopic (nucleat e boiling) contribution mich and a macroscopic (bulk convection) contribution mach, in addition, michis evaluated by pool boiling correlation times a suppression factor 2ReS ; while mach is proposed to be enhanced from single liquid convection with a enhancement factor tt F X. The Chens correlation gives: 2RepoolltthhShFX (6.70) where 0.790.450.49 0.240.75 0.50.290.240.240.00122lpll poolwslswl llvvkc hTTPPTP h (6.71) 0.80.40.023RePrl lllk h D (6.72) In Equation 6.70, 2Re is the two-phase Reynolds number, ttX is the Martinelli parameter. For details can refer to Chen (1966). In some other chilldown models (Kawa ji and Banerjee 1988; Hedayatpour et al. 1993), the location and the propa gation of the quenching front are a prior; these models begin with the IAFB and move back to the upstream of the quenchi ng front after solving the Post-CHF region. In this study, instead the rewetting temperature is used as the transition criterion from the film boili ng to nucleate boiling. Whenever the wall temperature is quenched below the rewetting temperature, the nucleate boiling model will be started. The rewetting temperature is not a fixed value but affected by flow rate, fluid and wall properties, etc. Fort unately, for the same experimental setup and limited range

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130 of working conditions, the rewetting temperatur e is generally a constant. Therefore, use the rewetting temperature acquired from the experiments as transition criterion is expected to be applicable to similar expe rimental conditions. A reliable correlation for rewetting temperature is desirable and w ill generalize current chilldown model. 6.4.1.2 Heat conduction in tube wall The wall temperature is obt ained by solving the 1-D transient heat conduction equation: 2 2 ww wpwwTT ck tz (6.73) 6.4.1.3 Initial and boundary conditions Initially the whole tube is at a constant temperature of 0T, the tube is filled with pure vapor which is in thermal equilibrium with the tube. Saturated liquid nitrogen is injected fr om the bottom of the tube under constant flow rate; a small inlet void fraction and a sm all inlet slip velocity are assigned at flow inlet, as summarized in Equation 6.29. Adiabatic boundary condition is set at the inlet wall, outlet wa ll and outer surface. For the inner surface, different correlations are used for the four regions, and are summarized in Table 6-2. Table 6-2. Inner wall boundary c onditions at different regions. Region Boundary condition Equation used Fully vapor wwvqq 6.69 DFFB ,, wwvwdrwvrwdqqqqq 6.46, 6.49, 6.53, 6.54 IAFB wwvrqqq 6.17, 6.23 Transition and nucleate boiling wwsqhTT 6.70

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131 6.4.2 Numerical method and solution procedure A semi-implicit, finite difference scheme is used in the chilldown model. Very small time step is used to avoid the instability that is inherent in the two-fluid model. The 1-D heat conduction equation is solved by TDMA method with totally 200 nodes. The solution procedure is illustrated in Figure 69. First, the initial conditions for both the tube wall and the flow field ar e given, and the CHF location CHFZ is set at the tube inlet. Then the calculation begins with a initial guess of P, lu, vu, vh. In this model, Post-CHF models are used for downstream of the CHF point, while nucleate boiling model is applied to upstream of CHF point. In Post-CHF calculation the void fraction increases along axial directi on, whenever the calculated void fraction reaches the two critical values, it is considered as a flow regime transition, and therefore a different model is selected. After solving th e flow field, the wall temperature is updated according to Equation 6.73. A pre-defined rewe tting temperature is used as transition criterion between the Post-CHF and nucleat e boiling region. The location where the wall temperature becomes lower than the rewetting temperature is set as the new CHF location, and the program iterates until the wall temp erature converges. This will finish the computation in one time step. For the whole chilldown process, the program ends until the calculation time is larger than the experiment time. 6.4.3 Results and Discussion The cryogenic chilldown model can be us ed for top-flooding, bottom-flooding and microgravity cases, and is capable of predicting both the flow field and temperature field. In this part, the feasibility of this model is addressed by comparing the model results with experimental data.

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132 Figure 6-9. Solution procedure of the cryogenic chilldown model.

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133 6.4.3.1 Experimental results One of the important aims to develop th e cryogenic chilldown model is for the prediction of chilldown process under microgr avity, for which systematic experiments are often difficult and costly In the literature, to th e authors knowledge, the only experimental investigation covers the whole cryogenic chill down process under low gravity environment was conducted by Antar an d Collins (1997). Their work is reviewed as follows. The cryogenic chilldown experiments we re carried by Antar and Collins (1997) under both terrestrial and low gr avity environments with same experimental apparatus. The low gravity environment, which has an average gravitational acceleration of0.01g was provided by a NASA KC-135 aircraft. Duri ng the test, the low gravity time lasted about 25 seconds, while the test section is usually chilled down within 20 seconds; therefore the low gravity dur ation is sufficient long. Two different test sections were used in the experiments. A quartz tube, having 1.275 cm OD and 1.05 cm ID and approximately 60 cm long, was used for the purpose of recording the flow regimes; another stainless steel test section was used for wall temperature measurement. The stainless steel test section, which has the dimension of 0.635 cm OD, 0.432 cm ID, and 70 cm length, w ill be modeled in current study. Both test sections were mounted vertically inside a vacuum jacket. Saturate d liquid nitrogen was injected from the bottom of the test section, while the top of the test section was opened to atmosphere. A stainless steel bellows, in side of a liquid nitrogen accumulator, was used to store the liquid nitrogen before each test. The bellows was compressed from the outside with gaseous helium at approximately constant pressure to supply liquid nitrogen.

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134 The two main variables in the experiment we re the nitrogen flow rate and the initial tube temperature. The results shown in the paper has a flow rate range of about 35-55 cc/s. The tube was initially at room temperat ure, after each test th e wall temperature was always brought above 00C. Three type T thermocouples we re soldered to the outside wall of the stainless steel test s ection; however, one thermocoupl e was reported to give erratic signals during the test, and onl y the other two thermocouple measurements were given. These two thermocouples located at 20 cm and 30 cm from the inlet, respectively. In low gravity tests, the flow sequence before rewetting was reported as: fully vapor flow, dispersed flow, and then followe d by filamentary flow, in which the liquid took the form of long liquid filaments meandering in the center of the pipe which were surrounded by a vapor blanket separating them from the test section wall. Single filaments were always observed to grater th an 10 tube diameter and in general had a diameter of about one third th at of the test section. Howe ver, the reported images are rather unclear. Although the author claimed that the obser ved filamentary flow structure in low gravity is a new and unique flow pattern, and has two characteristics that different from IAF regime in ground tests, it is believed th at the filamentary flow structure actually belongs to IAF regime by a further study a nd comparison with other experiments. The reasons will be given below. As described by Antar and Collins (1997), the two characteristics of the filamentary flow were: first, in low gravity the diameters of the liquid filaments were smaller than that of the IAF; and second, th e liquid filaments extended to longer distances than that in the IAF, which has a length about three tube diameters.

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135 However, liquid filament with smaller diam eter is actually classified as inverted annular flow pattern and had been reported in microgravity experiments previously. For example, a series microgravity quenchi ng experiments using R-113 conducted by Kawaji et al. (1991) reported that the inverted annular-like flow re gime in microgravity showed a much thicker vapor film in comparison with th at seen in 1-g tests. In microgravity, the liquid core was often much thinner, more closely resembling a th ick cylindrical liquid filament which was mostly smooth and continuous but sometimes bulged at some places nearly filling the tube volume wit hout rewetting the tube surface. On the other hand, the thicker vapor film in microgravity alleviates the heat transfer from the wall to the liquid core, and the liqui d core is expected to extend longer before breaking into dispersed flow. Even in the ground test, the IAFB re gion is not always short. If the heat flux from the wall is pretty low as in chilldown experiments, the liquid core in IAFB region could be much longer th an three tube diamet er (Lee and Kim 1987). From the above reasons, the sequence of th e flow regime in microgravity cryogenic chilldown process is modeled as fully vapor dispersed flow, IAF, and nucleate boiling. The temperature measurements (Antar a nd Collins 1997) show that the rewetting temperature is rather a constant, which is about 115K, in the expe rimental flow rate range. The wall temperature drops very quickly at this point. Therefore the transition criterion to nucleate boiling is set as 115K. The transition bo iling period is found to be very short and usually less than one second. 6.4.3.2 Model results and comparisons Figure 6-10 shows the measured and pr edicted wall temperatures under 1-g condition. The two thermocouples are located at 20cm and 30cm from the inlet, and the

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136 flow rate is approximately 40cc/s according to the inlet pressure and flow rate relation given by Antar and Collins (1997). The model slightly over-predicts the te mperature decreasing speed before the rewetting point and thus leads to an earlier transition to the nuclea te boiling region, the overall agreement is good. It is noted that th e initial condition of th e experiment was not well controlled so that there is a temperatur e difference of about 25K between the initial thermocouple responses as shown in Figure 610; while in current model, the tube is assumed at same initial temperature. The s catter between the model prediction and the experimental data for thermocouple location at 30cm from the inlet comes mainly from this initial difference. 0510152025 100 150 200 250 300 Condition: 1-g Experiment Model 20cm 30cm Temperature (K)Time (s) Figure 6-10. Comparison between measured and predicted wall temperatures under 1-g condition with flow rate of 40cc/s. Comparison between microgravity tests and model predictions is illustrated in Figure 6-11. Again, good agreement is achieve d. Contrary to the 1-g case, the model under-predicts the temperature decreasing speed very slightly. Th is discrepancy is

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137 believed to come from the residual gravity e ffect in the experiment. The KC-135 aircraft generally produces reduced to micro-g grav ity level (about 0.05~0.01g), the detailed glevel fluctuates in one test and differs from test to test. Antar and Collins (1997) did not give the approximated g-level in their tests. As shown by many re searchers the gravity force can improve the film boiling heat transfer In present study the model results are for 0-g, therefore the model s lightly under-predicts the temperature decreasing speed. 0510152025 100 150 200 250 300 Experiment Model 20cm 30cm Temperature (K)Time (s) Condition: 0-g Figure 6-11. Comparison between measured and predicted wall temperatures under 0-g condition with flow rate of 40cc/s. Figure 6-12 shows the prediction of the tr ansient wall temperatures at different axial locations along th e tube under both 1-g and 0-g c onditions with a flow rate of 40cc/s. The three locations in the figure are 1mm, 20cm and 30c m from the inlet, respectively. Obviously, the tube wall closer to the in let is quenched more quickly. Moreover, the gravity effect is found to be less important near the tube inlet (1mm line), because the

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138 void fraction is very small there and the flow is almost single liquid. The gravity effect is found to increase along the axial direction. 0510152025 50 100 150 200 250 300 1-g 0-g 1mm 20cm 30cm Temperature (K)Time (s) Figure 6-12. Model prediction of wall temperat ures at different axial locations under both 1-g and 0-g conditions. Effects of the inlet flow rate and gravity le vel are illustrated in Figure 6-13. As seen from Figure 6-13A, higher flow rate is associ ated with quicker temperature decrease, and this effect is more important further downs tream. Figure 6-13B illustrates that in film boiling region the heat transfer rate decreases with decreasin g gravitational acceleration. After rewetting point, the correlation us ed in this model does not include the gravity effect, therefore the temperatures decr easing at about the same speed at transition and nucleate boiling region under different g-le vels. The experiment of Merte and Clark (1964) showed that in the transition and nucleate boiling region, the boiling curve is almost unchanged under different g-levels. On the other hand, it is the rewetting point that usually of particular interest in engi neering application, th e current model clearly

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139 demonstrates the gravity effect on the film boiling region, and is, therefore, very important in Post-CHF flow a nd heat transfer prediction. 051015202530 100 150 200 250 300 30cc/sec 40cc/sec 1mm 20cm 30cm Temperature (K)Time (s) Condition: 0-gA 0510152025 100 150 200 250 300 Location:30cm 0-g 0.5g 1-gTemperature (K)Time (s) Flow rate: 40cc/secB Figure 6-13. Effects of inlet flow rate and gr avity level on chilldown pr ocess. A) Effect of inlet flow rate. B) Effect of gravity level. Figure 6-14 gives the wall temperature profil es at different time. Wall temperature decreases with time and increases along the axial direction. In the beginning, the

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140 maximum temperature gradient is at the t ube inlet, when QF appears, the maximum temperature gradient moves with the QF. 0.00.10.20.30.40.50.60.70.8 80 120 160 200 240 280 40cc/sec, 0-g 0.01S 0.5S 1S 5S 10S 15STw (K)Z (m) Figure 6-14. Wall temperature pr ofiles at different time. The void fraction at different time under 0g condition is shown in Figure 6-15. The void fraction increases along the axial direction since more and more liquid is evaporated as the flow propagates. The driving potential of the evaporation, the temperature difference between the wall and the liquid saturation temperature, keep s decreasing as the tube is being chilled down; therefore pace of the void fraction incr easing rate slows down as shown in Figure 6-15. Particularly, in the beginning stage the wa ll is very hot, the void fraction shows an abrupt increases along the axial direction, and the flow regime changes from IAF to dispersed flow and then to fully vapor flow. Later on, the fully vapor region and dispersed region are totally pushed out of the tu be and the exit state of the two-phase flow is in IAFB, and finally, QF appears and sweeps downstream.

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141 0.00.10.20.30.40.50.60.70.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.01s 5s 0.5s 7s 1.0s 8s Void FractionZ(m) 40cc/sec, 0-g Figure 6-15. Void fraction along the tube during chilldown. 6.5 Conclusions In this chapter, cryogenic chilldown proce ss is divided into f our regions which are fully vapor region, DFFB region, IAFB re gion, and nucleate boiling region. Then a cryogenic two-fluid chilldown model is deve loped with each of these four regions modeled in different strategy. The model can be applied to both vertical tube chilldown case and microgravity chilldown case. The m odel predictions and the experimental results have a good agreement.

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142 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS In current study, chilldown experiments have been conducted under both 1-g and microgravity conditions. A two-fluid model is developed for both vertical tube chilldown and chilldown under microgravity. Majo r conclusions of current study and recommendations for future research are to be given in this chapter. 7.1 Conclusions 1. The experiments show that the chilldown process can be generally divided into three regions: film boili ng region, transition boiling region and nucleate boiling region, and each region is associated with different flow regime and heat transfer mechanism. After data reduction, chilldown boiling curve, which is similar to the pool boiling curve, is generated based on the wall temperature measurement. The limits between different regions of the ch illdown process are clearly shown as the point of the critical heat flux (CHF) and the minimu m heat flux on the chilldown boiling curve. 2. Experiments have been conducted under three different low flow conditions. It has been observed that the two-phase flow is dispersed in the film boiling region with liquid phase in the form of long filaments as the tube is chilled down, while the vapor phase is generally s uperheated. The heat transfer mechanism at the bottom wall is film boiling to the liquid filaments and convection to the superheated vapor phase, the upper wall transfers heat mainly by convection. The statistic feature of the liquid filaments is studied and it ha s been shown that the thickness of the filaments shows very limited increase with increasing mass flux and does not present a strong correlation w ith the wall temperature; while the length of the filaments is more scattered at higher mass fluxes and lower wall temperatures. 3. Based on the experimental result, a phenom enological model, in which the heat transfer at the bottom is considered as a sum of vapor and liquid components, has been developed. Good agreement is achieve d between the model prediction and the experimental result. 4. Rewetting experiments show that rewetti ng temperature and rewetting velocity increases with increasing mass flux. The rewetting process is observed as the appearance of the rewet spots followed by th e growth and spread of the rewet spots in both direction, and finally the establishment of the quenching front.

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143 5. Cryogenic chilldown under microgravity conditi on is experimentally studied. In the film boiling region, the bottom wall heat flux is found to decrease under microgravity condition. Under current experi mental condition, the gravity effect does not show a strong dependence on wa ll temperature and inlet flow rate. 6. A two-fluid cryogenic chilldown model has be en developed to predict both vertical tube and microgravity chilldown process. Th e model contains four distinct regions, which are fully vapor region, dispersed fl ow film boiling (DFFB) region, inverted annular film boiling (IAFB) region, a nd nucleate boiling region. Two-fluid equations are applied to the DFFB regi on and the IAFB region, the fully vapor region and nucleate boiling region are depi cted with single-phase correlations. Constitutive relations and transition criteria between different regions are studied and provided to close the ch illdown model. Comparison between the model results with previous experimental data (Antar and Collins1997) shows a good agreement. 7.2 Recommendations for Future Research In current research, both experimental a nd modeling work have been conducted to advance the understanding of the cryogenic chilldown proces s and significant progress has been achieved, however, due to the comp licity of the problem there are several key issues remain unsolved and the following ar e recommended for future investigations: 1. The effects of the test section dimension and the thermal and surface properties of the wall have not been investigated in cu rrent experiments. It is suggested to include these effects in the future experiments. 2. The gravity effect on the film boiling region has been studied in this research. The transition region and nuclea te boiling region are not included and needs further exploration. 3. In chilldown model, the droplet diameter is the most important parameter in DFFB region. More experimental observations are desirable to provide reliable database of the droplet size and distri bution function for modeling work. 4. Transition from the IAFB region to the D FFB region has been observed by some researchers as large liquid chunks travel in vapor phase and break into liquid droplets shortly after their generation. Current model wo rk does not include this short transition region and use void fracti on as the transition criterion instead. Future research is suggested to advance this model by adding this transition region with necessary closing relations.

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144 APPENDIX CODE VALIDATION In this section, the code for chilldown m odel is validated in two ways. First, the code is used to simulate the dam-break problem and the computation results are compared with analytical solution. Next, th e grid independence of the code is tested. A.1 Dam-Break Problem Dam-break problem is one of the effectiv e tests of numerical prediction because it has an analytical solution that contains disc ontinuities, and this allows a sensitive check on the effects of numerical di ffusion in code predictions. Assume a reservoir contains still water with flat surface of height h1, on the other side of the reservoir, the water height is h0 (Figure A-1), suddenly the dam of the reservoir is removed and results a tran sient 1-D flow due to the gravity. X X=0 h1Reservoir Dam Y h0 Figure A-1. Dam-br eak flow model.

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145 If there is no friction on th e wall and no viscous stress in the fluid, and air pressure is constant, an analytical solution for the liquid level and liquid velocity is given by Zoppou and Roberts (2003). The result is shown in Table A-1. Table A-1. Analytical solution of dam-break problem for horizontal frictionless channel. Range Dependent variable 1 x tgh 0 u 1hh 122tghxtghu 312 3uu x gh t 2 314 92hh x gh g t 222tghxtSu 2 0 2 22 208 11 4uugh S S S g h 2 12 0 2 2 20 02 1 18 22hhhh h h hh h 2tSx 0u 0hh In Table A-1, 2S is the shock speed and given by: 12 22 0 22 2100 20088 211212 4 gh SS Sghghgh Sghgh (A.1) The governing equations for this 1-D dam-break problem can be expressed as: lll luuh ug txx (A.2) 0lllhuh tx (A.3) here, lu is liquid velocity, lh is liquid height, and 210 m/s g is the gravitational acceleration. Length of the computation re gion is 2000m, and the initial and boundary conditions are listed as: 0 15m if 1000m ,00, ,0 10m if 1000m hx uxhx hx (A.4)

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146 The dam break problem is solved based on the two-fluid code, in which only liquid phase equations are needed, and the pressure term is set as zero. Figure A-2 and Figure A-3 compare the numerical solution with the analytical solution at 25stand 50st after the dam break, respectively. 0500100015002000 5 6 7 8 9 10 h (m)X (m) numerical analytical t=25sA 0500100015002000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Velocity (m/s)X (m) numerical analtyical t=25sB Figure A-2. Comparison between numerical results and analytical solutions at 25s after dam break. A) Water depth. B) Water velocity.

