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CRYOGENIC TWOPHASE FLOW DURING CHILLDOWN: FLOW TRANSITION AND NUCLEATE BOILING HEAT TRANSFER By JELLIFFE KEVIN JACKSON 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 Jelliffe Kevin Jackson This work is dedicated to my parents, Victor and Eva Jackson. Without their continuous support and encouragement this work would not have been possible. ACKNOWLEDGMENTS The author would like to express his sincerest gratitude to his academic advisor and PhD committee chairperson, Professor James Frederick Klausner. His guidance, support, encouragement and insight contributed immensely to the accomplishment of this work. The author would also like to express his appreciation to Professor Renwei Mei for his invaluable input, which helped to guide this work through times when the path was cloudy. The author would like to thank Professor David Hahn, Professor William Lear and Professor Samim Anghaie for serving on his PhD committee. Their insight has helped the author to develop the necessary critical thinking skill needed to become a contributing member of the academic community. The assistance, encourage and friendship provided by the author's fellow research associates are greatly appreciated. The technical assistance provide by Mr. Christopher Velat, in the construction phase of the experimental facility is also greatly appreciated. This research was supported by the National Aeronautics and Space Administration Glenn Research Center, through contract NAG3270. Without its financial support this work would not be possible. Most importantly, the author wishes to express his deepest gratitude and appreciation to his wife, Aisha Ivette WoodJackson, for her unwavering support and patience throughout the course of this endeavor. She has provided the much needed encouragement in times when selfdoubt was creeping into the author's mind and she continues to be a source of comfort and inspiration. Without her support, encouragement and patience, this work would not have been possible. TABLE OF CONTENTS page A C K N O W L E D G M E N T S ................................................................................................. iv L IST O F TA B LE S ......... ............ .............................. .. .. ....... .............. viii LIST OF FIGURES ......... ......................... ...... ........ ............ ix N O M E N C L A T U R E .................................................. ................................................ xiv ABSTRACT ........ .............. ............. ...... ...................... xix CHAPTER 1 IN TRODU CTION ................................................. ...... ................. 2 LITER A TU RE SU RVEY .................................................. ............................... 6 H orizontal Flow R egim es ................................................. .... .............................. Flow Regime Maps for Horizontal Flow.......................................................... 8 T he B aker M ap .................................................................. ............... .. 8 The Taitel and Dukler M ap ............................................................................9 T he Steiner M ap .................................................................... 13 The W ojtan et al. M ap ............................................ .............. ...... .. ...... .. 14 Forced Convection Boiling Heat Transfer Correlations...........................................16 3 EXPERIM ENTAL FACILITY ............................................................................ 31 Sy stem O verview ........... .................................................................... .. .... .. 3 1 V isu al T est Section D esign .............................................................. .....................33 Instrum entation and Calibration ........................................... .......................... 34 Static Pressure Transducers ....................................... .................. 34 Test Section Pressure D rop ........................................ ........................... 34 F low M eter C alibration ............................................................ .....................35 Tem perature M easurem ents ........................................ .......................... 36 D ata A acquisition System .................................................. .............................. 38 D digital Im aging System ........................................... .................. ............... 39 E xperim mental P protocol ........................................................................ .................. 40 4 D A T A PR O C E SSIN G ................................................................ ..........................4 1 V apor Q quality Estim ation ........................................................................... 41 V apor V olum e Fraction ................................................. .... .............................. 43 Extracting the Heat Transfer Coefficient...................... ...... ...............44 Computing the Temperature Field in the Pipe Wall......................................46 Iteration Process for Guessing the Inner Heat Transfer Coefficient ...................50 T est for C onvergence ................................................. ................ ........ .... 50 Computational Code: Testing and Verification.........................................................51 Stability of Com putational Code ...................................................................... 