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147 0500100015002000 5 6 7 8 9 10 h (m)X (m) numerical analyticalt=50sA 0500100015002000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Velocity (m/s)X (m) numerical analyticalt=50sB Figure A-3. Comparison between numerical results and analytical solutions at 50s after dam break. A) Water depth. B) Water velocity. After the dam break, the water wave and velocity spread on both directions from the breaking point. The maximum velocity depends on the initial water levels and remains unchanged with time. Due to the numer ical dissipation, the sharp changes of the water depth and water velocity are smeared.

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148 Courant number ( t CFLu x ) is an important factor for the transient flow computation. With increasing CFL number the numerical results approaches the analytical solution gradually (Figure A-4). However, the numerical results are unstable for roughly0.7CFL 0500100015002000 5 6 7 8 9 10 h (m)X (m) analytical CFL=0.06 CFL=0.12 CFL=0.5 CFL=0.7 CFL increases t=50s Figure A-4. Effect of CFL number. A.2 Grid Independence Check Grid independence of the code is tested for the inverted annular film boiling region with a constant wall temperature under zero-gravity condition. The test section has a dimension of 0.432 cm ID and 70 cm length. At t=0, liquid nitrogen enters the test section with volumetric flow rate of 40 cc/s. The liquid nitrogen evaporates while traveling downstream due to the high wa ll temperature, therefore the void fraction increases along the test section. Three differe nt mesh sizes are used in the computation with total of 200, 400 and 600 grids, respectively. For a constant time step of 0.0001t the computation results of void fraction at t=1 second with different grids show very sm all difference (Figure A-5). In Figure A-6,

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149 the total grid number is fixed at 200 a nd different CFL number is used in the computation. Again, the resulted void fractions are very close. Therefore, it is believed that current scheme reaches grid independence. 0.00.10.20.30.40.50.60.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Void FractionZ (m) 200 grids 400 grids 600 grids 40cc/s, 0-g t=1s Figure A-5. Computation result s of void fraction with different grids at a fixed time step of 0.0001t 0.00.10.20.30.40.50.60.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 40cc/s, 0-g t=1sVoid FractionZ (m) CFL=0.14 CFL=0.28 CFL=0.56 Figure A-6. Computation resu lts of void fraction with diffe rent CFL number at a fixed grid number of 200.

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152 Chan, A. M. C., and Banerjee, S., 1981a, Ref illing and rewetting of a hot horizontal tube part I: experiment. ASME Journal of Heat Transfer 103, 281-286. Chan, A. M. C., and Banerjee, S., 1981b, Ref illing and rewetting of a hot horizontal tube part II: structure of a two-fluid model. ASME Journal of Heat Transfer 103, 287292. Chan, A. M. C., and Banerjee, S., 1981c. Ref illing and rewetting of a hot horizontal tube part III: application of a two-fluid mode l to analyze rewetti ng. ASME Journal of Heat Transfer 103, 653-659. Chang, Y. P., 1959, Wave theory of heat tran sfer in film boiling. ASME Journal of Heat Transfer 8, 1-12. Chang, Y. P., and Snyder, N. W., 1960, Heat transfer in saturated boiling. Chemical Engineering Progress, Symp. 56, 25-38. Chen, J. C., 1966, Correlation for boiling heat tr ansfer to saturated fluids in convective flow. Industry Engineering Chemistry Pr ocess Design and Development 5, 322-329. Chen, J. C., Ozkaynak, F. T. and Sundaram, R. K., 1979, Vapor heat transfer in post-CHF region including the effect of th ermodynamic non-equilibrium. Nuclear Engineering and Design 51, 143-155. Chen, W. J., Lee, Y., and Groeneveld, D. C ., 1979, Measurement of boiling curves during rewetting of a hot circular duct. Internati onal Journal of Heat and Mass Transfer 22, 973-976. Cheng, S. C., 1978, Transition boiling curves generated from quenching experiments using a two dimensional model. Letters in Heat and Mass Transfer 5, 391-403. Cheng, S. C., Ng, W. W. L. and Heng, K. T., 1978, Measurements of boiling curves of subcooled water under forced convective c onditions. International Journal of Heat and Mass Transfer 21, 1385-1392. Cheng, S. C., and Ragheb, H., 1979, Transitio n boiling data of water on inconel surface under forced convective conditions. International Journal of Multiphase Flow 5, 281-291. Chi, J. W. H., 1965, Cooldown temperatur es and cooldown time during mist flow. Advances in Cryogenic Engineering 10, 330-340. Chi, J. W. H., and Vetere, A.M., 1964, Tw o-phase flow during transient boiling of hydrogen and determination of nonequilibrium vapor fractions. Advances in Cryogenic Engineering 9, 243-253. Chung, J. N., and Olafsson, S. I., 1984, Twophase droplet flow convective and radiative heat transfer. International Journal of Heat and Mass Transfer 27, 901-910.

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153 Cokmez-Tuzla, A. F., Tuzla, K., and Chen J. C., 2000, Characteristics of liquid-wall contact in post-CHF flow boiling. Interna tional Journal of Heat and Mass Transfer 43, 1925-1934. Collier, J. G., 1981, Convective Boiling and Condensation. 2nd ed., McGraw-Hill, New York. Cross, M. F., Majumdar, A. K., Bennett Jr ., J. C., and Malla, R. B., 2002, Model of chilldown in cryogenic tran sfer linear. Journal of Sp acecraft and Rockets 39, 284289. Dhir, V. K., Duffey R. B. and Catton I ., 1981, Quenching studies on a zircaloy rod bundle. ASME Journal of Heat Transfer 103, 293-299. Dougall, R. S., and Rohsenow, W. M., 1963, Film boiling on the inside of vertical tubes with upward flow of the fluid at low qualities. MIT Report 9079-26. Duffey, R. B. and Porthouse, D. T. C., 1973, The physics of rewetting in water reactor emergency core cooling. Nuclear Engineering and Design 25, 379-394. Edelman, Z., Naot, D., and Elias, E., 1983, Optic al illustration of liqui d penetration to the vapor film in inverted annular boiling. International Journal of Heat and Mass Transfer 26, 1715-1717. Flynn, T. M., 1996, Cryogenic Engineeri ng. Marcel Dekker, Florence, KY. Frederking, T. H. K., Chapman, R. C., a nd Wang, S., 1964, Heat transport and fluid motion during cooldown of single bodies to low temperature. Advances in Cryogenic Engineering 10, 353-359. Gani E. N., Rohsenow, W. M., Dispersed flow h eat transfer, Intenti onal Journal of Heat and Mass Transfer 20 (1977) 855-866. Gebhart, B., Jaluria, Y., Mahajan, R.L., Sammakia, B., 1988, Buoyancy-induced flow and heat transport. Hemis phere Publishing Company. Groeneveld, D. C.,1975, Post-dryout heat tran sfer: physical mechanisms and a survey of prediction methods. Nuclear Engineering and Design 32, 283-294. Groeneveld, D. C., Leung, L. K. H., Vasic, A. Z., Guo, Y. J., and Cheng, S. C., 2003, A look-up table foe fully developed film-bo iling heat transfer. Nuclear Engineering and Design 225, 83-97. Gungor, K.E. and Winterton, R.H.S., 1987, Si mplified general correlation for saturated flow boiling and comparisons of correlat ios with data. Chemical Engineering Research and Design 65, 148-156.

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154 Guo, Y. J. and Mishima, K., 2002, A non-equilib rium mechanistic heat transfer model for post-dryout dispersed flow regime. Experi mental Thermal and Fluid Science 26, 861-869. Hammouda, N., Groeneveld, D. C., and Cheng, S. C., 1996, An experimental study of subcooled film boiling of refrigerants in vertical up-flow. Inte rnational Journal of Heat and Mass Transfer 39, 3799-3812. Hammouda, N., Groeneveld, D. C., and Chen g, S. C., 1997, Two-fluid modeling of inverted annular film boiling. Internationa l Journal of Heat a nd Mass Transfer 40, 2655-2670. Hedayatpour, A., Antar, B. N., and Kawaji, M ., 1993, Cool-down of a vertical line with liquid nitrogen. AIAA Journal of Therm ophysics and Heat Transfer 7, 426-434. Hsu, Y. Y. and Graham, R. W., 1963, A visual study of two-phase flow in a vertical tube with heat addition. NASA-TN-1564. Hsu, Y. Y., and Westwater, W., 1959, Appr oximate theory for film boiling on vertical surfaces. AIChE Symposium Series 56, 15-24. Iloeje, O. C., Plummer, D. N., Rohsenow, W. M. and Griffith, P., 1975, An investigation of the collapse and surface rewet in film boiling in forced vertical flow. ASME Journal of Heat Transfer 42, 3387-3407. Iloeje, O. C., Plummer, D. N ., Rohsenow, W. M., Griffith, P., 1982, Effects of mass flux, flow quality, thermal and surface properties of materials on rewet of dispersed flow film boiling. ASME Journal of Heat Transfer 104, 304-308. Incropera, F. P., and Dewitt, D. P., 2002, F undamentals of heat and mass transfer, 5th edition. John Wiley & Sons, New York. Ishii, M., 1975, Thermo-fluid dynamic theo ry of two-phase flow. Eyrolles, Paris. Ishii, M., and Dejarlais, G., 1986, Flow regime transition and interfaci al characteristics of inverted annular flow. Nuclear Engineering and Design 95, 171-184. Ishii, M., and Dejarlais, G., 1987, Flow visual ization study of invert ed annular flow of post dryout heat transfer region. Nucl ear Engineering and Design 99, 187-199. Ishii, M. and Mishima, K., 1984, Two-fluid model and hydrodunamic constitutive relations. Nuclear Engineer ing and Design 82, 107-126. Issa, R. I., and Kempf, M. H. W., 2003, Simulation of slug fl ow in horizontal and nearly horizontal pipes with the twofluid model. International J ournal of Multiphase Flow 29, 69-95.

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155 Kalinin, E. K., Yarko, S. A., Yskochelaev, V., and Berlin, I. I., 1969, Investigation of the crisis in film boiling in channels. Pr oceedings of Two Phase Flow and Heat Transfer in Rod Bundles, ASME Winter Annual Meeting, Los Angeles, CA, 89-94. Kandlikar, S.G., 1990, A general correlation for saturated two-phase flow boiling heat transfer inside horizontal a nd vertical tubes. ASME Jour nal of Heat Transfer 112, 219-228. Kao, H. S., Morgan, C. D., Crawford, M., a nd Jones, J. B., 1972, Stability analysis of film boiling. AIChE Symposium Series 68, 147-155. Kataoka, I., and Ishii, M., 1983, Entrainment and deposition rates of droplets in annular two-phase flow. Proceedings of ASME/JSME Thermal Engineering Joint Conference, Vol. 1. Kataoka, I., Ishii, M., and Mishima, K., 1983, Generation and size distribution of droplet in annular two-phase flow. ASME Jour nal of Fluid Engineering 105, 230-238. Kawaji, M. and Banerjee, S., 1987, Applicati on of a multifield model to reflooding of a hot vertical tube part I: model structure and interfaci al phenomena. ASME Journal of Heat Transfer 109, 204-211. Kawaji, M. and Banerjee, S., 1988, Applicati on of a multifield model to reflooding of a hot vertical tube part II: an alysis of experimental resu lts. ASME Journal of Heat Transfer 110, 710-720. Kawaji, M., Ng, Y.S., Banerjee, S., and Ya digaroglu, G., 1985, Reflooding with steady and oscillatory injection: Pa rt I-flow regimes, void fraction, and heat transfer. ASME Journal of Heat Transfer 107, 670-678. Kawaji, M., Westbye, C. J. and Antar, B. N., 1991, Microgravity experiments on twophase flow and heat transfer during quen ching of a tube and filling of a vessel. AIChE Symposium Series 87, 236-243. Kays, W. M., 1993, Convective Heat and Mass Transfer. 3rd ed., McGraw-Hill, New York. Kim, J. and Moin, P., 1985, Application of a fractional step method to incompressible Navier-Stokes equation. Journal of Computational Physics 59, 308-323. Klimenko, V.V., Fyodorov, M.V. and Fomic hyov, Yu. A., 1989, Channel orientation and geometry influence on heat transfer with two-phase forced flow of nitrogen. Cryogenics 29, 31-36. Kline, S. J. and McClintock, F. A., 1953, Describing uncertainties in single sample experiments. Mechanical Engineering 75, 3-8.

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158 Thome, J. R. and Hajal, J. E., 2003, Two-phase flow pattern map for evaporation in horizontal tubes: Latest version. He at Transfer Engineering 24, 3-10. Thompson, T. S., 1972, An analysis of the wet-side heat-transfer coefficient during rewetting of a hot dry patch. Nucl ear Engineering and Design 22, 212-224. Thompson, T. S., 1974, Process of rewetti ng a hot surface by a falling liquid film. Nuclear Engineering and Design 31, 234-245. Tian, W. X., Qiu, S. Z., and Ji a D. N., 2006, Investigations on post-dryout heat transfer in bilaterally heated annular channels. Annals of Nuclear Energy 33, 189-197. Tien, C. L., and Yao, L. S., 1975, Analysis of conduction-controlled rewetting of a vertical surface. ASME Journal of Heat Transfer 97, 161-165. Van Dresar, N. T. and Siegwarth, J. D., 2001, Near-horizontal, two-phase flow patterns of nitrogen and hydrogen at low ma ss and heat flux. NASA TP 2001-210380. Van Dresar, N.T., Siegwarth, J.D., and Ha san, M.M., 2002, Convective heat transfer coefficients for near-horiz ontal two-phase flow of n itrogen and hydrogen at low mass and heat flux. Cryogenics 41, 805-811. Velat, C., 2004, Experiments in cryogenic tw o phase flow. Master thesis, University of Florida. Westbye, C. J., Kawaji, M., and Antar B.N., 1995, Boiling heat transfer in the quenching of a hot tube under microgravity. AIAA Journal of Thermophysics and Heat Transfer 9, 302-307. Wright, C. C., and Walters, H. H., 1959, Singl e tube heat transfer tests, gaseous and liquid hydrogen. WADC T echnical Report 59, 423. Xu, J. J., 1998, Flow boiling heat transfer in the quenching of a hot surface under reduced gravity conditions. Ph.D. disserta tion, University of Toronto. Xu, J. L., Wong, T. N., and Huang, X. Y ., 2006, Two-fluid modeling for low-pressure subcooled flow boiling. International J ournal of Heat and Mass Transfer 49, 377386. Yadigaroglu, G., 1978, The reflooding phase of the LOCA in PWRs. Part I: core heat transfer and fluid flow. Nuclear Safety 19, 20-36. Yadigaroglu, G., Nelson, R. A., Teschendorff, V., Murao, Y., Kelly, J., and Bestion, D., 1993, Modeling of reflooding. Nuclear Engineering and Design 145, 1-35. Yamanouchi, A., 1968, Effect of core spray coo ling in transient state after loss of coolant accident. Journal of Nuclear Science and Technology 5, 547-558.

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159 Yang, L., and Zhang, C-L., 2005, Two-fluid mo del of refrigerant tw o-phase flow through short tube orifice. Inte rnational Journal of Refrigeration 28, 419-427. Zivi, S. M., 1964, Estimation of steady st ate steam void-fraction by means of the principle of minimum entr opy production. ASME Journal of Heat Transfer 86, 247. Zoppou, C., and Roberts, S., 2003 Explicit schemes for dam-break simulations. Journal of Hydraulic Engineering 129, 11-34. Zuber, N., 1958, On stability of boiling heat transfer, Transaction of ASME 80, 711-720. Zuber, N., 1959, Hydrodynamic aspects of boili ng heat transfer. Ph.D. dissertation, UCLA.

PAGE 179

160 BIOGRAPHICAL SKETCH Kun Yuan was born in Chongqing, China, on December 24, 1976. After receiving his Bachelor of Science in air-conditioning and refrigeration from the University of Science and Technology of China in 1999, he received a Master of Science degree in cryogenic engineering and refrigeration from the Chinese Academy of Sciences in 2002. In pursuit of a Ph.D. degree in mechanical engineering, Kun Yuan began his studies at the University of Florida in August 2002.


Permanent Link: http://ufdc.ufl.edu/UFE0015664/00001

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Copyright Date: 2008

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Material Information

Title: Cryogenic Boiling and Two-Phase Chilldown Process under Terrestrial and Microgravity Conditions
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
Holding Location: University of Florida
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CRYOGENIC BOILING AND TWO-PHASE CHILLDOWN PROCESS UNDER
TERRESTRIAL AND MICROGRAVITY CONDITIONS















By

KUN YUAN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006





























Copyright 2006

by

Kun Yuan















ACKNOWLEDGMENTS

First, I would like to express my greatest appreciation to my advisor, Dr. Jacob N.

Chung, for his continuous support, encouragement, motivation, and guidance. Without

his direction and support, this work would not have been possible.

My sincere thanks are extended to my committee members, Drs. James F. Klausner,

Renwei Mei, William E. Lear, Jr., and Gary G. Ihas. Thank you for your time,

encouragement, valuable advices, and wonderful classes you gave. Special thanks go to

Dr. Ihas for the help on design of the experimental apparatus, and to Dr. Mei for his

guidance on numerical computation.

I would also like to recognize my fellow graduate associates Renqiang Xiong,

Adam Robinson, and Yun Whan Na for their kindly assistance. Special appreciation is

given to Dr. Jun Liao for the interesting discussion and his helpful suggestion on code

validation.

I am deeply indebted to my parents and my brother for their never-ending love,

dedication, and support through my long journey of study. Finally, I would like to thank

my wife Yan Ji for her continual support, encouragement, and love.















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S .................................................................... ......... .............. iii

LIST OF TABLES ...................... .......... ........ ..................... viii

LIST OF FIGURES ......... ......................... ...... ........ ............ ix

N O M EN C L A TU R E ............... .................................................. .................................xiii

A B ST R A C T .........x.....viii...........................................