51 G rid R e so lu tio n ............................................................................................. 5 1 Testing the Inverse Procedure ............................................................................. 52 5 CHILLDOWN FLOW TRANSITION AND HEAT TRANSFER............................57 F low R egim es ....................................................... 62 Experim ental O observations ........................................ ........................... 64 Performance of Current Flow Regime Maps.................................................. 65 Calibration of Taitel and Dukler Flow Regime Map........................................68 F ilm B oiling H eat T ransfer.............................................................. .....................75 Nucleate Flow Boiling Heat Transfer.......................................... ..... ..... ............... 76 Performance of Current Flow Boiling Heat Transfer Correlations.................78 Correlating the Nucleate Flow Boiling Heat Transfer Coefficient ......................82 6 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH...... 98 APPENDIX A PHYSICAL PROPERTIES OF NITROGEN................................ ...............101 B EXPERIMENTAL DATABASE: FLOW REGIME, HEAT TRANSFER COEFFICIENT, AND PRESSURE DROP DURING CHILLDOWN....................103 L IST O F R E FE R E N C E S ........................................................................ ................... 174 BIOGRAPHICAL SKETCH ............................................................. ............... 180 LIST OF TABLES Table pge 21 Empirical constants for the Kandlikar correlation. ...............................................25 41 Influence of grid resolution on the computed outer wall temperature ...................52 51 Sample data points for cryogenic chilldown. SW denotes stratifiedwavy flow; I denotes intermittent flow; A denotes annular flow ...............................................70 53 Summary of measured average nucleate flow boiling heat transfer coefficients using inverse m ethod for regions. ........................................ ........................ 81 LIST OF FIGURES Figure pge 21 Schematic representation of flow regimes observed in horizontal twophase flo w .......................................................................... ............ 7 22 The Baker flow regim e m ap ............................................................. ............... 10 23 The Taitel and Dukler flow regime map. ..................................... ............... 13 24 The Steiner flow regim e map. ...... ......................................................................14 25 The Wojtan et al. flow regime map ........................... .......... ............... 15 26 Flow structures used to evaluate stratified flow liquid film thickness and stratifi ed angle. .........................................................................28 27 Flow structures used to evaluate (a) annular flow liquid film thickness, (b) annular flow liquid film thickness and partialdry out angle .................................29 31 Schematic of chilldown experimental facility................... ................ ............... 31 32 Schematic of the flange assembly. ............. .............. ..........................33 33 Calibration plot of the actual velocity versus the ideal velocity (Velat [56]). .........36 34 Thermocouple arrangement on the steel transfer line prior to the visual test se ctio n ...................................... .................................. ................ 3 7 35 Thermocouple placement for heat transfer test section................ ... ..... ...... 38 41 Model used for the stratified, wavy and intermittent flow volume fraction c o m p u tatio n ..............................................................................................................4 4 42 Diagram of the model used for the annular flow volume fraction computation......44 43 Flow chart for transient heat transfer coefficient extraction. ..................................45 44 Coordinate system for heat conduction through the pipe wall.............................47 45 Calibration for determining the outer pipe surface heat transfer coefficient. ..........48 46 Assumed variation of heat transfer coefficient on the inside surface of the pipe. ...50 47 Computation of a parabolic varying heat transfer coefficient using the inverse m eth o d ........................................................................... 5 5 48 Comparison of heat transfer coefficient computed using the inverse procedure and the DittusBoelter correlation for singlephase nitrogen gas flow. ..................56 51 Quenching front that marks transition for film boiling to nucleate boiling .............57 52 Temperature profile during chilldown for low mass flux experiment ...................58 53 Temperature profile during chilldown for moderate mass flux experiment. ...........59 54 Transient mass flux for low mass flux experiment. ............................................59 55 Transient mass flux for moderate mass flux experiment. ......................................60 56 Transient vapor volume for low mass flux experiment............. .................60 57 Transient vapor volume fraction for moderate mass flux experiment ...................61 58 Transient vapor quality for low mass flux experiment. ........................................61 59 Transient vapor quality for moderate mass flux experiment.............................. 