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 R research B background ................................................... .... ...... .... .......... .. 1
1.2 Research Objectives .................. ............................. ........... .... ........ 3
1.3 Scope..................................................... . 3

2 BACKGROUND AND LITERATURE REVIEW ..................................................5

2 .1 B a ck g ro u n d ................................................................................. 5
2.1.1 B oiling C urve ....................... ....... ... ........................... ............
2.1.2 Two-Phase Flow Regimes and Heat Transfer Regimes.............................6
2.1.3 Gravity Effect ................ .. ........ .. ...... .......... ................. .9
2.2 Literature Review ................................... .. .. ...... ........... ... 10
2.2.1 Experimental Studies...... ........... .. .... .. ...... ................ 11
2.2.1.1 Terrestrial cryogenic boiling and two-phase flow experiments....... 11
2.2.1.2 Terrestrial chilldown experiments..................................................12
2.2.1.3 Reduced gravity boiling and two-phase flow experiments .............15
2.2.2 M odeling of Chilldown Process .... .......... ....................................... 16
2.2.2.1 H om ogeneous m odel ................................... ........... .................. 16
2.2.2.2 Tw o-fluid m odel ...................................... ........................... ........ 18

3 EXPERIM ENTAL SYSTEM ......................................................... ............... 23

3.1 E xperim mental Setup ............................................. ................... ............... 23
3.1.1 Sy stem O verview ............ .... ........................................ ........ .... .......... 23
3.1.2 F low D riven Sy stem ........................................................... ............... 25
3 .1.3 T est Section ................................................................... 27









3.1.4 Experim mental R ig ............ ................................................. ............... 28
3.2 D ata A acquisition System ..................... ........................... ............... ... 29
3.3 Drop Tower for Providing Microgravity Condition ............... ..................30
3.3.1 Introduction of M icrogravity Facilities ................................. ............... 30
3.3.2 Drop Tower Design and Microgravity Condition ....................................30
3.3.2.1 Release-retrieve mechanism ......................................... ............... 31
3 .3 .2 .2 G u ide w ires ............................................. .................. ..............32
3.3.2.3 D rag shield ........................... .. .. ................ ...... ......... ...... .... 32
3.3.2.4 A irbag deceleration system ................................... ............... ..34
3.3.2.5 External connections ............................................. ............... 35
3.3.2.6 M icrogravity condition.................................. ....................... 35
3.3.3 Safety Sum m ary ............................. .. .. .............. ............ .... .. ...... .. 35
3.4 Experimental Condition and Procedure.....................................................36
3.4.1 Experim ental C ondition......................................... .......... ............... 36
3.4.2 G round T est P rocedure................................................................... ......37
3.4.3 Microgravity Test Procedure ....................................... ...............38
3.5 U uncertainty A analysis ................. .... ... ................................................. 39
3.5.1 Uncertainties of Temperature Measurement ...........................................39
3.5.2 U uncertainty of M ass Flux ................................. ............................. ....... 40
3.5.3 O their U ncertainties.......................... .. .............................. ............... 4 1

4 CRYOGENIC TWO-PHASE CHILLDOWN UNDER TERRESTRIAL
CONDITION ............... ................. ........... ........................... 43

4.1 G ravity-D riven Experim ent...................................................................... .. .... 43
4.1.1 H eat Transfer Study ......................................................... ............... 43
4.1.1.1 W all tem perature profiles...................................... ............... 44
4.1.1.2 D ata reduction .............................. ........ .. .... .......... ....45
4.1.1.3 H eat transfer m echanism s ..................................... ............... ..50
4.1.2 V isualization Study ............................................................................. 55
4.2 Bellow s-D riven Experim ent...................................................................... 59
4 .2 .1 Introduction ................................................................... 59
4.2.2 V isualization Study ............................................................................. 59
4 .2 .3 H eat T ran sfer Stu dy ............................... .......................... .....................62
4.2.4 Phenomenological Model of the Film Boiling Region.............................66
4 .2 .4 .1 M odel description .................................................. .....................67
4.2.4.2 Film boiling correlation......................................... ............... 71
4.2.4.3 M odel evaluation ........................................ .......................... 74
4.3 R ew getting Experim ent ................................................ .............................. 75
4.3.1 Types of Rewetting.................... ..... .... .... ................... 76
4.3.2 Rewetting Temperature and Rewetting Velocity .......................................77
4.3.3 V isualization Study ............................................................................. 83

5 CRYOGENIC TWO-PHASE CHILLDOWN UNDER MICROGRAVITY
C O N D IT IO N ............................ ........................................... 8 5

5.1 Introduction ............................................................................. 85.. ............... .......... 85


v









5.1.1 Film Boiling under M icrogravity .................................... ............... 85
5.1.2 Current Experimental Condition ......................... ...........................87
5.2 Flow Regime Visualization under Microgravity Condition...............................89
5.3 H eat T transfer Study ................ .............................................. .................. .. 90
5.3.1 W all Tem perature Profiles ........................................ ...... ............... 91
5.3.2 W all H eat F lux ..................... .. ........................ .. ...... ........... 94

6 MODELING CRYOGENIC CHILLDOWN .................................. ...............96

6 .1 In tro du ctio n ................. .............. ........ ....... ............... ................ 9 6
6.1.1 Flow Regimes and Transition Criteria ............................ ............... 96
6.1.2 Different Modeling Methods and Current Approach..............................100
6.2 Inverted Annular Film Boiling M odel..... .......... ...................................... 101
6 .2 .1 Introdu action ...........................................................10 1
6.2.2 M odel Description ............... ............ .... .............. .... 102
6.2.2.1 Assumptions and conservation equations .....................................102
6.2.2.2 Heat transfer in inverted annular film boiling............................104
6.2.2.3 Constitutive relations............... ....... ...............107
6.2.3 Boundary Condition and Solution Procedure.........................................109
6.2.3.1 Boundary condition ........._....... .......... ............ .. ............... 109
6.2.3.2 Numerical method and solution procedure ..................................110
6.2.4 Results and Discussion ............... ......................... ....... ........ 112
6.3 Dispersed Flow Film Boiling M odel ........................................ ....... ............ 117
6.3.1 Introduction ........................ ........ .........117
6.3.2 M odel Description ............... .......... ....... ....... .......... ..... 120
6.3.2.1 Assumptions and conservation equations ...................................120
6.3.2.2 Heat transfer in dispersed flow film boiling and constitutive
relations ......... ................................... .. ..... ................... .. 122
6.4 Application of a Two-Fluid Model to Cryogenic Chilldown.................................127
6.4.1 M odel D description ............ ..... ....... .. .......... ..................... 127
6.4.1.1 Fluid flow ............ ........................................................ .... ........ .. 127
6.4.1.2 Heat conduction in tube wall................ ................... 130
6.4.1.3 Initial and boundary conditions.................................................130
6.4.2 Numerical method and solution procedure..............................................131
6.4.3 R results and D discussion .................................... .......................... ......... 131
6.4.3.1 Experimental results ............ ................................. ............... 133
6.4.3.2 M odel results and comparisons.................... ................. ................135
6 .5 C o n c lu sio n s ................................................................................................... 14 1

7 CONCLUSIONS AND RECOMMENDATIONS ........................ ............... 142

7 .1 C o n c lu sio n s ............... ....... ... ............................................... .............. 14 2
7.2 Recom m endations for Future Research ......................................... .................143

APPENDIX

C O D E V A L ID A T IO N ............................................................................ ... ................ 144









A 1 D am -B reak Problem ................................................. ............................. 144
A .2 G rid Independence C heck........................................................ ............... 148

LIST OF REFEREN CE S ....... ................ ........................................... ............... 150

BIOGRAPHICAL SKETCH .................................. ............................. 160
















LIST OF TABLES


Table page

3-1. W working condition of the experiments. ......................................... ...............37

5-1. Basic findings of flow film boiling in previous chilldown experiments .................87

6-1. Post-CHF flow regime transition criteria. ..................................... ............... 99

6-2. Inner wall boundary conditions at different regions ......................... ............130

A-1. Analytical solution of dam-break problem for horizontal frictionless channel......145
















LIST OF FIGURES


Figure page

2-1. Typical boiling curve ..................... ........ ........ ....................

2-2. Two-phase flow regimes inside a horizontal tube ............................................. 7

2-3. Gravity effect on flow regimes ......... ......................... .................9

2-4. Scaling analysis of gravity effects on two-phase flow. ...........................................10

2-5. Different conduction controlled models. ........................................ ............... 18

3-1. Cryogenic boiling and two-phase flow test apparatus.............................................24

3-2. Photographic view of cryogenic boiling and two-phase flow test apparatus. ...........24

3-3. Cryogenic flow driven system ...................................................... ............... 26

3-4. Test section and thermocouple locations ......... ...... .. ......... ...............28

3-5. Drop tower system ................ ........................ .. .............. 31

3-6. Release-retrieve mechanism of the drop tower. .............................. ................32

3-7. Drag shield and the experimental system before a drop ....................................34

4-1. Sketch of the test section and thermocouple locations for gravity-driven test..........44

4-2. Temperature profiles of gravity-driven test at different cross-sections...................45

4-3. Typical curve fit line of the experimental data .....................................................49

4-4. Temperature derivatives calculated by least square fit method and by finite
difference m ethod ............................................. ..... .......... ..... ........ 49

4-5. Bottom wall heat flux and transient wall temperature profiles at the outlet cross-
se ctio n ...................................... ...................................................... 5 1

4-6. Bottom wall heat flux at the outlet cross section as a function of time....................52

4-7. Bottom wall heat fluxes at different axial locations ................................................54









4-8. Characteristics of horizontal chilldown under low flow rate. ................ ............56

4-9. Flow visualizations at different stages of chilldown. ..........................................57

4-10. Propagation of the quenching front ....................................................................... 58

4-11. Typical flow images under different mass flux ............................................. 60

4-12. Thickness of the liquid filaments at different mass fluxes. .......................... ...61

4-13. Length of the liquid filaments at different mass fluxes.......................... .........62

4-14. Temperature profiles of the inlet section with different mass flux........................62

4-15. Temperature profiles of the outlet section with different mass flux......................64

4-16. Middle section bottom wall heat fluxes under different mass fluxes....................65

4-17. Middle section local wall heat fluxes under mass flux of 7.2 kg/m2 ....................66

4-18. Description of the heat transfer mechanism under horizontal dispersed flow
con edition .............. ...................................................... ................ ... .6 8

4-19. Fractional of liquid filament associated area at different wall temperature and
m ass flu x ......................................................... ................ 6 9

4-20. Stable film boiling inside a horizontal tube...................... .... ...............72

4-21. Vapor film thickness and vapor velocity along the vapor channel.......................73

4-22. Comparison between experimental and model results of the bottom wall heat
flux es at outlet section............................................................ ........ ........ 75

4-23. A typical chilldown boiling curve and the corresponding transient wall
tem p eratu re ......... .. ......... ................ ....... ......... ...................................7 8

4-24. Typical temperature profiles during a rewetting test.............................................79

4-25. Axial variation of the averaged rewetting temperature at different mass fluxes.....80

4-26. Comparison of rewetting temperatures between experiments and different
correlations. ........................................... ........................... 82

4-27. Average rewetting velocity under different mass fluxes......................................82

4-28. Visualization result of the rewet process ...................................... ............... 83

5-1. Two-phase flow images under both 1-g and microgravity conditions. .....................89









5-2. Temperature profiles with different mass fluxes in microgravity test.....................91

5-3. Wall temperature response to microgravity............................................................93

5-4. Ratio of heat flux under microgravity to 1-g condition with different flow rates
and comparison with model prediction. ...................................... ............... 94

6-1. Post-C H F flow regime es. ..................................................................... ..................97

6-2. Heat transfer mechanisms in IAFB. .............................................. ............... 106

6-3. Solution procedure of steady IAFB two-fluid model. ..............................................111

6-4. Comparison of wall temperatures between the IAFB model and the correlation
prediction under different heat fluxes ........... ............................. .................. 113

6-5. IAFB model prediction of the liquid velocity and the vapor velocity along the
tube for down-flow, up-flow, and 0-g. ...................... ............................... 115

6-6. IAFB model prediction of different variables along the tube for down-flow, up-
flow and 0-g. ................ .......... .................................. .. .. ........... 116

6-7. Heat and mass transfer mechanisms in DFFB...... .............. ........................122

6-8. Electrical analog of radiation heat transfer in DFFB............................................... 125

6-9. Solution procedure of the cryogenic chilldown model ..........................................132

6-10. Comparison between measured and predicted wall temperatures under 1-g
condition with flow rate of 40cc/s ............................ ............. ............... 136

6-11. Comparison between measured and predicted wall temperatures under 0-g
condition with flow rate of 40cc/s ............................ ............. ............... 137

6-12. Model prediction of wall temperatures at different axial locations under both 1-g
and 0-g conditions. ........................................... ........................ 138

6-13. Effects of inlet flow rate and gravity level on chilldown process. .........................139

6-14. Wall temperature profiles at different time. ........................................................140

6-15. Void fraction along the tube during chilldown............................141

A-1. Dam -break flow m odel. ...... ........................... ........................................ 144

A-2. Comparison between numerical results and analytical solutions at 25s after dam
b reak ............................................................................... 14 6









A-3. Comparison between numerical results and analytical solutions at 50s after dam
b reak ............................................................................... 14 7

A -4. Effect of CFL num ber ......... .................................. .................... ............... 148

A-5. Computation results of void fraction with different grids at a fixed time step of
A t = 0 .0 0 0 1 ................................................................... .... ....... .... 14 9

A-6. Computation results of void fraction with different CFL number at a fixed grid
nu m b er of 2 00 ................................................................................................ 14 9















NOMENCLATURE


a Acceleration [ms2 ]

A Area [m2]

Ca Capillary number

CD Drag coefficient

CFL Courant number

Cp Specific heat capacity [J kg-' K- ]

d Diameter of liquid droplets [m]

D Diameter of the flow channel [ m]

E Liquid droplet entrainment fraction

f Friction factor

FD Drag force [N]

F, Time averaged fraction of bottom wall surface that is associated with liquid

filaments

g Gravitational acceleration constant 9.8[ms-2

G Mass flux [kgm2s-1 ]

h Heat transfer coefficient [ Wm-K-' ]; Enthalpy [ Jkg' ]; Water level [m ]

hL Liquid filament height [m ]









hlv latent heat of evaporation[ Jkg-K-1 ]


hiv Latent heat plus vapor sensible heat content [ Jkg-K- ]

Ja Jacob number

k Thermal conductivity [Wm K ']

m" Mass transfer rate per unit area [kgm-2s ]

m" Mass transfer rate per unit volume [ kgm3s ]

Nu Nusselt number

P Pressure [Pa] ; Perimeter [m]

Pr Prandtl number

q" Heat flux [Wm-2

R Ridius of the flow channel [m ]

R Gas constant

Ra Rayleigh number

Re Reynolds number

S Slip velocity; Suppression factor in flow nucleate boiling

S2 Shock speed [ms1 ]

t Time [s]

T Temperature [K]

AT7 wall superheat [K]

u Velocity [ms1 ]

V Volume flow rate [m3s 1]









We Webber number

x Quality

X, Martinelli parameter

z Position


Greek letters

a Void fraction; Thermal diffusivity [m2s- ]

3 Vapor film thickness [m ]

S, Bottom wall vapor film thickness [m ]

6 Emissivity

IU Viscosity [kgm- s- ]

P Density [kgm-3]

o7 Surface tension [ N m ]

UB Stefen Boltzmann constant 5.67 x 108 [W m-2K-4]

T Shear stress [ N m2 ]


Subscripts

0 Initial value

20 Two-phase

b Bottom wall

Ber Berenson's correlation

CHF Critical heat flux

con Convection









crit Critical

d Droplet

e Equilibrium

evap Evaperation

fb Film boiling

g Gas

i Interfacial; Inner

in Inlet

j Vacuum jacket

1 Liquid phase

lh Liquid heating

max Maximum

min Minimum

o Outer

pool Pool boiling

r Radiation

rw Rewet

s Saturation

u Upper wall

v Vapor phase

vd Vapor to droplet

vl Vapor to liquid

vs Vapor saturated









w Wall

wd Wall to droplet

wv Wall to vapor


Superscripts

Quantity per unit area

'" Quantity per unit volume


Abbreviations

CHF Critical heat flux

DFFB Dispersed flow film boiling

QF Quenching front

IAF Inverted annular flow

IAFB Inverted annular film boiling

IHCP Inverse heat transfer problem

LOCA Loss of coolant accident

SOU Second order upwind

TDMA Tri-diagonal matrix algorithm

TVS Thermodynamic vent system















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CRYOGENIC BOILING AND TWO-PHASE CHILLDOWN PROCESS UNDER
TERRESTRIAL AND MICROGRAVITY CONDITIONS
By

Kun Yuan

August 2006

Chair: Jacob N. Chung
Major Department: Mechanical and Aerospace Engineering

Chilldown or quenching is a complicated process that initiates the cryogenic fluids

transport, and it involves unsteady two-phase heat and mass transfer. To advance

understanding of this process, we conducted both experimental and modeling

investigations.

An experimental apparatus was designed and fabricated to investigate the cryogenic

chilldown process under both 1-g and microgravity conditions. Liquid nitrogen was used

as the working fluid. We found that the chilldown process can be generally divided into

three regions: film boiling region, transition boiling region and nucleate boiling region,

and each region is associated with a different flow regime and heat transfer mechanism.

Under low flow conditions, we observed that the two-phase flow regime is

dispersed flow in the film boiling region. The dispersed liquid phase is in the form of

long filaments as the tube is chilled down, and the vapor phase is generally superheated.

Statistic feature of the liquid filaments was studied and a phenomenological model, in


xviii









which the heat transfer at the bottom is considered as a sum of vapor and liquid

components, was developed.

Microgravity tests were conducted for chilldown in the film boiling region. Bottom

wall heat flux was found to decrease under microgravity condition. Under current

experimental conditions, the gravity effect does not show a strong dependence on wall

temperature and inlet flow rate.

A cryogenic chilldown model was also developed. The model focuses on both

vertical tube chilldown and microgravity chilldown. In this model, the chilldown process

is characterized as four distinct regions, which are fully vapor region, dispersed flow film

boiling region, inverted annular film boiling region, and nucleate boiling region. Two-

fluid equations were applied to the dispersed flow film boiling region and the inverted

annular film boiling region, while the fully vapor region and nucleate boiling region are

depicted by single-phase correlations. The model results show a good agreement with

previous experimental data.














CHAPTER 1
INTRODUCTION

Cryogenic fluids are widely used in industrial, aerospace, and cryosurgery systems

and so on. In these systems, proper transport, handling and storage of cryogenic fluids are

of great importance. The chilldown or quenching process which initiates cryogenic fluids

transport is complicated, involving unsteady two-phase heat and mass transfer, and was

not fully understood until now. Cryogenic chilldown shares many common features with

other industrial processes such as the reflooding process, which is often encountered in

Pressurized Water Reactors (PWR) and Boiling Water Reactors (BWR). Therefore,

further knowledge of the cryogenic chilldown process may be applicable to those

processes also.

In this study, we experimentally investigated the cryogenic two-phase chilldown

process under terrestrial and microgravity conditions, and a numerical model was also

developed to predict the chilldown process.

1.1 Research Background

One important application of cryogenic fluids is in space exploration. Efficient and

safe use of cryogenic fluids in thermal management, power and propulsion, and life-

support systems of a spacecraft during space missions involves transport, handling, and

storage of these fluids under both terrestrial and microgravity conditions. Uncertainties

about the flow regime and heat transfer characteristics pose severe design concerns.

Moreover, the thermo-fluid dynamics of two-phase systems in microgravity encompass a









wide range of complex phenomena that are not understood sufficiently for engineering

design to proceed.

Cryogenic fluids are also widely used in industrial systems. Until the early 1970s,

liquid hydrogen was mainly used by NASA as a rocket fuel; however, development and

growth of commercial markets have since outpaced this use. For example, liquid

hydrogen is used in industrial applications such as metal processing, plate glass

production, fat and oil hardening, semiconductor manufacturing, and pharmaceutical and

chemical manufacturing. Today, the commercial market is many times larger than the

government market.

For any process using cryogenic fluids, chilldown is inevitably the initial stage;

therefore, efficiency of the chilldown process is a significant concern since the cryogen

used to cool down the system is not utilized for propulsion, power generation or other

applications. In a hydrogen economy, chilldown must be accomplished with a minimum

consumption of cryogen for the overall energy efficiency to be within tolerable limits.

Current understanding on chilldown process is, however, very limited. For

example, there is considerable disagreement over the chilldown heat fluxes and whether a

unique rewetting temperature exists (Dhir et al. 1981; Piggott and Porthouse 1975). For

similar experimental observations, quite different explanations were also suggested by

different researchers. For example, it was reported that the rewetting velocity increased

with increasing inlet flow rate, given the same initial wall temperature (Yamanouchi

1968; Duffey and Porthouse 1973). Duffey and Porthouse (1973) suggested that this flow

rate effect is resulted from increasing the wet side heat transfer coefficient with higher

inlet flow. This improves the rate of axial heat conduction and hence leads to a faster









rewetting rate. Thompson (1974), however, argued that the inlet flow rate affects

precooling on the dry side rather than the heat transfer in the wet side.

Another driven force of present investigation comes from the need for further

understanding of the cryogenic chilldown process under low mass flux in a

thermodynamic vent system (TVS) on spacecrafts. A TVS is a system where a small

amount of liquid is withdrawn from a cryogenic propellant tank and vented to remove

heat from the bulk liquid cryogen in the tank and thus lower the tank pressure (Lin et al.

1991; Van Dresar et al. 2001, 2002). The mass flux in TVS system is generally very low.

Systematic experiments for steady state low mass flux cryogenic two-phase flow were

conducted by Van Dresar et al. (2001, 2002), the highly transient chilldown process was,

however, not included.

1.2 Research Objectives

For liquid hydrogen to be adopted as a routine fuel, the chilldown process must be

fundamentally understood. The objective of the experimental investigations in this

research work is to seek a fundamental understanding on the boiling regimes, two-phase

flow regimes, and heat transfer characteristics for chilldown in pipes under both

terrestrial and microgravity conditions. Further more, a cryogenic chilldown model is to

be developed based on the experimental observations and will contribute to the prediction

of the chilldown process.

1.3 Scope

In Chapter 2, background of boiling heat transfer, two-phase flow pattern and heat

transfer regime is briefly introduced. Then previous experimental works for two-phase

flow, chilldown and microgravity boiling are reviewed, followed by a short discussion of

the two-phase flow modeling.









In Chapter, the experimental system, experimental conditions, and experimental

procedure for current study are introduced. The uncertainties of the data measurements

are evaluated. The design and working conditions of the drop tower, which is used to

provide the microgravity condition, are also given.

Chapter 4 presents the ground test results of cryogenic chilldown process.

Visualized flow regimes and heat transfer data with different mass fluxes are discussed.

A phenomenological model is developed based on the experimental observation.

Chapter 5 gives the experimental results of cryogenic two-phase chilldown under

microgravity condition.

In Chapter 6, a two-fluid cryogenic chilldown model is developed for both

microgravity chilldown and vertical tube chilldown. Four regions of the chilldown

process, namely the fully vapor region, dispersed flow film boiling region, inverted

annular film boiling region, and nuclear boiling region, are included in this model.

Chapter 7 concludes the research with a summary of the overall work and suggests

future works.














CHAPTER 2
BACKGROUND AND LITERATURE REVIEW

Cryogenic chilldown involves complex interaction of energy and momentum

transfer among the two phases and the solid wall. Understanding of the boiling

phenomenon, flow regime and heat transfer regime provides foundation for further

insight into this dynamic process. This chapter gives background information of boiling,

two-phase flow regime and heat transfer regime. Previous works on both experimental

and modeling part that related to chilldown and microgravity boiling are reviewed and

qualitatively assessed.

2.1 Background

2.1.1 Boiling Curve

A boiling curve shows the relationship between the heat flux that the heater

supplies to the boiling fluid and the heater surface temperature. According to the typical

boiling curve (Figure 2-1), a chilldown (quenching) process usually starts from point E,

and then goes towards point D in the film boiling regime as the wall temperature

decreases. Point D is called the Leidenfrost point which signifies the minimum heater

temperature required for the film boiling. For the film boiling process, the wall is so hot

that liquid will vaporize before reaching the heater surface which causes the heater to be

always in contact with vapor. When cooling beyond the Leidenfrost point, if a constant

heat flux heater was used, then the boiling would shift from film to nucleate boiling

(somewhere between points A and B) directly with a substantial decrease in the wall

temperature because the transition boiling is an unstable process.









region I: region II: region III: region IV: region V:
natural partial nucleate fully developed transition film boiling
convection boiling nucleate boiling boiling





qmax ..... :....... C- --- E








qmin ... .. --'--
D
A

logAT

Figure 2-1. Typical boiling curve.

2.1.2 Two-Phase Flow Regimes and Heat Transfer Regimes

The flow in cryogenic chilldown process is typically two-phase flow, because the

wall temperature usually exceeds the liquid boiling temperature to several hundred

Celsius in the beginning. The topology of two-phase flow has an important effect on heat

transfer and pressure drop in the flow channel. Therefore, generally the first step in two-

phase flow experiment or modeling is to determine the two-phase flow regime.

Commonly observed flow regimes in horizontal tubes are shown in Figure 2-2.

General descriptions of the two-phase flow regimes can be referred from Carey

(1992) and Van Dresar and Siegwarth (2001). Flow regimes of common two-phase flow

such as air-water have been extensively mapped from experiments. However, the

published data for cryogens are limited.









It is also noted that definitions of the flow regimes are somewhat arbitrary.

Qualitative assessment has not been done yet, and transition criteria between different

flow regimes are not fully understood.


u Bubbly flow




Plug flow




Stratified flow




Wavy flow




Slug flow




_Annular flow


Figure 2-2. Two-phase flow regimes inside a horizontal tube.

Different flow regimes are often associated with different heat transfer regimes.

When phase change occurs as two-phase mixture flows along the channel, as that

encountered in chilldown process, the situation is even more complicated (Carey 1992):

different flow regimes are generally observed at different positions along the channel

length. The sequence of flow regimes will primarily depend on the flow rate, channel

orientation, fluid properties, and wall heat flux.









Some general information could be drawn from the findings of reflooding

experiments designed for hypothetical loss-of-coolant accident (LOCA) in nuclear

reactors, for example, Chan and Banerjee's result for horizontal tube (1981a, b, c) and

Cheng et al.'s work for vertical tube (1978).

When the two-phase flow first enters the hot tube, the liquid phase evaporates very

quickly and forms a vapor film that separates the liquid phase from touching the tube

wall, and the two-phase flow is in film boiling state. Depends on the local quality and

other thermo-hydraulic parameters, the flow regime can be dispersed flow or inverted

annular flow. The corresponding heat transfer regime will be dispersed flow forced

convection, which is also called dispersed flow film boiling (DFFB) in literature

(Yadigaroglu et al. 1993; Andreani and Yadigaroglu 1996; Hammouda et al. 1997; Shah

and Siddiqui 2000), or inverted annular film boiling (IAFB).

As the wall temperature decreases under certain degree, the liquid phase is able to

contact the tube wall. The liquid-wall contacting front, which is often referred as

quenching front (QF) or sputtering region, is characterized by violent boiling associated

with significant wall temperature decrease, and propagates downstream with the flow.

The heat transfer mechanism at the QF is transition boiling, which is more effective than

the film boiling heat transfer. This establishment of liquid-wall contact is called rewetting

phenomenon and has been a research interest for several decades.

After the QF, nucleate boiling heat transfer dominates. For vertical tube, the flow

regime can be annular flow, slug flow or bubbly flow; for horizontal tube, the flow

regime is generally stratified flow. With further wall temperature decrease, the nucleate









boiling stage gradually changes to pure convection until the wall temperature reaches the

steady state, which denotes the end of the chilldown process.

2.1.3 Gravity Effect

Because of the differences in density and inertia, the two phases in two-phase flow

are usually non-uniformly distributed across the pipe under terrestrial condition. The

absence of gravity has important effects on flow regimes, pressure drop, and heat transfer

of the two-phase flow. Surface-tension-induced forces and surface phenomena are likely

to be much more important in space than they are on earth. Actually, all flow-regime-

specific phenomena will be influenced by gravity level. As an example, Figure 2-3

compares the flow regime under both terrestrial and microgravity conditions; the

difference is obvious.











A B


Figure 2-3. Gravity effect on flow regimes. A) Flow regime in 1-g test. B) Flow regime
in microgravity test.

Following is a simple scaling analysis that examines the gravity effects. For annular

flow film boiling in a horizontal tube, the effect of gravity is assessed based on the ratio

of Gr/Re3, where Gr is the Grashof number and Re is the Reynolds number. The gravity

effect is measured by the natural convection contribution characterized by the Gr, while

the forced convective film boiling is scaled by the Reynolds number. According to







10


Gebhart et al. (1988), Re3 is used in the denominator when the flow is perpendicular to


gravity for a horizontal tube. Re2 is used when the flow is in the same direction of


gravity. All the thermal properties are those of vapor because of film boiling. Figure 2-4


shows this ratio with the vapor flow velocity range of 0-0.5 m/s and a AT of 100 C for


the Gr estimation.



Nitrogen
09 .------ -- --------------------------------------- Hydrogen -
0. ....... -- .... -....... ... ....... I I ...... I ...... -------
0.9 ------- ---- ------- ---- --------------------- Hydrogen------






0.3 ---- ------ -------------------- --- ---- ---- -----
0.7



0.6
0.2 -----------------------------------------------------------
0.5
0.4

0.23 -*---- ^--------------- ____----------------------___

0.1 ----- ----- -------------- ------
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Vapor Velocity [m/s]

Figure 2-4. Scaling analysis of gravity effects on two-phase flow.

Based on Figure 2-4, if the vapor velocity is greater than 10 cm/s, then the Gr/Re3


is less than 0.2. The natural convection is negligible for Gr/Re3 less than 0.225 according


to Gebhart et al. (1988). Therefore, a terrestrial gravity experiment with the vapor


velocity greater than 10 cm/s would provide results that mimic the microgravity


phenomenon.


2.2 Literature Review

Cryogenic two-phase flow and chilldown process is a complex problem for the


scientific community to solve. The following summarizes the previous accomplishments


on both experimental and modeling aspect.









2.2.1 Experimental Studies

2.2.1.1 Terrestrial cryogenic boiling and two-phase flow experiments

Numerous studies of cryogenic boiling in 1-g environment were conducted in the

1950s and 1960s. Brentari et al. (1965) gave a comprehensive review of the experimental

studies and heat transfer correlations. For the fluids of oxygen, nitrogen, hydrogen and

helium, it was found that for pool boiling, the Kutateladze (1952) correlation had the

greatest reliability for nucleate boiling, while the Breen and Westwater (1962) correlation

was best for film boiling. Maximum nucleate flux data were reasonably well predicted by

the Kutateladze (1952) correlation. Although these correlations were selected as the best

available, neither has particularly good agreement with experimental data. For the case of

forced convection boiling, Brentari et al. (1965) reported that no correlation was found to

be distinctly better. Some simple predictive methods were found to work as well as more

complex schemes. In all boiling cases, it was questioned as to whether or not the

predictive correlations include all of the significant variables that influence the boiling

process. In particular, it was suggested that more detailed and better controlled

experiments are needed and that more attention to surface and geometry effects is

required.

Another comprehensive review of cryogenic boiling heat transfer addressing

hydrogen, nitrogen and oxygen is given by Seader et al. (1965). It was reported that

nucleate pool boiling results cannot be correlated by a single line but cover a range of

temperature difference for a given heat flux. The spread is attributed to surface condition

and geometry, and orientation. Maximum heat flux can be reduced by about 50% when

going from 1-g to near 0-g. Seader et al. (1965) reported a fair amount of data for film

pool boiling. Film boiling heat flux is reduced considerably at near 0-g conditions. Only a









very limited amount of data is available for subcooled or saturated forced convective

boiling and few conclusions were drawn. The lack of data for cryogenic forced

convective boiling was also reported by Brentari and Smith (1965).

Relatively recent correlations have been published for 1-g saturated flow boiling of

cryogens (Shah 1984; Gungor and Winterton 1987; Klimenko et al. 1989; Kandlikar

1990; Van Dresar et al. 2002) using the Convection number Co, Boiling number Bo and

Froude number Fr as correlating parameters. Klimenko et al. (1989) investigated the

effects of tube diameter and orientation on two-phase nitrogen flow and concluded that in

vertical channels diameter effect was revealed in a transition from convective to less

intensive nucleate boiling when the Froude number of a mixture Frm decreases from 40 to

10. On the contrary, in horizontal non-stratified flow, the reduction of the Frm number

was accompanied by cross-section averaged heat transfer coefficient incensement of 20-

30% in the nucleate boiling region. With Frm > 40, the geometry and orientation did not

affect the heat transfer coefficient. Van Dresar et al. (2001) experimentally studied the

near-horizontal two-phase flow of nitrogen and hydrogen. Unlike most of the other works

which based on turbulent liquid flow, their work focused on laminar liquid flow and the

results for low mass and heat flux flow were correlated with Froude number.

2.2.1.2 Terrestrial chilldown experiments

Research on cryogenic chilldown began in the 1960s with the development of

rocket launching systems. Burke et al. (1960) studied the chilldown process of stainless-

steel transfer lines of 60, 100 and 175 ft long with a 2.0 in. OD. The transfer lines were

quenched by flowing liquid nitrogen. A sight glass was located near the discharge end for

flow phenomena observation. Based on the wall temperature, liquid flow rate, and the









observation, the chilldown process was simply divided into three stages: gas flow, two-

phase flow and liquid flow. However, the flow regime information was lack in the

experiments; moreover, the averaged wall temperature was used in their study. While

other researchers (Bronson et al. 1962) pointed out that circumferential temperature

gradient could be very large in cryogenic chilldown process. Early visualized study of

flow regimes in a horizontal pipe during chilldown can be retrospect to Bronson et al.

(1962). A 50 ft long with 1 in. ID test section was quenched by liquid hydrogen in this

work. Results showed that the stratified flow is prevalent in the cryogenic chilldown

process. Based on their experiments, rudimental models (Burke et al. 1960; Bronson et al.

1962) were also suggested to calculate chilldown time. Differences in flow regimes were

not considered in these models; instead a gross effect was used. The work of both Burke

et al. (1960) and Bronson et al. (1962) based on extremely long transfer lines, it is

doubtful that their results can be applied over a short tube.

Chi and Vetere (1964) studied the chilldown process of hydrogen flowing through

a 2-ft long thin wall copper tube. Thermocouples were installed on the outside wall and in

the center of the tubing to measure the wall and stream temperatures at both the inlet and

the outlet of the test section. The thermocouple beads in the center of the tubing were

treated as control volume and their responses were used to identify different flow

regimes. Chi and Vetere (1964) found that the void fractions were much larger, more than

five times in some cases, than those given by previous investigators (Wright and Walters

1959; Hsu and Graham 1963). They attributed this difference to the effect of non-

equilibrium nature of the chilldown process and concluded that thermodynamic

equilibrium cannot exist in film boiling and transition regimes during chilldown. Another









research work by Chi (1965) used several 26-in long aluminum tubes with 3/16 -in ID

and ODs from 1/2 to 2 inch. Unlike the thin wall copper tubing experiments (Chi and

Vetere 1964), the temperature responses showed that slug flow was not observed until the

aluminum test sections were almost cooled down, and the dominant flow regime was mist

flow.

As mentioned before, chilldown of a hot surface or tube is of fundamental

importance for the re-establishment of normal and safe temperature level following

dryout in a LOCA in nuclear reactors. Liquid water or common refrigerant are usually

used in this type of experiments. For example, Chan and Banerjee (1981a, b, c) and later

Abdul-Razzak et al. (1992) used water to chilldown a preheated horizontal tubes. In their

experiments, the chilldown process was divided into three regions, namely film boiling

region, partially quenched region and totally quenched region. Different heat transfer

mechanisms were involved in different regions.

Kawaji et al. (1985) experimentally investigated the chilldown process inside a

vertical tube with different flow rates. Their results showed that for high flow rate, the

entering liquid will initially boil through film boiling mechanism and then develop into

inverted annular flow, dispersed flow and fully vapor flow, for low flow rate, the

corresponding sequence was saturated boiling, annular flow, dispersed flow and fully

vapor flow.

Recently, Velat (2004) experimentally studied the cryogenic chilldown in a

horizontal pipe using nitrogen as working fluid. Pyrex glass tube with vacuum jacket was

used for visualization. The flow regimes were recorded by high speed camera. Wall









temperature histories and pressure drop along the pipe were recorded and associated with

the visualized images.

2.2.1.3 Reduced gravity boiling and two-phase flow experiments

Because of the experimental difficulties there are very little heat transfer data for

cryogenic flow boiling in reduced gravity. We were able to find just one report done by

Antar and Collins (1997) investigated the cryogenic flow boiling in low gravity

condition. The experimental results of two-phase flow under reduced gravity conditions

using regular working fluids, such as R113, are also summarized here.

Adham-Khodaparast et al. (1995) investigated the flow film boiling during

quenching of a hot flat surface with R- 13. Micro-sensors were used to record

instantaneous heat flux and heater surface temperature. They reported lower heat transfer

rates during microgravity as compared to normal gravity and contributed that to

thickening of the vapor layer. The wall superheat and the surface heat flux at the onset of

rewetting and the maximum heat flux were found to increase with the inlet liquid

subcooling, mass flux and gravity level. The effect of gravity was determined to be more

important for low flow rates and less relevant for high flow rates. The two-phase flow

regimes were not reported in their work.

Another quenching test under microgravity was done by Westbye et al. (1995). A

hot thin-walled stainless steel tube was quenched by injection of subcooled R113 into the

tube under both 1-g and microgravity conditions. The injection mass flux was 160-850

kg/m2s. It was found that the rewetting temperatures were 150C-250C lower in

microgravity than those obtained in 1-g, and the film boiling heat transfer coefficients in

microgravity were less than those in 1-g tests. This resulted in much longer cooling

periods in microgravity. It was also reported that once the tube was cooled sufficiently to









allow axial propagation of the QF, the rewetting velocity was slightly greater in

microgravity. The nucleate and transition boiling curves under microgravity were

reported to be shifted to lower wall superheats as compared to 1-g results.