62 510 Transient inlet pressure profile for low mass flux experiment ..............................63 511 Transient inlet pressure profile for moderate mass flux experiment ..................63 512 Comparison of Van Dresar and Siegwarth data with the Baker map.....................67 513 Comparison of Van Dresar and Siegwarth data with the Taitel and Dukler map....67 514 Comparison of Van Dresar and Siegwarth data with the Wojtan et al. map...........68 515 Comparison of current chilldown data with the Baker map................................69 516 Comparison of current chilldown data with the Taitel and Dukler map ................69 517 Comparison of current chilldown data with the Wojtan et al. map........................71 518 Liquidvapor 2D channel flow configuration. .............................. ............... .72 519 Comparison of current chilldown data with the modified Taitel and Dukler map. .75 520 Heat transfer coefficients for each region in the film boiling regime of the low m ass flux experim ent. ..................................................................... ...................77 521 Heat transfer coefficients for each region in the film boiling regime of the moderate mass flux experiment...................................... ................. ......... 77 522 Average twophase heat transfer coefficient variation with time...........................79 523 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using Gungor and Winterton correlation ..............................83 524 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using Kandlikar correlation. .............. ................................... 83 525 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using MillerSteinhagen correlation .......................................84 526 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using W ojtan et al correlation. .............................................. 84 527 Method for assigning the heat transfer coefficient on the inside surface of the pipe. ...................... ...................................... 85 528 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................87 529 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................87 530 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version .......................88 531 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version .......................88 532 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................89 533 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................89 534 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................90 535 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................90 536 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................91 537 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................91 538 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................92 539 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................92 540 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................93 541 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................93 542 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................94 543 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................94 544 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................95 545 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................95 546 Comparison of the predicted and measured temperatures using both the Miller Steinhagen and Jamialahmadi correlation and the modified version.....................96 547 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using modified MUllerSteinhagen correlation.....................97 NOMENCLATURE A crosssectional area (m2) a constant in the MtillerSteinhagen and Jamialahmadi correlation Bo Boiling number CO empirical constant in Zuber Findlay correlation C C5 constants in the Kandlikar correlation C2 coefficient dependent on the size of disturbance Co Convection number c interface wave speed (m/s) Cp specific heat capacity (J/kgK) D inner diameter of pipe (m) d pipe wall thickness (m) E enhancement factor F modified Froude number Fk fluid property enhancement factor for nucleate boiling in the Kandlikar correlation Fp pressure function Fr Froude number G mass flux (kg/m2s) g gravitational acceleration (m/s2) h heat transfer coefficient (W/m2K) hfg latent heat of vaporization (J/kg) K wavy flow dimensionless parameter k thermal conductivity (W/mK) M molecular weight Ma Mach number m wave number n exponent P pressure (Pa) Pr Prandtl number q" heat flux (W/m2) R inner radius of pipe (m) Re Reynolds number Rp surface roughness (m) r radial coordinate S suppression factor also slip velocity (m/s) S, modified suppression factor s shelter coefficient T dispersed bubble floe dimensionless parameter also temperature (K) t time (s) Uv empirical constant in ZuberFindlay correlation U V X, x Y z Greek Symbols a 3( 8 0 p  fluid velocity (m/s) voltage output (V) Martinelli parameter vapor quality parameter encompassing relative forces acting on the fluid due to Gravity and pressure axial coordinate vapor void fraction fluid film height (m) scaling factor annular correction factor azimuthal coordinate angle of inclination of pipe (rad.) also ratio of specific heats dimensionless temperature fluid property correction factor for vapor mass flux in the Baker map fluid viscosity (Pas) kinematic viscosity (m2/s) angle film occupies (rad.) density (kg/m3) surface tension (N/m) enhancement factor of Shah fluid property correction factor for liquid mass flux in the Baker Map Subscripts 0 denotes reference quantity It denotes singlephase 