Antar and Collins (1997) reported cryogenic chilldown process under 1-g condition

and on board a KC-135 aircraft. They observed that a sputtering leading core followed by

a liquid filament annular flow regime. This flow regime is composed of a long and

connected liquid column that is flowing in the center of the tube and is surround by a

thick vapor layer. They attributed the filamentary flow to the lack of difference in the

speed of vapor and liquid phases. On the heat transfer side, they reported that the quench

process was delayed in low gravity and the tube wall cooling rate was diminished under

microgravity conditions. The QF speed was found to be slower under the low gravity

conditions.

2.2.2 Modeling of Chilldown Process

Mainly two types of flow models were developed for chilldown process modeling.

Homogeneous model treats the two-phase mixture as homogeneous fluid, while two-fluid

model considers the difference of the two phases and solves the equations for the

conservation of mass, momentum and energy for each phase.

2.2.2.1 Homogeneous model

The primary assumptions of the homogeneous model are: (1) the fluid, either

single-phase or two-phase mixture is homogeneous; (2) incompressible flow; (3) one-

dimensional flow; (4) thermal equilibrium exists between the two phases.

Burke et al. (1960) developed a crude chilldown model based on their experiments

of quenching large cryogenic piping system. The model was one-dimensional and the

entire transfer line was treated as a single control volume. This lumped system provided a









simple estimation of chilldown time but lacked accuracy due to its broad assumptions and

averaging of fluid properties and flow rates over the chilldown time. Bronson et al.

(1962) developed a one-dimensional model by assuming constant wall-to-coolant

temperature difference along the entire transfer line. This model was used to estimate the

chilldown time, however, it did not permit the estimation of the instantaneous wall and

bulk fluid temperature. Chi (1965) developed an analytical model for mist-flow-

dominated chilldown based on the assumptions of constant flow rate, constant heat

transfer coefficient, constant fluid properties, homogeneous flow and film-boiling-

dominated heat transfer. Steward et al. (1970) modeled chilldown numerically using a

finite difference formulation of the one-dimensional, unsteady mass, momentum and

energy equations. Cross et al. (2002) used the homogeneous model to solve three

chilldown cases with hydrogen as the working fluid: the first case got a simplified

analytical solution; the second case treated superheated vapor flow and the third case

modeled the initially subcooled liquid flow.

In LOCA research, a so-called conduction controlled model was used by many

researchers. By assuming constant wet front speed and introducing coordinate

transformation, the main focus in conduction controlled model was shifted to solve the

steady state conduction equation of the tube wall within a moving reference frame.

The conduction controlled model was first studied by Yamanouchi (1968). The

phenomenon was described by one-dimensional quasi-steady heat conduction in a wall

with two distinct regions. The region covered by the liquid film had a constant heat

transfer coefficient, while the bare region was adiabatic. The major flaw of this model is

the absence of the sputtering region and this leads to unreasonable heat transfer










coefficient. Thompson (1972) suggested the liquid film can be characterized by a

temperature-dependent nucleate boiling heat transfer coefficient, and numerically solved

the two-dimensional heat conduction equation. However, the sputtering region and the

film boiling region were still not considered distinctively. Sun et al. (1974) was the first

one to distinguish and attribute different heat transfer coefficient to these two different

regions. In their model, the one-dimensional heat conduction equation was solved

analytically. Figure 2-5 schematically compares the above three models. Tien and Yao

(1975) further developed the conduction controlled model to two-dimensional and

analytically solved the limiting cases for both small and large Peclet numbers.








I ,T,'L i" ,1'.r,
lnapiiit Boiling








0 h 0 h h
Rrettig Sunet a1.'s Yan~taucli's Thumpson's
Pherntemn Model (1974) Model (1968) Model (1972)


Figure 2-5. Different conduction controlled models.

2.2.2.2 Two-fluid model

Although homogeneous model is simple and has gained success in certain

applications, its drawback is obvious: it can not describe the thermal and hydraulic

differences between the two phases. In the homogeneous model, it is assumed that









thermal equilibrium exists between the two phases, however, for IAFB and DFFB in

chilldown process the vapor phase is generally superheated (Chen et al. 1979; Guo et al.

2002; Tian et al. 2006). The vapor superheat can up to several hundred Kelvin under

some operating conditions. In that situation, predictions by homogeneous model will

inevitably lead to large discrepancy from the experimental results. Moreover, for

stratified two-phase flow, the homogeneous assumption is not valid. Therefore, the

homogenous model is generally not applicable to horizontal pipe chilldown.

In engineering applications, usually only the averaged quantities are of engineering

interest. Thus one of the main approaches for two-phase flow modeling is to average the

local instantaneous conservation equations, while the information lost in the averaging

process is supplied in the form of auxiliary relationships. This leads to the two-fluid

model or separated flow model (Ishii 1975; Banerjee and Chan 1980; Ardron 1980; Ishii

and Mishima 1984). Two-fluid model consists of two sets of conservation equations for

the mass, momentum and energy of each phase. Since the averaged fields of one phase

are not independent of the other phase, interaction terms appear in the field equations as

source terms. For most practical applications, the model can be simplified to the

following forms (Ishii and Mishima 1984):

Continuity equation:

aakPk (a v,)= k (2.1)
at

Momentum equation:

aakPkV +V.(apkVV) = -akV +V ak (k + ) (2.2)
at (2.2)
+ak pg + VF + M Vak ,









Enthalpy energy equation:


akP k kk k +V.(akpkHkVk)=-V.(akk +q
at (2.3)
+a k ~k + HkF +q"/L +
+a k Dt kk ki

Here the subscribe k denotes k-phase and i stands for the value at the interface. L,

denotes the length scale at the interface. Fk, Mk z-, qr, and Dk are the mass

generation, generalized interfacial drag, interfacial shear stress, interfacial heat flux and

dissipation, respectively. These interfacial transfer terms should obey the balance laws at

the interface given as:


Fk = 0
k
Z M, =0 (2.4)
k
Z(FkHkl +cq"tL) = 0
k

Chan and Banerjee (198 la, b, c) developed a two-fluid model for horizontal

chilldown process based on the experimental results of quenching a hot Zircaloy-2 tube,

and pointed out that the propagation of the QF was largely controlled by hydrodynamic

mechanisms instead of by conduction mechanism. The model was one-dimensional and

the vapor phase was assumed to be at saturated temperature. The occurrence of rewetting

at the bottom of the tube was evaluated based on studying of the Kelvin-Helmholtz

instability at the vapor film-liquid interface in the film boiling region. The results agreed

reasonably well with experimental data. Later, a new rewetting criterion based on vapor

film collapse was added into the horizontal two-fluid chilldown model by Abdul-Razzak

et al. (1993).









For vertical tube, Kawaji and Banerjee (1987, 1988) employed the two-fluid model

to predict the thermo-hydraulic criteria for the bottom reflooding problem in steam-water

system. Their model was further developed by Hedayatpour et al. (1993) to model the

chilldown mechanism in a vertical tube with four distinct regimes: fully liquid, inverted

annular flow (IAF), dispersed flow and fully vapor flow. The IAF, which comprised of a

liquid core surrounded by a vapor film next to the tube wall, was considered as

immediately downstream of the quench front. The two-fluid model was used in the IAF

and dispersed flow regimes. A one-dimensional energy equation was formulated for

predicting the temperature history of the tube wall. The model was consistent with the

experimental results. The major drawback of this approach was the requirement of

knowing both the flow pattern as well as the QF speed.

Recently, Liao (2005) did a comprehensive study in modeling the cryogenic pipe

chilldown and achieved good agreement with the experimental data. Three models were

used for different situations. A simple homogeneous model was suggested for simulating

vertical pipe chilldown. A pseudo-steady chilldown model, which is similar to

conduction-controlled model to some extent, was developed to simulate horizontal

chilldown. Coordinate transformation was introduced to eliminate the transient term and

resulted in a two-dimensional parabolic equation. By assuming constant wet front speed,

the main emphasis was to model the heat transfer coefficients for the stratified flow and

the thermal field within the solid pipe. Correlations for film boiling and forced

convection boiling were used for different flow regimes. The study showed that the

current film boiling correlations are not appropriate for the cryogenic pipe chilldown due

to neglecting the information of the flow regime, and a new film boiling correlation was






22


proposed. The predicted pipe wall temperature history matched well with the

experimental results. To include the prediction of the flow fields, a more comprehensive

two-fluid model was also developed and combined with three-dimensional heat

conduction in the solid wall to study the stratified flow regime in a horizontal pipe. The

predicted wall temperature variations showed good agreement with the experimental

measurements.














CHAPTER 3
EXPERIMENTAL SYSTEM

To investigate the cryogenic chilldown process, a cryogenic two-phase flow

experimental facility has been designed, fabricated and tested under both terrestrial and

microgravity conditions. A drop tower is used to provide the microgravity condition. The

experimental system, experimental condition and procedure are introduced in this chapter.

3.1 Experimental Setup

3.1.1 System Overview

Most two-phase flow experimental apparatus are designed as a close loop. The

vapor phase is usually cooled back to liquid through the condenser and then sent back

into the loop. However, the close loop design is not suitable for current cryogenic two-

phase flow experiment. The reasons are first the boiling temperatures of the cryogens are

extremely low, to condense the vapor phase back to liquid phase, special cryocooler must

be used, and this will highly increase the complicity of the system; secondly no common

commercial pump can work at the cryogenic temperature and using cryogenic pump is

not economically possible.

Considering the above reasons, the experimental system is designed as a once-

through flow pass using motor-driven bellows as flow generator. Figure 3-1 shows the

schematic of the experimental system, which locates in two side-by-side aluminum

cubicles and is fabricated for both terrestrial and microgravity experiments. The

experimental system mainly consists of a nitrogen tank, a motor-driven bellows, test

section inlet portion, test section, test section outlet portion, vacuum jacket, vacuum











pump, data acquisition system, lighting and video system. A photographic view of the

apparatus is shown in Figure 3-2.


Standard Rig
SMowving PlnA 1 To Data Ac uistin

Tark Feed Fi edP lathe oc oples and
VaIhe P BeLOWh i ower S3uply
S--Feed V Lil'a
Control
S' J'k Vacunm 3.
Li uid Le.el Fedth ough Vacuumn Acet










Figure 3-1. Cryogenic boiling and two-phase flow test apparatus.
























Figure 3-2. Photographic view of cryogenic boiling and two-phase flow test apparatus.

Nitrogen flow is generated by a motor-driven stainless steel bellows. The test


section is transparent. Temperature measurements are taken at different downstream









locations along the test section when the two-phase nitrogen flow is passing through;

video images are also recorded simultaneously.

3.1.2 Flow Driven System

Following the traditional method to control cryogenic flow (Swanson et al. 2000),

nitrogen flow is generated by a motor-driven stainless steel bellows (Figure 3-3). The

basic idea is using a constant speed motor to pull a moving plate which is attached to the

bottom of a bellows filled with liquid nitrogen. Therefore, a constant volumetric flow rate

can be achieved when the motor is turned on.

The bellows used in the experiment is made by thin-wall stainless steel. It has an

OD of 4.0 inch and a free length of about 7.5 inch. The bellows is inside of a stainless

steel tank, which has an OD of 6.75 inch, ID of 6.35 inch and inner depth of 10.24 inch.

A stainless steel flange is fabricated as the tank cap and a copper O-ring is used to seal

between the tank and the cap. There are two opening on the tank cap, one for feeding

liquid nitrogen to the tank and the other for feeding the bellows. After assembling, the

bellows is at the lower part of the tank, so that the liquid nitrogen in the tank will flow

into the bellows when the tank liquid level is high enough, therefore, a full tank will be a

sufficient condition for the bellows is also full and immersed in liquid nitrogen. The

experimental time is usually only several minutes, during which only a little amount of

the liquid nitrogen surrounds the bellows will be boiled off, and it is assumed that the

flow from the bellows is pure liquid at saturation temperature.

A stainless steel connector welded with a valve is designed and fabricated to

assemble the bellows to the tank cap. The valve is used to fill the bellows and will be

closed manually when the bellows is full. Copper O-ring and Teflon gasket seal are

adopted at top and bottom of the connector, respectively. The bottom of the bellows is










attached to an aluminum plate. The top of the bellows is stationary while the bottom

travels.








Tank I" / 'o
Feeding

Hole









,-" Rods

Depetior1
Kolt.


Figure 3-3. Cryogenic flow driven system.

A commercial constant speed motor is mounted on the tank cap by three brass rods.

The shaft of the motor is coupled with a drive screw, which pulls the bottom moving

plate by three pull rods and therefore compresses the bellows with constant speed when

the motor is turned on. Totally three motors with different speed are used in the

experiments. The bellows compression speed is determined by the motor speed and the

pitch of the drive screw. Foam insulation is applied around the outside of the whole tank

to reduce the heat loss.









Before using the bellows driven system, an insulated reservoir was also used for

ground tests, and the flow is driven by the hydraulic head of the reservoir. With this

configuration the system is easy to control, and the experimental time can be extended

much longer, however, the major drawback is the larger uncertainty of the flow rate

compared with bellows driven system.

3.1.3 Test Section

The test section is a Pyrex glass tube of 25.4 cm long. The ID and OD of the test

section are 11.1 mm and 15.8 mm, respectively. The test section inlet and outlet are

stainless steel tubes. At both ends of the test section, stainless steel adaptors and Teflon

ferrules are used to connect the test section to the test section inlet and outlet portion.

There are 9 drilled holes of approximately 2mm depth in the test section. The

diameter of each hole is 1mm. A total of 15 type-T thermocouples are placed on the test

section, 9 are embedded very close to the inner surface through drilled holes at three

downstream cross-sections. At each cross-section, three thermocouples are located

circumferentially at equal separation distance. The other 6 thermocouples are used to

measure the outside wall temperatures at two cross-sections, also located

circumferentially at equal separation distance. The test section can be rotated along its

axis before being fastened at two ends. Figure 3-4 sketches the test section and the

thermocouple locations in one of the tests.

The test section inlet, test section and test section outlet are enclosed in a vacuum

jacket built from stainless steel vacuum components. Two transparent quartz windows in

the vacuum jacket enable the observation and record of the two-phase flow regimes

inside the test section. The diameter of each window is 7.62 cm. A ceramic sealed

vacuum feed-through flange is used to connect the thermocouple wires from the vacuum










side to the air side. The vacuum is maintained by a potable vacuum pump during the

experiments.






Flow Diection

KKIJBiI f Bacr~n 3 Ke4n 1
-S- .-




4Sarn 4 10,12,13 e,:.n 2 7,3,9

I L54P.-

Figure 3-4. Test section and thermocouple locations.

A CCD camera (CV-730 from Motion Analysis Inc.) set with 1/1,000 sec shutter

speed faces one of the quartz windows to record flow images, while lighting is provided

by a fluorescent light at the other widow.

3.1.4 Experimental Rig

A rig consists of an aluminum frame that houses the experimental apparatus. The

main function of the rig is to secure all the equipment during the microgravity tests. The

important qualities of a rig are:

* Strong enough to withstand the deceleration (with all equipment attached).

* Have sufficient room to house the necessary equipment.

* Minimize weight as much as possible.

Two rigs of 16 inch wide, 32 inch long and 20 inch high are connected and used in

the experiments. Bottom of the two rigs is covered by two thin aluminum plates. For

ground experiments, the flow driven system and the vacuum jacket are fastened to the









bottom aluminum plates. For microgravity experiments, all the equipment include the

light, the CCD camera and the vacuum pump are fastened to the bottom plates and no

part of the equipment can stretch out the rigs. A mirror is used in this situation for

adjusting light path so that the camera can be set inside the rig. To ensure smooth drop

process the equipment need also to be evenly distributed.

3.2 Data Acquisition System

A data acquisition system is built for recording temperatures and flow images

during experiments. Type T thermocouples (Omega) with Teflon insulation are used for

temperature measurement. The gauge size of the thermocouple wires is 30 AWG. The

thermocouples are wired to a screw terminal board and then connected to a 16-channel

thermocouple board (PCI-DAS-TC from Measurement Computing) plugged into the PCI

slot of a computer. The thermocouple board has built in cold junction compensation and

programmable gain ranges. All the thermocouples are tested and calibrated with boiling

nitrogen prior to the chilldown experiments. A Labview program is developed to read the

temperature measurements to the computer. The program has a friendly graphical user

interface and updates the temperature profiles simultaneously during the tests.

Video images are monitored and recorded by connecting the CCD camera to a

frame grabber board (FlashBus MV Lite from Integral) plugged into the PCI slot of the

computer. A commercial software records the flow images and also shows the real-time

images on the computer screen.

For microgravity tests, thermocouple extension wires about 20 m long are used to

connect the thermocouples to the temperature acquisition board, so that temperature data

can be collected during the drop with comparable accuracy.









3.3 Drop Tower for Providing Microgravity Condition

3.3.1 Introduction of Microgravity Facilities

There are mainly four facilities that can provide microgravity environment:

sounding rocket, spacecraft, aircraft flying parabolic trajectories and drop tower. With

continuing increase in microgravity research, many researchers have found, and will

continue to find, the high cost and distant locations associated with many of the world's

microgravity facilities limit their progress. This is especially true for lower-budget, small-

scale research projects. It is also very difficult for many researchers to quickly develop

and perform rough microgravity testing on a new concept or idea. However, drop towers

can be built on-site, are relatively inexpensive to operate, and provide good to excellent

microgravity levels. Compared with other facilities, the available microgravity time from

drop tower is relatively short, however, for many research applications especially those in

the preliminary testing stages, this is not a limiting factor.

3.3.2 Drop Tower Design and Microgravity Condition

An empty elevator shaft located in the Nuclear Science Building at the University

of Florida is used as the foundation for the drop tower. The drop tower is 5-story high and

has a maximum drop height of 15.25 m, which approximately equals to free fall time of

1.7 seconds. This drop tower is a reconstruction of the 2.1 seconds drop tower in the

Washington State University. Many parts came from that 2.1 seconds drop tower and

most of the designs are similar to the 2.1 seconds drop tower also. For more detail of the

drop tower design can refer to the Master Thesis of Snyder (1993).

Figure 3-5 gives the sketch and some dimensions of the drop tower. The drop tower

mainly consists of a release-retrieve mechanism, a drag shield, an airbag deceleration

system, power and experimental control system.
















Shield


Airbag Access
Window



Pressure Relief
Windows


Blower--.


Winch

I-beam
Olbs. Max load

Retrieve
Mechanism

Drag
Shield


Hatch
Door


Guide
Wires


Airbag
144"X79"X83"


Windows


High Density Foam
30" Thick


Figure 3-5. Drop tower system.

3.3.2.1 Release-retrieve mechanism

The release-retrieve mechanism is composed of a steel cross member with two

arms extending out the sides similar to that of the drag shield (Figure 3-6). Before a drop,

the release-retrieve mechanism can lower the experiment and the drag shield down the

shaft to any drop height desired. After a drop, the release-retrieve mechanism can

remotely retrieve the experimental system and drag shield with its self-locking hitches. A

tapered pin release mechanism is designed that uses frictional forces to hold the









experimental system and the drag shield before release. The tapered pin is pounded into

place similar to that of a drill chuck. A solenoid is used to release the frictional forces by

simply allowing the chuck to split open as shown in Figure 3-6. During the release the

tapered pin glides along the chuck and provides a symmetrical release which helps avoid

any rotation. The connection from the tapered pin to the experimental system is also

specially designed to reduce the adverse effects during the release.






I2.. 1 !


ii -"






Figure 3-6. Release-retrieve mechanism of the drop tower.
"c ,T :ii| -








3.3.2.2 Guide wires

Two guide wires stretch the length of the shaft on both sides of the drag shield. The

guide wires are used to keep the drag shield vertical during deceleration and also insure

that the release-retrieve mechanism and the drag shield are aligned for remote retrieval

after a drop.

3.3.2.3 Drag shield

The drag shield is used to isolate the exterior drags that come from the guide wire,

the friction of the air and etc. Bottom section of the drag shield is a semi cylinder filled

with sand as ballast. The purpose of this design is to ensure the impact can be evenly









distributed to the airbag deceleration system during the deceleration period. A cart

matches the shape of the bottom section is used to slide the drag shield. Top section of

the drag shield is rectangular with two arms extending outside to the guide wires. The

bottom section of the drag shield is connected to the top section with the use of 6

enclosed latches, so that the drag shield can be taken apart. When disconnected, the

bottom semi cylinder section can stay on the sliding cart and be slid out from under the

top section. This allows the experimental apparatus to be placed onto the bottom section

and then slid back into place under the drag shield top again, thus, loading the experiment

apparatus. A similar process is followed when unloading the experimental apparatus.

There are two doors on both side of the drag shield, and can also be used for loading

experimental apparatus with light weight.

Figure 3-7 gives the sketch and some dimensions of the drag shield and the

experimental system. Before each drop, the drag shield and the experimental system are

held to the release-retrieve mechanism by the tapered pin. The tapered pin is released

when the drop button is pushed to trigger the solenoid. During the drop, the drag shield

moves slower than the inside experimental system, because there are some resistant

forces on the drag shield from the guide wires and the exterior air while the only resistant

force on the experimental system comes form the inside air, which is also moving with

the drag shield. Therefore, high microgravity level can be achieved on the experimental

system.

To minimize the deceleration impact, it is desirable that the experimental system

hits the drag shield at the same time when the drag shield hits the airbag. However, there









is no effective method to evaluate the drags on the drag shield during the drop. So this is

just ensured by trial and error to find the best drop distance of the experimental system.


Guide Wire


Drag Shield


Tapered Pin Conneted to the Release-
Retrive Mechanism








Experimental System


Ballast


Figure 3-7. Drag shield and the experimental system before a drop.

3.3.2.4 Airbag deceleration system

Airbag deceleration system built at the bottom of the drop tower is used to

decelerate the drag shield at the end of the drop with relatively small impact. The system

consists of 144 x 79 x 83 inch wooden box which encloses a vinyl coated polyester airbag

of approximately the same dimension. High density foam of 30 inch thick is laid down

between the ground and the airbag. There are four pressure relief windows on the box

with two on each side. The windows open at the deceleration period to insure smooth

deceleration process. Windows at opposite sides of the wooden box are connected

together with high tension bungee cord. A one horsepower blower is used to fill the









airbag. The test results show that the airbag deceleration system works efficient and is

simple to use. The same air venting settings can cover a large variety of drop weight and

drop height with no more than 20-g deceleration.

3.3.2.5 External connections

Power, video, data acquisition, and experimental control are all connected

externally in this design. Thus less equipment has to be on the experimental system, and

the data acquisition can be accomplished on a standard PC.

3.3.2.6 Microgravity condition

The drop tower described here is inexpensive to build, easy to operate, has

relatively low deceleration, low release vibration and rotation, and has a good

microgravity level. This drop tower can provide a maximum microgravity time of 1.7

seconds with the microgravity level between 10-5 to 10-4 g.

3.3.3 Safety Summary

Safety is the most important issue in the drop tower microgravity tests. A brief

summary concerning safety issues is given below.

To release the drag shield, a 5V pulse is needed to be sent to the release mechanism

by the computer. A control circuit, which consists of two switches, is added between the

computer and the release mechanism. The first switch is controlled by a key that insures

no one can operate the drop tower without permission. The second is a spring type switch

that is activated only when it is pushed down. Thus if the computer sends a 5V pulse to

the release mechanism "on accident" the solenoid will not get power unless this button is

also pushed.

Four aluminum bars are installed to the ground floor door to enhance and lock the

door while the drop tower is in operation. As mentioned earlier, the two guide wires









insure that the drag shield cannot come off course during the drop. Safety railing is

installed at three sides of the drag shield. The other side is secured when the hatch door is

open. An expanded wire mesh is installed completely around the guide wires in the drop

level in case the wires come loose during a drop. Four cameras are installed to monitor

the drop process, three on the ground level one on the drop level. The drop process is

shown on the computer screen, and a copy is also recorded in the computer, which could

be used for reviewing and improving the design of the drop tower.

3.4 Experimental Condition and Procedure

3.4.1 Experimental Condition

In the experiment, liquid nitrogen is chosen as the working fluid because of its non-

flammable and non-toxic nature. Liquid nitrogen is also inexpensive to use. Before each

test, the tank and the bellows are fed several times until the liquid nitrogen inside the tank

and the bellows is in a quasi-steady state. Since the bellows is totally immersed in liquid

nitrogen, it is assumed that the exit state from the bellows is saturated liquid nitrogen at

latm. The pipes before the test section are also pre-cooled by liquid nitrogen through

bypass lines before the test.

Efforts have been tried to control the back pressure at the exit of the flow. A tank

installed with a check valve is used for this purpose; however, it is found that this method

is not applicable for cryogenic fluids: the liquid boils off very quickly inside the tank and

causes the check valve to open and close frequently, and thus introduces large fluctuation

to the back pressure. So the flow is vented to the atmosphere directly during the tests.

Three constant speed motors are used to drive the bellows. The speed of the motor

is 5 rpm, 10rpm and 15 rpm, respectively. The bellows compression speed is determined

by the driven motor rotation speed and the pitch of the drive screw:









Ybel = V,,tLt (3.1)

in which Vbel is the bellows compression speed, Vro is the motor rotation speed, Lp,, is

the pitch of the drive screw, and the mass flux inside the test section can be expressed as:


G = p ) VrotLplt (3.2)


where G is the mass flux, p, is the saturation liquid density of the nitrogen, D is the ID

of the test section and Dbel is ID of the bellows.

Table 3-1 shows the working condition of the experiments. The vacuum level

during the test is maintained at about 0.9 by a portable vacuum pump.

Table 3-1. Working condition of the experiments.
Motor speed Liquid velocity entering Mass flux Approximated test
(rpm) the test section (cm/s) (kg/mzs) duration limit (minute)
5 0.446 3.606 15
10 0.891 7.205 7.5
15 1.337 10.811 5

3.4.2 Ground Test Procedure

The ground test procedure is as follows:

1. Install the top moving plane at the bottom position of the drive screw.

2. Turn on the light and the camera.

3. Turn on the vacuum pump; make sure the vacuum level is normal.

4. Close the control valve to the test section, open the feeding valve to the bellows
and the tank, and open the valve on the bellows.

5. Feed liquid nitrogen to both the bellows and the tank. This step is repeated several
times until the tank is cooled down.

6. Close the feeding valve and the valve on the bellows.

7. Begin to collect data, run the data acquisition and video record programs.

8. Open the control valve to the test section.









9. Turn on the motor to compress the bellows and liquid nitrogen is introduced to the
test section.

10. Finish one test, turn off everything and loose the bellows.

3.4.3 Microgravity Test Procedure

The microgravity test procedure includes the operation of the drop tower, and is

much more complicated compared with the ground test. The procedure is summarized as

follows:

1. Open the blower to inflate the airbag; check and make sure the air bag and the
windows at the 1st floor work properly. This step is very important for the safe
operation of the drop tower. The airbag must strong enough to provide proper
deceleration for the drag shield and the experimental setup, yet it can not be too
stiff to bounce the drag shield back and cause damage. The stiffness of the airbag is
determined by the tension of the bungee cords connected the relief windows. The
tension of the bungee cords is checked before each drop.

2. Insert and knock in the tapered pin connector to the release-retrieve mechanism.

3. Open the doors on the drag shield and load the experimental apparatus to the drag
shield.

4. Raise the experimental apparatus until it reach the top of the drag shield.

5. Connect the experimental apparatus to the threaded head of the tapered pin.

6. Lift the drag shield up a little so that the sliding card under the drag shield can be
moved out of the space.

7. Lift the drag shield just high enough to open the hatch door on the 5th floor, and
then lower it down for feeding the liquid nitrogen.

8. Follow the ground test procedure from step 1 to step 10. The only difference is that
the feeding pipes are removed after finish. So there is no equipment stretches out
the rigs.

9. Replace the doors on the drag shield; open the two self-locking hitches on the
release-retrieve mechanism. Now the drag shield and the experimental apparatus
are hung by the tapered pin.

10. Raise the drag shield to the drop position and wait the drag shield to stabilize,
recheck every thing on the 5th floor (external wiring video equipment, data
acquisition program, etc.).









11. Turn the first switch, the key switch, on the control. Now the release mechanism
will work and release the drag shield whenever the second switch, the drop button,
is pressed.

12. Turn on the bellows driven motor to generate the nitrogen flow. The driven motor
uses a power cable connects externally to the drag shield. A power outlet with
on/off switch connects the power cable to the wall. So the driven motor can be
controlled at the drop level.

13. Wait for the desired working condition. The temperatures and the flow images are
shown simultaneously on the monitor, so the release can be made at desired
working condition.

14. Push the drop button and release the drag shield.

15. Turn off the driven motor to stop the nitrogen flow.

16. Close the two self-locking hitches on the release-retrieve mechanism; retrieve the
drag shield and the experimental apparatus at the ground floor.

17. Stop the data acquisition program.

18. Check the drag shield and the experimental apparatus when they are retrieved back
to the drop level, and loose the bellows.

19. Check the airbag deceleration system at the ground level and finish one test.

3.5 Uncertainty Analysis

For single sampled experiments, the method introduced by Kline and McClintock

(1953) has been widely used to determine the uncertainty. In current experiments, one

needs to solve the inverse heat conduction problem (IHCP) to get the surface heat flux

from temperature measurements (Ozisik 1993; Ozisik and Orlande, 2000), and simple

equation that relates the measured data to the heat flux does not exist. Therefore, only the

uncertainty of the measurement itself and the uncertainty from the experimental

apparatus will be given here.

3.5.1 Uncertainties of Temperature Measurement

The type T thermocouples used for temperature measurement have the uncertainty

of +0.50C declared by the manufacturer. For highly transient process like chilldown the








response time of the thermocouples is also important. To get quick response, the tip style

of the thermocouples is chosen as exposed and the wire diameter of the thermocouples is

used as smaller as possible. With the wire diameter of 0.25 mm the responding time is

less than 0.2 second according to the chart given by the manufacturer.

Another uncertainty source of temperature measurement comes from the data

acquisition (DAQ) system. The DAQ board for temperature measurement has

programmable gain ranges and A/D pacing, and accepts all the thermocouple types. The

accuracy of the measurement depends on the gain, the sample rate and the thermocouple

type. The uncertainty of type T thermocouple is 0.90C for worst case from the product

specification. For current experiment, the gain is set at 400 and the sample rate is about

60 Hz. It is found that the uncertainty for current settings is about 0.30C.

3.5.2 Uncertainty of Mass Flux

The uncertainty of mass flux ,G is evaluated as (Kline and McClintock, 1953):


aG (G ('G, a G 4 G + a G 3 )
G = -g) +\ -8 + ---8'd_ +\ --83 + --8 2 (3.3)
p P) ODd) s dec vrot Lt Lpt

where 3 is the absolute error. The relative error for mass flux measurement is then:

2 d 2 2 ,2 2 2
S+ 22 dbel+b_22 d V Lt (3.4)
G p) DA D V) V,) L,}

The diameter of the test section has an ID of 11.1 0.2 mm given by the

manufacturer. The absolute error of the bellows ID is within 0.2 mm. The error of the

motor rotation speed is not given by the manufacturer. Simple tests have been conducted

to calibrate the motor rotation speed. For each motor used, let the motor run for a









relatively long time and record the time and the total revolution times, then calculate the

motor speed. It is found that the relative error of the motor rotation speed is with in 5%.

The error of the drive screw pitch can be estimated by measuring the length of several

screw threads and then divide the number of threads. The relative error of the drive screw

pitch is found to be approximately 3%. The error of quoted density data can be formed by

comparing values from different sources. In Appendix II of the book written by Carey

(1992) gives the saturation liquid density of the nitrogen as 807.10kg/m3, while another

book (Flynn 1996) gives the value of 808.9kg/m3. So the relative error of the saturation

liquid nitrogen density is evaluated as 0.22%. From Equation 3.4, the relative error for

mass flux measurement is 6.88%.

Because the diameter of the test section is relatively small and in Equation 3.3 the

diameter term is squared, the error of the test section ID contributes most to the total

error. The uncertainty of the mass flux can be greatly reduced by using tubes with higher

accuracy.

3.5.3 Other Uncertainties

The vacuum level is measured by a vacuum gauge that has the minimum scale of

0.02 bar, so the uncertainty of the vacuum level is approximately 0.01 bar.

Thermocouple feed-through is used to connect the thermocouple wires from the

vacuum side to the air side. For this situation, a third metal other than the two metals

(copper and constantan) used in the thermocouples is introduced in, this will cause error

in temperature measurement unless the third metal in both wires are identical, have the

same length, and are kept at same temperature. These requirements are satisfied in the

experiment, so the error introduced by the thermocouple feed-through is comparably






42


negligible. However, attention must be paid to avoid large temperature gradient along the

feed-through flange during the tests.














CHAPTER 4
CRYOGENIC TWO-PHASE CHILLDOWN UNDER TERRESTRIAL CONDITION

Cryogenic two-phase chilldown under terrestrial condition are experimentally

studied in this chapter. Three different experimental methods have been performed.

Gravity-driven experiments enhance the basic understanding of the chilldown process,

while bellows-driven experiments have more accurate flow control. In rewetting tests, the

test section is pre-cooled so that transition flow boiling and nuclear flow boiling stages

can also be covered. Based on the experimental results, a phenomenological model is

developed. Good agreement is achieved between the model predictions and the

experimental results.

4.1 Gravity-Driven Experiment

In gravity-driven experiments, an insulated reservoir is used to generate the flow

with estimated mass flux of 18-23 kg/m2s by reviewing the recorded flow images. The

results show that the cryogenic chilldown process can be divided into three stages

associated with different heat transfer mechanisms.

4.1.1 Heat Transfer Study

For horizontal tube orientation, the two-phase flow is generally stratified because

of the gravitational force. Therefore bottom of the tube is chilled down first. The heat

transfer mechanism at the bottom of the tube includes film boiling, transition boiling, and

nucleate boiling, while the heat transfer mechanism at the top of the tube is mainly

convection to superheated vapor.






44


4.1.1.1 Wall temperature profiles

Wall temperatures are measured by 16 thermocouples, 9 are embedded very close

to the inner surface of the tube wall; the other 7 thermocouples measure the outside wall

temperature of the test section. The thermocouple locations are shown in Figure 4-1 and

different from that described in Chapter 3. The unit for dimension is mm.


7 5 2
13 -- --11
16- .- .... l 14 1 0-7 ,*.i, -il 8 4- ,,t7,i -


Flow Direction 1 5 93


70 -70- 70-------






----- ----------------- --------------0---------- ----------------------- ---- ------
210-

Figure 4-1. Sketch of the test section and thermocouple locations for gravity-driven test.

Figure 4-2 gives the temperature profiles at the inlet and middle section. It is found

that large temperature difference exists between the top and bottom of the test section,

which was also reported by Bronson (1962) in the experiments of chilldown heavy-wall

transfer line. This temperature difference suggests different heat transfer mechanisms are

encountered at the top and the bottom of the test section. Since the two phases are

separated by gravitational force, the heat transfer mechanism at the bottom is boiling heat

transfer, while the heat transfer at the top is forced convection to the vapor phase.


























0 50 100 150 200 250
Time (s)


300 350


A


0 50 100 150 200 250 300 35(
Time (s)
B
Figure 4-2. Temperature profiles of gravity-driven test at different cross-sections. A)
Inlet section. B) Middle section.

4.1.1.2 Data reduction

In boiling heat transfer experiments, surface heat flux as a function of wall super

heat is often of particular interest, because it denotes different heat transfer mechanisms

and is crucial for engineering applications. However, in chilldown or quenching

experiments surface heat flux is not controllable. The surface heat flux can be inferred









from the temperature history by solving the IHCP. For quenching of vertical tube, in

which axial-symmetrical assumption is generally held, the situation is much simpler.

Based on exact solution of the IHCP, Burggraf (1964) developed a method to obtain the

temperatures and heat fluxes at the inside tube wall from the temperature history data of

the thermocouple welded on the outside of the test section:

2
T=T+ r I- 21n -
4a ir ri dt
(4.1)
(1 22 r 4 r2 2\d2
+ (4 -5r4 lnr o lnr+ +...
64a22 2 8a2 ro 16a2 ro 16a2 dt2

where r and ro denote the inner and outer radius, respectively; T and T are the inside

wall temperature and temperature measured by thermocouple, respectively; a is the

thermal diffusivity of the wall. Then the inside wall heat flux with the first three leading

terms can be written as (Iloeje et al. 1975):

,, rz2 rf dT+((c)2 r3 4l d2T

S2r,) dt k 16 16r, 4 ro dt2

q(pc)3 (5 3rr, 343 r r6 2 3 r d3
k2 384 128 128 384r 32 ro 32 r dt3

For horizontal chilldown experiments, the axial-symmetrical assumption is not

valid, and the solution of the IHCP surfers from ill-posedness. In order to calculate heat

transfer data from the transient temperature profiles, an energy balance is performed

locally on a control volume of the tube wall at thermocouple location. The change in

stored heat in the control volume is equated to the heat transported to the fluid and heat

transferred by conduction, minus losses to the environment. This method was used by

many researchers in analyzing data from quenching tests (Abdul-Razzak et. al 1992;









Westbye and Kawaji 1995; Chen et al. 1979). The inside wall heat flux is then given as:


q -dT + k 2 d2T (q" + q )+ q" (4.3)
S 2r, dt U2 2r, dt2 r r dp

The first term in the right-hand-side (RHS) of Equation 4.3 comes from the change

of the stored heat in the control volume and is the dominant term in chilldown

experiments. It is also interesting to note that this term equals the first term from the

IHCP solution given in Equation 4.2.