21! denotes twophase quantity oo denotes far field condition a denotes air actual denotes actual quantity b denotes nucleate boiling bottom denotes bottom of the pipe c denotes singlephase convection crit denotes critical quantity dry denotes dry perimeter of pipe fl denotes fluid inside pipe fo denotes liquid only g denotes vapor phase i denotes liquid vapor interface ib denotes point of incipient boiling ideal denotes ideal quantity in denotes inner surface of the pipe known denotes known quantity I denotes liquid phase xvii new ONB out pres prev r sat side top w wa wet Superscripts s denotes new quantity denotes onset of nucleate boiling denotes outer surface of pipe denotes present quantity denotes previous quantity denotes reduce denotes saturation condition denotes side of the pipe denotes top of the pipe denotes quantity is evaluated at the pipe inner wall denotes water denotes wetted area of inner pipe wall denotes superficial quantity denotes dimensionless quantity xviii 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 TWOPHASE FLOW DURING CHILLDOWN: FLOW TRANSITION AND NUCLEATE BOILING HEAT TRANSFER By Jelliffe Kevin Jackson August 2006 Chair: James F. Klausner Major Department: Mechanical and Aerospace Engineering The recent interest in space exploration has placed a renewed focus on rocket propulsion technology. Cryogenic propellants are the preferred fuel for rocket propulsion since they are more energetic and environmentally friendly compared with other storable fuels. Voracious evaporation occurs while transferring these fluids through a pipeline that is initially in thermal equilibrium with the environment. This phenomenon is referred to as line chilldown. Large temperature differences, rapid transients, pressure fluctuations and the transition from the film boiling to the nucleate boiling regime characterize the chilldown process. Although the existence of the chilldown phenomenon has been known for decades, the process is not well understood. Attempts have been made to model the chilldown process; however the results have been fair at best. A major shortcoming of these models is the use of correlations that were developed for steady, noncryogenic flows. The development of reliable correlations for cryogenic chilldown has been hindered by the lack of experimental data. An experimental facility was constructed that allows the flow structure, the temperature history and the pressure history to be recorded during the line chilldown process. The temperature history is then utilized in conjunction with an inverse heat conduction procedure that was developed, which allows the unsteady heat transfer coefficient on the interior of the pipe wall to be extracted. This database is used to evaluate present predictive models and correlations for flow regime transition and nucleate boiling heat transfer. It is found that by calibrating the transition between the stratifiedwavy and the intermittent/annular regimes of the Taitel and Dukler flow regime map, satisfactory predictions are obtained. It is also found that by utilizing a simple model that includes the effect of flow structure and incorporating the enhancement provided by the local heat flux, significant improvement in the predictive capabilities of the MiillerSteinhagen and Jamialahmadi correlation for nucleate flow boiling is achieved. CHAPTER 1 INTRODUCTION Cryogenic fluids have been used in various applications over the past century. One application that has continuously been getting attention has been the use of cryogenic propellants for rocket propulsion. This interest has been sparked by the fact that cryogenic propellants yield more energy and are more environmentally friendly, when compared to noncryogenic propellants [1] and the storage systems for these cryogenic propellants are lighter than those required for their noncryogenic counterparts [1]. Before these propellants can be used for propulsion in space they must first be filled in their respective storage containers while still on the ground. The introduction of the cryogenic fluid in a transfer line that is in thermal equilibrium with environment results in voracious boiling within the line; this phenomenon is referred to as line "chilldown" or line "cooldown". Chilldown is characterized by large temperature differences, rapid transients and pressure fluctuations. The phenomenon of chilldown is of interest since it directly impacts the design of the delivery system for the propellant. For example the magnitude of the pressure oscillations determines the thickness of the material used for the transfer lines, and the heat transfer rate determines the type and thickness of insulation to be used. Other important factors that must be considered when dealing with chilldown are the quantity of liquid propellant vaporized, the time it takes for the transfer line to be completely cooled, and the degree to which bowing of the transfer lines occur, especially during the instances where the flow is in the stratified regime. Hence a proper understanding of the chilldown process would allow for more economical and robust designs of cryogenic propellant delivery systems. Over the past few decades attempts have been made to understand this complex process through experiments and numerical simulations. In 1960 Burke et al. [2] applied the principle of conservation of energy and conservation of mass to the entire transfer line, and as result he developed a simple model to estimate chilldown time. The model showed reasonable agreement with their experimental results; however the overall accuracy is limited due to broad assumptions, averaging