To estimate the axial heat conduction term in rewetting experiments, Chen et al.

(1979) assumed a constant rewetting velocity U, and the axial temperature gradient

(dT/dz) was represented by(1/U)(dT/dz). Then the effect of the axial conduction on

the inside wall heat flux can be evaluated from the second term in the RHS of Equation

4.3. The axial conduction term is generally very small, and it is only important at location

near the quenching front, where maximum axial temperature gradient exists between the

dry side and the wet side of the wall. A comparison between heat fluxes based on a 2-D

heat transfer model (Cheng 1978), which considers the axial heat conduction, with those

obtained by neglecting axial conduction was given by Cheng et al. (1979). The

comparison for the copper test section showed that the two mid-plane boiling curves were

approximately the same and the net axial conduction at the mid-section is negligible

small. In our experiments, the temperature measurements show that the axial temperature

gradient is relatively small, and additionally the heat conductivity of the glass is much

smaller than that of the copper used by Cheng et al.(1979), therefore the axial heat

conduction along the test section is neglected in heat flux calculation. It is left in

Equation 4.3 only for integrity.









The third term in Equation 4.3 accounts for the contribution from the radiation and

natural convection inside the vacuum jacket. The details of how they are evaluated will

be given later.

The last term in Equation 4.3 comes from the circumferential heat transfer. Here,

d(p is the azimuthal angle of the control volume and depends on the size of the control

volume. In our calculation, the control volume is approximately assumed to be in thermal

equilibrium with the embedded thermocouple. Based on this assumption, the control

volume size is chosen with an average arc length of 2.0mm. The circumferential

temperature gradient is calculated by linear interpolation between the thermocouple

measuring points.

Derivative of the temperature history is needed in calculating the first term in

Equation 4.3. Generally, the finite difference method is not suitable to obtain the

temperature derivatives, because it is very susceptive to small fluctuations, which are

inevitable in measurements. Therefore, a least square technique, proposed by Iloeje et al.

(1975) in similar situation, is used to get smooth profiles. To increase accuracy, the

temperature data are divided into segments and the order of the curve fit used for each

segment is made as high as possible (but less than 6, otherwise will subject to

temperature fluctuations) without reintroducing irregularities inherent in the pure data.

Figure 4-3 shows a typical result obtained with the least square fit procedure, and Figure

4-4 compares the first term in Equation 4.3 calculated from the least square fit line with

that from the finite difference method. It is clear that the finite difference method is not

suitable for calculating the derivatives of measured temperature profiles.



























0 5 10 15 20 25 30
Time (s)

Figure 4-3. Typical curve fit line of the experimental data.


30000
A -- Least Square Method
25000 -A- Finite Difference Method

E
20000
r \A
15000
LL

I 10000

5000

0 .
0 5 10 15 20 25 30
Time (s)

Figure 4-4. Temperature derivatives calculated by least square fit method and by finite
difference method.

Assume the vacuum jacket and the test section as long concentric cylinders, the

radiation contribution to the heat flux, q "d, is obtained by (Incropera and Dewitt 2002;

Liao 2005):


o Measured Data
- Lease Square Fit Line









B (T4 T4(44)
rad (4.4)
-+


where o(B is Stefen Boltzmann constant, T is the temperature of the vacuum jacket,

and is assumed to equal room temperature, To is the outer wall temperature of the test

section, s, and er are emissivity of the vacuum jacket and the test section, respectively,

and ro and r are outer radius of the test section and the inner radius of the vacuum

jacket, respectively.

To evaluate the natural convection heat transfer due to the residual air inside the

vacuum jacket, Raithby and Hollands' correlation (Raithby and Hollands 1975; Liao

2005) is used:

k
q"n e (T T (4.5)


where kef is the effective thermal conductivity given by Raithby and Hollands (1975).

4.1.1.3 Heat transfer mechanisms

The data reduction method given above is used to analyze the transient temperature

measurements. Left part of Figure 4-5 shows the calculated bottom wall heat flux as a

function of bottom wall temperature at the outlet cross-section, while the right part

represents the corresponding temperature profiles.

The shape of bottom heat flux is similar to the boiling curve from steady-state pool

boiling experiments. This suggests that the chilldown process may share many common

features with pool boiling experiments. Following the method to characterize different

heat transfer mechanisms in pool boiling experiments, a maximum or critical heat flux










(CHF) q"H and a minimum heat flux qmi are used to divide the chilldown heat transfer

into three stages, which are film boiling, transition boiling and nucleate boiling, as shown

in Figure 4-5.

Wall Temperature (K)

--o-Bottom Wall Heat Flux I o -oo" 300- Upper Thermocouple 1
Initial Effect 275- Upper Thermocouple 2
-o- Bottom Thermocouple
250
"mn 225- Film Boiling
.-- -- -- -- -- ------- ^ - -- -_^ _. - --- ----- -------- ^ --
0' 1_500_O-. Transition Boiling
175
- ----- 6 Nucleate Boiling
qCHF 150
125
p 1 IpI I I p I I
50 40 30 20 10 0 0 100 200 300
Heat Flux (kW/m2) Time (s)

Figure 4-5. Bottom wall heat flux and transient wall temperature profiles at the outlet
cross-section.

Initially, the wall temperature is very high, liquid nitrogen evaporates drastically

when enters the test section; a vapor film will form and separate the liquid from

contacting the wall, the two-phase flow is therefore in film boiling state. At decreased

wall temperature, the liquid begins to contact the wall; the heat transfer mechanism is

transition boiling, which is characterized by increasing wall heat flux with decreasing

wall superheat that contrary to what in the film boiling region and nucleate boiling region.

After passing the CHF point the heat transfer mechanism then changes to nucleate boiling.

The calculated bottom wall heat flux as a function of time is shown in Figure 4-6. It

is obvious that the time of transition boiling is very short compared with the other two

boiling stages.










45 | -o-Bottom Wall Heat Flux
40 -
S .Film Boiling Transition Boiling
Nj 35 -


25
S20 -

N 15 ucleate Boiling
10
5
0 I *II I
0 50 100 150 200 250 300
Time (s)

Figure 4-6. Bottom wall heat flux at the outlet cross section as a function of time.

Similarity between the chilldown boiling curve and the pool boiling curve naturally

leads one to compare the chilldown data with pool boiling correlations. The comparisons

between the two turning points, namely the minimum heat flux and the CHF, are given

below.

For steady state film boiling, the correlation developed by Zuber (1959) is widely

used to predict the minimum heat flux:


q gCh -(P Pv) (4.6)
(in = Ch p p )2 (4.6)


here, o is surface tension; g is gravitational acceleration; hv is the latent heat of

vaporization, while C was variously given as 0.177 (Zuber 1959), 0.13 (Zuber 1958), or

0.09 (Berenson 1961). The resulting q"mi is then 13.0kW/m2, 9.6 kW/m2 and

6.6kW/m2, respectively. In Figure 4-5, the qm'in for chilldown is calculated as

13.3 kW/m2, which is a slightly larger than steady state prediction with C = 0.177.









Based on the similarity between the CHF condition and column flooding,

Kutateladze (1948) derived the following relation for the pool boiling CHF:


q" = 0.131hjp, 0(P (4.7)
qCHF 2 _(47)


Zuber (1959) got the identical correlation based on the analysis of Taylor and Helmholtz

instability. For liquid nitrogen under atmospheric pressure, Equation 4.7 gives a CHF

value of 160.7kW/m2 The chilldown measurement in Figure 4-6 is only about 27% of

this value. This big discrepancy is believed to come from the different experimental

condition between the chilldown and the pool boiling tests. In pool boiling experiments,

the heat supplied to the fluid is maintained by a heater, while in chilldown tests it comes

from the stored heat in the tube wall. In the film boiling region, the heat flux is generally

small, therefore the tube wall can maintain a near constant heat flux condition and

function like the heater used in the pool boiling tests. However, in the transition boiling

region, the stored energy in the tube wall is depleted so quickly that the experimental

condition is very different form that of the pool boiling tests. The limited energy stored in

the tube wall put a restriction on the value of CHF, which, therefore, is much less than the

pool boiling data. Previous work by Bergles and Thompson (1970) also concluded that

quantitively the differences between chilldown and steady-state boiling curves can be

very large.

In Equation 4.6 and Equation 4.7 the minimum heat flux and CHF are not

correlated with the thermal properties of the wall for pool boiling tests. However, as seen

from above, the available heat flux to the flow is closely related to the energy stored in

the wall. Therefore, the thermal properties, e.g. thermal conductivity, heat capacity, of the










wall are expected to play a role in the chilldown process. For example, for a wall with

higher thermal conductivity, the energy transferred to the flow can be more quickly

supplied by the surroundings, and therefore will result a higher value of CHF.

Figure 4-7 shows the calculated heat flux in different axial locations. It is found

that both the CHF and the minimum heat flux decrease with increasing axial distance

from the inlet. This is also associated with an increase in the rewetting temperature.


50 --- inlet section
/ P -o- middle section
40 outlet section





0
2 20

CUI I *
S10



100 120 140 160 180 200 220 240 260 280 300
Temperature (K)

Figure 4-7. Bottom wall heat fluxes at different axial locations.

In most of the previous quenching experiments, the film boiling heat flux was

reported as either keeps a relatively constant value (Westbye et al. 1995; Cheng and

Ragheb 1979) or decreases as the test section is chilled down (Ganic and Rohsenow

1977; Bergles and Thompson 1970). In our experiments, however, the local heat flux first

increases in a short period then decreases gradually. This is consistent with the transient

nature of the experiments. Generally the increasing period is expected to be shorter at

higher mass flux if the other conditions are kept the same. The mass fluxes in previous

investigations were much larger than that in current experiments, and therefore associated









with very short increasing time of the heat flux in the film boiling regime. This might be

the reason that the increases of the heat flux were not recorded before.

4.1.2 Visualization Study

Heat transfer analysis shows the chilldown process can be divided into three stages

with each stage associated with different heat transfer mechanisms. The visualization

study casts more light on the characteristic of flow regimes during the chilldown process.

Figure 4-8 illustrates the overall chilldown sequence in our experiments, while

some selected flow images in different region of chilldown are shown in Figure 4-9. In

the beginning of the film boiling region, the flow pattern is basically dispersed flow, in

which the liquid phase is dispersed as near spherical drops within a continuous vapor

phase. The void fraction of the two-phase flow decreases as the tube is chilled down, and

long liquid filaments, separated from wall by a thin vapor film, are observed to flow

along the tube bottom. The length of the liquid filaments generally increases with

decreasing wall temperature. For short liquid filaments, the flow regime is close to

dispersed flow, while for very long filaments, the flow regime can be classified as highly

skewed inverted annular flow. In the film boiling region, heat is primarily transferred

from the wall by conduction through the vapor film and thus evaporate the liquid

filaments, and by convection to the vapor phase.

Once the bottom wall temperature has been reduced low enough, transient boiling,

characterized by intermittent liquid-wall contact and violent bubble generation, is

observed. Shortly after the transient boiling, a continuous liquid-wall contact is

established and the liquid nitrogen begins to pile up on the bottom wall. Many nucleation

sites are observed to be suppressed as the wall temperature keeps decreasing. The









prevailing boiling regime is nucleate boiling and the flow pattern is stratified flow or

wavy flow.

Previous horizontal quenching tests (Chan and Banerjeel981a; Abdul-Razzak et al.

1992) showed the same sequence as our experiments, however, with different flow

regimes mainly in the film boiling region. In their experiments, the flow regime in film

boiling was inverted annular flow. The thickness of the liquid core increases with

decreasing wall temperature, and then follows the stratified flow regime. While in our

experiments, the thickness of the liquid filament is generally a constant, instead the liquid

thickness increases in the nucleate boiling region as shown in Figure 4-8.


*



Quenching Front Liuid Filaments

Nucleate Boiling- Transition -Film Boiling
Boiling

Figure 4-8. Characteristics of horizontal chilldown under low flow rate.

The difference in flow regimes is believed mainly due to different flow rates. The

flow rate in the test of Chan and Banerjee (1981a) was about 150-450 kg/m2s, while it


was even higher (400-1300 kg/m2s) in the experiments by Abdul-Razzak et al. (1992).

In current chilldown test, the flow rate is much lower. The heat stored in the tube wall

causes dry-out of the liquid phase in the film boiling region and thus leads to the

dispersed flow.

The visualization study also gives the detail of propagation the quenching front and

how the liquid rewets the tube wall (Figure 4-10). The arrow in Figure 4-10 indicates the

limit between the quenching front and the nucleate boiling region.












4 t i,

/11


C-.~
rI


Figure 4-9. Flow visualizations at different stages of chilldown. A) Initial stage. B)
Film boiling stage. C) Transition boiling stage. D) Nucleate boiling stage.


ul I- 1""~














Quenching Front
/


Figure 4-10. Propagation of the quenching front.

As shown in Figure 4-10, the quenching front is characterized by vehement bubble

generation and intermittent liquid-wall contact. Following the quenching front, a

continuous liquid-wall contact is established, the flow regime changes to stratified flow,

and many nucleation sites are suppressed.









4.2 Bellows-Driven Experiment

4.2.1 Introduction

The flow rates in current bellows-driven experiments are very low. As a

comparison, previous quenching experiments were generally conducted with flow rates

higher than 40 kg/m2s For example, the liquid nitrogen flow rate was in the range of

550-1940 kg/m2s in the experiments of Antar and Collins (1997) and was 40.7-

271.3 kg/m2s in the experiments of Iloeje et al. (1982), while the flow rate of R-113 used

by Westbye et al. (1995) was from 160 to 850 kg/m2S No experimental work has been

reported for cryogenic chilldown process under relatively low flow rate.

On the other hand, further understanding of the cryogenic chilldown process at low

flow rate is of crucial importance for some applications, for example the cooling process

in the TVS on a spacecraft. The mass flux in a TVS system is generally very low, in

steady state test by Van Dresar et al. (2001, 2002) the nitrogen mass flux ranged from3.3

to 33 kg/m2 The highly transient chilldown process under low flow condition has not

been fully studied.

In present study a horizontal test section is quenched by the liquid nitrogen flow

with mass flux form 3.6 to 10.8 kg/m2s, the flow regimes and heat transfer behavior are

studied experimentally, and a phenomenological model is developed based on the

experimental observations.

4.2.2 Visualization Study

The test section is initially at room temperature. The visualization study shows that

in the film boiling region the flow regimes are similar to that illustrated in Figure 4-8.

When the chilldown is initiated, the liquid phase is in the form of droplets that bounce









back and forth on the bottom wall while traveling downstream. As the wall temperature

decreases, the liquid droplets tend to form filaments and settle down on the bottom wall.

Images of typical liquid filament at different mass fluxes are shown in Figure 4-11.


A


C

Figure 4-11. Typical flow images under different mass flux. A) Mass flux of 3.6kg/m2s.
B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8 kg/m2s.







61


Generally, the thickness of the liquid filaments does not change much as the test

section is chilled down; however, the length of the filaments increases with increasing

mass flux and decreasing wall temperature. The drop-wall interaction from several

experiments was summarized by Ganic and Rohsenow (1977). They listed the most

frequently observed states of drop-wall interaction and the interaction sequence, as the

wall is cooled down. Current observations generally agree with their summarization.

The statistic feature of the liquid filaments is shown in Figure 4-12 and Figure 4-13.

It is clear that the thickness of the filaments shows very limited increase with increasing

mass flux and does not present a strong correlation with the wall temperature; the length

of the filaments, however, is more scattered at higher mass fluxes and lower wall

temperatures. In other wards, the probability of observing a longer liquid filament is

larger under higher mass flux and lower wall temperature.


6
A 3.6kg/m2s
o 7.2kg/m2s
E + 10.8kg/m2s
v 4

)+ + +
S+ + + o

2+ 0 +

E L"0o
EU A 0 0
LLI o
"5 0


180 200 220 240 260 280 300
Bottom Wall Temperature (K)


Figure 4-12. Thickness of the liquid filaments at different mass fluxes.







62



30
A 3.6kg/m2s
25 7.2kg/m2s
E + 10.8kg/m2s

+ + +
20 +
) + +
E 15 + +
S + 0 +
o + ++ + o0
I 10 ,. V + 0
So10 0 + 0 o + o o o



o0

I I I I I I*I
180 200 220 240 260 280 300

Bottom Wall Temperature (K)
Figure 4-13. Length of the liquid filaments at different mass fluxes.

4.2.3 Heat Transfer Study

The temperature profiles measured from the embedded thermocouples at the inlet

and the outlet cross-sections with different mass fluxes are shown in Figure 4-14 and

Figure 4-15, respectively.



300 TC 1
-----TC2
'--... TC 3
280 -

260 ,

_- 240 -
E
I--
220 --

200 "-

180
0 100 200 300 400 500 600
Time(s) A
Figure 4-14. Temperature profiles of the inlet section with different mass flux. A) Mass
flux of 3.6 kg/m2s. B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8 kg/m2s.


























0 50 100 150 200 250
Time (s)


0 25 50 75 100 125 150 175
Time (s)


Figure 4-14. Continued.

It is obvious that the bottom wall of the test section is chilled down more quickly,

because most of the liquid phase is confined at the bottom. The temperature difference

between the bottom and the top of the test section is found to increase with increasing

mass flux at each cross section.






64


The quality of the two-phase flow and vapor superheat generally increase along the

test section, consequently, the temperature difference between the top and bottom wall is

expected to be smaller at further downstream locations. This is confirmed by comparing

Figure 4-14 with Figure 4-15.


0 100 200 300
Time(s)


0 50 100 150 200
Time (s)


400 500 600


250 300


B
Figure 4-15. Temperature profiles of the outlet section with different mass flux. A)
Mass flux of 3.6 kg/m2s. B) Mass flux of 7.2 kg/m2s. C) Mass flux of 10.8
kg/m2s.


























0 25 50 75 100 125 150 175
Time (s)


Figure 4-15. Continued.

The calculated middle section bottom wall heat fluxes under different mass fluxes

are shown in Figure 4-16 as a function of the local wall temperature. The bottom wall

heat fluxes first increase during the initial stage, and then decreases gradually with

decreasing wall temperature.


12000

10000

8000

6000

4000

2000

0


180 200 220 240 260 280 300
Wall Temperature (K)

Figure 4-16. Middle section bottom wall heat fluxes under different mass fluxes.












Figure 4-17 shows the local heat fluxes at three circumferential locations at the

middle cross-section as a function of local wall temperature under a mass flux of

7.2 kg/m2s. It is found that the two heat fluxes at the upper portion of the test section

increase at the beginning during the chilldown process, and then maintain at almost

constant values. The heat fluxes at the upper portion of the test section are much smaller

than the bottom wall heat flux in a wide wall temperature range. Because the upper wall

losses heat mainly by convection to the superheated vapor, while the main heat transfer

mechanism at the bottom wall is film boiling, and is more efficient than convection.



8000 --TC4
-o- TC5

6000 -
E

x 4000


T 2000



180 200 220 240 260 280 300
Wall Temperature (K)

Figure 4-17. Middle section local wall heat fluxes under mass flux of 7.2 kg/m2s.