of fluid properties and averaging of mass flow rates. The experiments performed demonstrated the unsteady and oscillatory nature of the chilldown process. Two years after the study of Burke et al., Bronson et al. [3] performed experiments of their own, where they evaluated the model of Burke for chilldown time and a model for estimating the frequency of pressure oscillations. It was determined that these models gave an acceptable prediction of chilldown time. Bronson et al. were able to highlight the existence of circumferential temperature variations. Steward, Smith and Brennan [4] carried out the first detailed numerical simulation of the process in 1970. They were able to utilize the computational technology available at the time to solve the continuity, momentum and energy equations. With the aid of numerous assumptions, they were able to investigate pressure variations, estimate chilldown time and predict temperature profiles. It was concluded that pressure surges are exacerbated by a high degrees of subcooling of the inlet fluid, long transfer lines, dense fluids and rapid opening of the inlet valve. In the mid 1970's a series of studies [57] on the cooldown of short transfer lines were performed. These studies utilized an energy balance for an elemental length of pipe to determine the temperature of the pipe wall as a function as time. The flow structure and the momentum transport were neglected in the analysis, and heat transfer coefficient correlations utilized were those developed for steady, noncryogenic systems. Thus there was poor agreement between the results of their analytical model and the experimental data. With the rapid advancement of computing technology during the past two decades, more sophisticated numerical simulations of the chilldown process were attempted. Papadimitriou and Skorek [8] developed a thermohydraulic code for the calculation of system variables for both steady state and transient processes for twophase cryogenic flows. They utilized the conservation equations for both the liquid and vapor phases coupled with various correlations for heat transfer coefficient and pressure drop, none of which were developed for unsteady flow or cryogenic fluids. They were able to predict the temperature and pressure history of the cooldown process; however their predicted results consistently underpredicted the temperature and pressure. In 2002 Cross et al. [9] developed a numerical procedure that utilizes the unsteady conservation equations in conjunction with a thermodynamic equation of state and correlations for boiling heat transfer. These correlations for boiling heat transfer were not developed for twophase cryogenic flows. They concluded that when the fluid enters the transfer lines as a subcooled liquid 9.41 times the amount of fluid is consumed to achieve chilldown as opposed to having the fluid enter as a superheated vapor. The chilldown process is physically similar to the rewetting phenomenon encountered in the nuclear industry when reestablishing normal and safe temperature levels following a loss of coolant accident (LOCA). In the event of a LOCA, the temperature in the reactor core raises rapidly as a result of poor heat transfer due to the dryout. In order to prevent catastrophic failure an emergency core cooling is done by introducing a cooling fluid (usually water) into the reactor core. The cooling fluid is several hundred degrees colder than the temperature of the reactor; thus voracious evaporation takes place. The process proceeds in a similar manner to that of cryogenic chilldown as it goes from the film boiling regime to the nucleate flow boiling regime and eventually to the single phase convective heat transfer regime. Research in the area of re wetting usually focuses on the prediction of the quenching velocity [1012]. Chan and Banerjee [1315] used a twofluid numerical model to investigate the rewetting and re filling in a horizontal tube and achieved reasonable agreement in the prediction of quenching velocity. However the predictions of the temperature profile is not good especially in the nucleate flow boiling regime, where it is observed that the discrepancy in temperature is greater than 100 'C. This is a result of utilizing over simplified models for the heat transfer coefficient. It is evident from the previous studies on the chilldown process that the focus has been on predicting chilldown time and simulating the flow so as to obtain the pressure history, the temperature history and the fluid expenditure. However, all models to date use empirical correlations for determining the heat transfer coefficient and the pressure gradient that were developed steady noncryogenic flows. The agreement with experimental data has been fair at best. Hence the purpose of this research investigation is to develop a database of flow regime and heat transfer coefficient for cryogenic chilldown in horizontal transfer lines. Techniques are also provided to predict flow regimes and nucleate flow boiling heat transfer coefficients. This information will help practitioners develop more accurate and reliable models, thus leading to more efficient and economical cryogenic delivery systems. To carry out this study a horizontal once through chilldown facility utilizing nitrogen as the working fluid was constructed. The facility allows for the flow structure to be observed while simultaneously measuring and recording the mass flow rate, temperature, and pressure within the test sections. At present, there is no database that exists that includes a compilation of data for temperature, pressure, mass flow rate