4.2.4 Phenomenological Model of the Film Boiling Region

For dispersed flow film boiling (DFFB), it is widely accepted that a significant

thermodynamic non-equilibrium condition exists between the vapor phase and the liquid

phase (Laverty and Rohsenow 1967; Koizumi et al. 1978; Chen et al. 1979; Chung and

Olafsson 1984; Tian et al. 2006). A model for vertical dispersed flow boiling suggested

by Koizumi et al. (1978) assumed that heat transfer takes place in steps: from the wall to









the vapor and then from the vapor to the droplets suspended in the stream; and from the

wall to the droplets in contact with the wall. Chen et al. (1979) proposed a model for

post-CHF region that considered the total heat transfer as a sum of vapor and liquid

components and ignored radiation heat transfer to the two-phase mixture.

During the chilldown process, the inlet quality and vapor superheat are not

constants but change with time and mass flux, and are hard to identify from the

experiments. Therefore, a phenomenological model, which also includes information

form visualization results, is developed to analyze the dispersed flow boiling heat

transfer.

4.2.4.1 Model description

As mentioned before, the visualization shows that except in the very beginning

stage, most of the liquid filaments are flowing along the bottom of the tube. Consequently,

in this model the heat transfer mechanism at the bottom of the test section is considered

as the sum of vapor and liquid components, while the heat transfer mechanism at the

upper portion of the test section is forced convection to superheated vapor. It has been

shown (Guo and Mishima 2002; Tian et al. 2006) that for wall superheat up to several

hundreds Kelvin the radiation heat transfer in post-dryout dispersed flow is generally

negligibly small. It is also judged that thermal radiation is minor in our case; therefore

radiation heat transfer is ignored in this model.

The heat transfer mechanisms in this model are illustrated in Figure 4-18. As an

idealization, the liquid filaments are modeled as half cylinders in a film boiling state and

move along the bottom of the tube. The filaments are at the saturation temperature and

separated from the tube wall by a thin vapor film. The bottom wall heat flux is a sum of

vapor and liquid components, and can be written as:









q =q"FL +q2(1- FL)=qFL + q c (1- FL) (4.8)

where q" is the effective bottom wall heat flux, and q" is the heat flux from the portion

of the bottom surface where a liquid filament is in the vicinity and separated from the

wall by a thin vapor film, therefore, q" is a film boiling heat flux. q, co is the heat flux

from the bottom surface where there is no liquid filament around, so it is due to pure

forced convection to the superheated vapor. FL is defined as the time averaged fraction

of bottom wall surface that is associated with liquid filaments.


I u
I




Superheated
Vapor


Liquid Filament



qb2q '
T "b

Typical Model Section

Figure 4-18. Description of the heat transfer mechanism under horizontal dispersed flow
condition.

The upper wall of the test section is fully in contact with the vapor phase, and the

upper wall heat flux is described as:

q" = q F (- FL ,,,,F +FL coq 2 (1-FL) (4.9)

where q" is the effective upper wall heat flux, and q"' con is the convective heat flux to










the superheated vapor for the portion that is directly opposite to the bottom portion that is

associated with liquid filaments as shown in Figure 4-18. q", con2 is for the portion that is


directly opposite to the bottom portion that is not associated with liquid filaments. q" con


and q' con2 are different due to different bulk vapor velocities in their respective sections.


The fractional of liquid filament associated area FL is expected to increase with


increasing mass flux and decreasing wall temperature. The transient liquid fractions in

recorded frames are widely scattered. Therefore FL is calculated by averaging over a


certain time period, the result is shown in Figure 4-19. The fitted linear curves in Figure

4-19 are used in the model calculation.

0.40
Experiments Model
0.35 3.6kg/m2s o
7.2kg/m2s A -
0.30 + 10.86kg/m2s +
+
0.25 + +
+ +
+


0.15
u- 0.20 A + -A



0.10
0 0 o
0.05 o o

180 200 220 240 260 280 300
Wall Temperature (K)

Figure 4-19. Fractional of liquid filament associated area at different wall temperature
and mass flux.

Another information referred from the recorded images is the local void fraction a.

Generally, the vapor film between the liquid filament and the tube wall is very thin,

therefore at a cross-section that contains liquid filament, the local void fraction can be

approximately expressed as:










a= ~arccos(1-h/R)-(1-h/R) 2hL/R-(h/R) (4.10)
a= = 1- (4.10)



here, hL is the measured thickness of the liquid filament, and R is tube inner radius.

The forced convective heat transfer to the vapor phase is evaluated by Dittus-

Boelter equation as:

q" = 0.023 Re.sPr.4 (T -T) (4.11)
con D D

in which kv is the vapor phase thermal conductivity; D is the hydraulic diameter of the

vapor flow; ReD is Reynolds number; Pr is the vapor Prandtl number; T7 and T1 are

the wall temperature and balk vapor phase temperature, respectively. It is noted that both

q', conl and q" con2 are evaluated using Equation 4.10, the difference is that each is

evaluated based on the respective bulk vapor velocity in its section as shown in Figure 4-

18. For the cross-section contains only vapor phase, the vapor velocity is simply

evaluated by:

u, = G/p, (4.12)

in which G is the mass flux, while for the cross section contains both liquid filament and

vapor phase, the vapor velocity is calculated by:

u,= G[pa+ p,( -a)/S] (4.13)

where S is two phase slip velocity, it is defined as u,/u and can be evaluated as (Zivi

1964):

S =(2.5 pl/pv )13 (4.14)









In current model, upper wall heat flux is described as containing only convective

heat transfer; the vapor phase temperature can be calculated by matching the measured

upper wall heat flux. Then the bottom heat flux can be calculated from Equation 4.8 if the

film boiling heat flux to the liquid filament q" is known. The correlation used to

evaluate this heat flux is given below.

4.2.4.2 Film boiling correlation

Film boiling, in which a thin vapor film blankets the heating surface due to the high

wall superheat, is often encountered in the handling of cryogenic fluids. Many studies

have been conducted on stable film boiling on external geometries, such as vertical

surface, (Bromley 1950; Chang 1959) horizontal surface (Bromley 1950; Chang 1959;

Berenson 1961), outer surface of horizontal cylinders (Bromley 1950; Breen and

Westwater 1962), and spheres (Merte and Clark 1964; Frederking et al. 1964). However,

not enough effort has been paid to film boiling inside of a horizontal tube, which is

common in engineering systems, the known investigations include research work by

Chan (1995) and Liao (2005). In both of these two works, it was assumed that the vapor

phase flows in a thin channel as shown in Figure 4-20, and a linear temperature profile

exists in the vapor layer, then an analytical solution of the local vapor film thickness 3

and vapor velocity in the vapor channel in the circumferential direction were derived, and

the local film boiling heat transfer coefficient was obtained as:

k
h g (4.15)


here, to differ from the vapor phase that is not inside of the vapor film, subscript g is used

to denote the gas in the vapor film.









In Liao's study (2005), the vapor flow was simplified to boundary-layer type flow,

and by neglecting the vapor thrust pressure and surface tension, the film boiling heat

transfer coefficient was given as:

1
h DF-) 0.6389 a (4.16)
5 DF (0) Ja


in which Ra = gD3 ( g )/gPg is the Raleigh number, Ja = C (T T )/hg is

the Jacob number, and F (0) is a geometry influence factor needs numerical integration.




















Figure 4-20. Stable film boiling inside a horizontal tube.

As a comparison, in deriving the analytical solution for film boiling inside a

horizontal tube, Chan (1995) included the vapor thrust effect but assumed a constant

vapor velocity in the cross section of the vapor channel, and obtained a simpler

expression for the heat transfer coefficient at the bottom of the tube. In this derivation the

interfacial velocity is assumed to be half of the vapor velocity, however, in most of the

research works, the interfacial velocity is assumed to equal the liquid phase velocity,






73


which is often much smaller than the vapor velocity. Therefore, in current study, the

interfacial velocity is assumed to be zero. The vapor film thickness and the vapor velocity

are then calculated based on this modified boundary condition. For stable film boiling of

liquid nitrogen inside a horizontal tube, Figure 4-21 shows typical results for different

liquid level hL.

One can find that approximately in the first half of the vapor channel, the vapor

film thickness remains almost a constant value, and the vapor velocity increases linearly;

while in the second half of the channel, the vapor film thickness increases very fast

accompanied with a fast decrease of the vapor velocity, and the vapor velocity drops to

zero at the top of the liquid filament.

8
hL/R=1.0 hL/R=0.75 I
-u ---.u
S2.0 I
E --6 ---- E
E I 6
^ T =200C I
15 -Fluid: LN2 o

/ I 4 >
r1.0 0
EI-

.T -2
S0.5 /


0.0 0
0.0 0.1 0.2 0.3 0.4 0.5
Location Along Vapor Channel, o/7

Figure 4-21. Vapor film thickness and vapor velocity along the vapor channel.

Calculation of the local vapor film thickness and vapor velocity requires numerical

solution as finite difference method (Chan 1995), however, a simple expression exists for

the vapor film thickness at the bottom of the tube as:











5 = 1.189 -p (4.17)


in which AT7 is the wall superheat, and hg is defined as the latent heat plus vapor

sensible heat content:

h = hg + 0.5CgATw (4.18)

It should be noted that in the above equations, all the thermodynamic properties of the

gas in the vapor film are evaluated at an average film temperature given by:

Tg = 0.5(T7 +Ts) (4.19)

Because the vapor film remains essentially constant over a relatively long distance

from the bottom of the tube as shown in Figure 4-21, the heat transfer to the liquid

filament at the bottom of the tube can be evaluated by:


q" = k A (4.20)
50


4.2.4.3 Model evaluation

The phenomenological model described above permits calculation of bottom wall

heat flux with known upper wall heat flux. Figure 4-22 compares the experimental results

with the model prediction of the bottom wall heat fluxes at the outlet section under

different mass fluxes.

It is seen that the model over predicts the heat fluxes in the beginning stage of

chilldown, after that the model is reasonably accurate. The flow visualization shows that

in the beginning stage the liquid droplets bounce back and forth on the wall rather than

settle down on the bottom wall, therefore the above film boiling model with a stable

liquid filament in the wall vicinity is not adequate for the beginning period. Because of










the much higher heat flux for a stable film boiling condition than that of bouncing liquid

droplets, the current model over-predicts the heat transfer in the beginning stage.


14000 Experimental Model
3.6kg/m2s -- -
12000 7.2kg/m2s
10.8kg/m2s -
10000
E
8000 -

6000

S4000 .

2000

200 220 240 260 280 300
Wall Temperature (K)

Figure 4-22. Comparison between experimental and model results of the bottom wall
heat fluxes at outlet section.

4.3 Rewetting Experiment

Rewetting is the establishment of liquid-wall contact and characterizes the

transition from film boiling to transition boiling. Early researchers tend to believe that the

liquid will contact the hot surface at a fixed temperature usually called Leidenfrost

temperature, however, more and more results show that there is no unique temperature at

which a hot surface will rewet, instead, the rewetting temperature is a function of many

thermal, hydrodynamic and geometric parameters pertinent to the system (Chan and

Banerjee 1981a, Abdul-Razzak et al. 1992, Barnea et al. 1994). In this section, the

rewetting phenomenon is experimentally investigated by pre-cooling and then quenching

the test section with different mass fluxes.









4.3.1 Types of Rewetting

Rewetting phenomenon is rather complex and involves the interaction among the

liquid phase, vapor phase, and the solid wall. Iloeje et al. (1975) was the first one who

successfully isolated three different controlling mechanisms for forced convective rewet.

These are: impulse cooling collapse, axial conduction controlled rewet and dispersed

flow rewet.

The impulse cooling collapse was proposed as the controlling mechanism for the

IAFB region, in which the liquid-vapor interface is wavy and fluctuates about a mean

position. If the wall temperature or heat flux is lowered, the vapor thickness decreases

and eventually the liquid may contact the wall. Depending on the temperature and the

wall heat flux, permanent liquid-wall contact is either maintained or the liquid will be

pushed away from the surface with the formation of vapor. In the second case, each

liquid-wall contact is equivalent to an impulsive cooling of the surface. For a chilldown

process, repeated contacts will lower the surface temperature enough to permit rewet.

Recent experiments (Cokmez-Tuzla et al. 2000) employed a special rapid-response probe

validate this impulsive liquid-wall contact in film boiling region. Some researchers (Chan

and Banerjee 1981b, Adham-Khodaparast et al. 1995) used the Kelvin-Helmhlotz

instability to explain the growth of the interfacial wave. Based on this controlling

mechanism, Kalinin et al. (1969) proposed that the wall temperature corresponding to the

minimum heat flux can be obtained from their empirical correlation:

0 0.25
mm s =1.65 0.16+ 2.4 (k (4.21)
T (kpc


in which, Tent is the thermodynamic critical temperature, subscript / is for liquid and w is









for wall. The hydrodynamic parameter of the flow rate is, however, completely absent in

this model.

In a system with an already wetted upstream surface, Simon and Simoneau (1969)

suggested that the transition from the film boiling to nucleate boiling is governed by axial

conduction. They assumed that the rewet temperature is a thermodynamic property of the

fluid, and is determined by using the Van der Waals equation of state (Spiegler et al.

1963):


0.13 + 0.84 (4.22)
Tcrit Pcrnt

here, T] denotes the rewet temperature, p,,t is the critical pressure.

In dispersed flow regime, Iloeje et al. (1975) postulated that rewetting was

controlled by the limiting effects of two processes, namely, heat transfer to the vapor

assuming no effect of the existence of droplets, and heat transfer due to the presence of

the droplets, which may or may not be touching the surface. The sum of the two heat

transfer components gives the total heat flux and indicates the location of the minimum

heat flux and T, ..

4.3.2 Rewetting Temperature and Rewetting Velocity

The local wall temperature at the onset of rewetting is very important for

theoretical modeling and engineering applications. Many definitions have been used in

the literature, such as rewetting temperature, apparent quenching or rewetting

temperature, minimum film boiling temperature, Leidenfrost temperature, etc. In

different investigations, usually one of the above definitions was selected according to










the experimental configuration. This partly reflects the limited understanding on

rewetting phenomenon.

Figure 4-23 shows a typical chilldown boiling curve and the corresponding

transient wall temperature. Since the liquid-wall contact indicates the end of the film

boiling, the rewetting temperature should be defined as the minimum film boiling

temperature Tmi, which corresponds with the minimum film boiling heat flux, as shown

in Figure 4-23.

Wall
Temperature




Apparent rewetting
Film Boiling" temperature
q MIN TMIN

F e 3 yl or Complete rewetting
CHF CHF temperature

Nucleate Boiling


TONB

TSAT
Forced Convection


Heat Flux Time

Figure 4-23. A typical chilldown boiling curve and the corresponding transient wall
temperature.

However, the apparent rewetting temperature, which is the intersection of tangent

lines to the "knee" of the measured temperature-time trajectories, was also used by many

researchers (Chen et al. 1979, Abdul-Razzak et al. 1992, Barnea et al. 1994, Westbye et

al. 1995). Other definitions of rewetting temperature include the temperature at the

"knee" of the temperature-time trajectory (Iloeje et al. 1982) and complete rewetting










temperature defined at the CHF point (Adham-Khodaparast et al. 1995). The rewetting

temperatures from those above definitions are generally not equal. In current test, it is

shown that the wall temperature has an abrupt decrease at the rewetting point; therefore

the temperature at the "knee" of the temperature-time trajectory is used to define the

rewetting temperature.

Typical temperature profiles of a rewetting test are shown in Figure 4-24. The test

section is pre-cooled to certain temperature and then quenched by injecting liquid

nitrogen from the bellows with constant mass flux. The wall temperatures decrease very

slowly at the beginning and then drop abruptly at the rewetting point.


240 -- TC1
-- TC2
---------- TC3
210 TC4
o TC5
-- TC6
18 0 -- - -----








500 600 700 800 900 1000 1100
Time (s)
Figure 4-24. Typical temperature profiles during a rewetting test.

The axial variation of the averaged rewetting temperature at the bottom of the tube

under different mass fluxes is illustrated in Figure 4-25. The rewetting temperature

increases with increasing mass flux; this has also been reported in high mass flux

experiments (Chan and Banerjee 1981a, Abdul-Razzak et al. 1992, Westbye et al. 1995,

Xu 1998). It was proposed by Xu (1998) that the vapor film thickness would decrease at










higher mass flux, and therefore lead to rewetting at a higher wall temperature. No clear

trend of axial variation is shown in Figure 4-25.

210
-o-3.6kg/m2s
S --- 7.2kg/m2s
200 10.8kg/m2s

E 190
0_
E
180


S170 -


160
160 .
60 80 100 120 140 160 180
Axial Location (mm)
Figure 4-25. Axial variation of the averaged rewetting temperature at different mass
fluxes.

Although it is quite complicated and difficult to fully analyze the rewetting

phenomenon, many researchers have tried to predict rewetting temperature by theoretical

models and experimental correlations. Berenson (1961) extended Zuber's vapor escape

model to analyze the minimum heat flux condition in steady film boiling over a flat

horizontal surface. The heat transfer through the vapor film was described as a pure heat

conduction problem, and the following correlation was obtained to predict the minimum

film boiling temperature for pool boiling:

2 1 1
hi-v K(p, -+Pv) Pl v g(P p) )- (4.23)
ATmi =0.127 f)3 7 2 P- (4.23)
mm (P,+ Pv) ) ( P) g(PI P)

The minimum film boiling temperature calculated from Equation 4.23 is 142.3K.

The impulse cooling collapse model (Kalinin et al. 1969), which is given in Equation

4.21, considers the properties of the solid wall and gives a minimum film boiling









temperature of 189.97K, which is close to the experimental values. Predicted rewetting

temperature from the axial conduction model is only 106.4K, which is much less than the

present data. Under current experimental condition, long liquid filaments are observed to

flow at the tube bottom, the impulse cooling collapse model was proposed for IAFB and

therefore gives a better result over the axial conduction model.

The flow rate effect has not been shown in the above correlations; however, as

mentioned before all the previous experiments indicated the rewetting temperature also

depends on hydrodynamic parameters. Iloeje et al. (1975) conducted vertical flow boiling

experiments with water in an inconel tube and observed minimum film boiling superheats

asymptotically approaching certain values. They suggested that this asymptote would be

close or equal to a pool boiling value and correlated their data in the following empirical

form:

AT.i = AT,Be (1- Ax )(1+ BGm) (4.24)

where AT7,Ber is Berenson's minimum film boiling temperature for pool boiling

(Equation 4.23), x is quality, G is mass flux, A, B, m and n are constants. Xu (1998) used

R113 to quench a hot surface and suggested a similar form as Equation 4.24 to correlate

his experimental data as:

ATmi = AT, (1+BGm) (4.25)

A correlation similar in the form of Equation 4.25 is used in current study, with the

same exponent as Iloeje et al. (1975), the best fit is obtained as:

AlTm=inA. = ( 1+ 0.242G049) (4.26)