and flow regimes that occur during chilldown. Hence the first step is to compile a large database of temperature, pressure, mass flow rate and flow structure data for the chilldown process. This database will be used to evaluate the heat transfer coefficients that are experienced during chilldown, which will allow present predictive models and correlations to be evaluated and calibrated for use in chilldown models. A literature survey of flow structure and heat transfer predictions is given in the next chapter. This is followed by a detailed description of the experimental facility in chapter 3 that has been developed to compile the required database for cryogenic chilldown. Chapter 4 describes the methods used to regress the experimental data and extract the heat transfer coefficient. Chapter 5 compares the experimental data with existing models or correlations and the modifications required to fit the data. CHAPTER 2 LITERATURE SURVEY In order to reliably predict the thermal transport associated with cryogenic chilldown, it is important to know the flow structure and temperature variations. It is useful to examine existing models for flow regime and heat transfer in twophase flow. The intent of this review is to examine the most widely employed predictive models and examine their strengths and weaknesses, which allows the useful elements of the models to be highlighted. Horizontal Flow Regimes During the chilldown process, the vapor and liquid are flowing simultaneously inside the pipe. The resulting twophase flow is more complex than singlephase flows. Apart from the inertia, viscous, and pressure forces experienced in singlephase flow, twophase flows also experience interfacial tension forces, exchange of momentum, mass and energy between the liquid and vapor phases, as well as the wetting characteristics of the liquid on the pipe. The flow structure that the twophase flow evolves into is referred to as flow regime and may take various forms depending on the flow rate of the various phases, fluid property, and pipe geometry and orientation. The twophase flow regimes that are typically encountered for horizontal flow are illustrated in Fig. 21. . ...... ..ct n Bubbly Flow Plug/Intermittent Flow SIg/I ntermittel Flow Wavy Flow Stratilied Flow Annular Flow Figure 21. Schematic representation of flow regimes observed in horizontal twophase flow. At very low vapor quality, bubbly flow is usually observed, with the bubbles residing in the upper portion of the pipe (as a result of buoyancy forces). As the quality is increased, the bubbles tend to coalesce producing larger plugtype bubbles, this is referred to as plug flow. At low mass flow rates and higher qualities, stratified flow is observed; as the flow rate and/or quality are increased the liquidvapor interface becomes unstable (due to Helmholtz instability), resulting in stratifiedwavy flow. At high liquid flow rates the amplitude of the waves may grow until the crest spans the crosssection of the pipe forming large vapor slugs. This is referred to as slug flow. At higher vapor velocities and moderate liquid flow rates the flow structure is observed to be annular, with liquid film covering the entire circumference of the pipe with an inner vapor core. If the vapor flow rate is very high and the vapor quality is also very high, it is possible for the liquid to be entrained in the vapor forming what is known as mist flow. Flow Regime Maps for Horizontal Flow The prediction of the flow patterns existing in twophase flows is essential for developing phenomenological models for mass, momentum and energy transport within those flow systems. Throughout the past decades numerous flow regime maps have been developed for horizontal and vertical flows. Few maps have been developed mechanistically [16, 17, and 18] as the vast majority of maps were developed through empirical correlation methods [19, 20, and 21]. In this section the focus will be placed on the most widely used maps for horizontal flow. An exhaustive review of all the existing transition maps is not pursued here. The Baker Map The flow regime map proposed by Baker [19] in 1954 is one of the most widely cited flow regime transition maps. This map was developed by an empirical correlation method, which is comprised of plotting the observed flow pattern for airwater and steamwater flows on a chart of liquid mass flux (G,) versus gas mass flux (G,). The transition lines were then simply drawn onto the chart in such a manner as to divide the area into regions associated with the flow pattern that was observed in that particular area. In order to create maps for twophase flow with fluids other than airwater and steamwater, fluid property correction factors were introduced. Thus the coordinates of the map are modified by the factors A and Vf, = K X P 2 (2.1) ljPa )] S [wa DL Pwa (2.2) where the subscripts g, 1, a, and wa represent the gas, the liquid, air and water respectively. p is the fluid density of the respective fluid, PI is the fluid viscosity of the respective fluid, a is the surface tension between the liquid and the gas and o, is the surface tension between water and air. The new coordinates of the map become G1, G versus  2 This map has been used in studies involving cryogenic fluids [3, 22] with some success. However this map has a severe shortcoming, which is the fact that the map cannot take into account variations in pipe diameter or orientation. Variations in these parameters were shown by Taitel and Dukler [16] to significantly affect the point at which the transitions between flow regimes occur. The Taitel and Dukler Map The Taitel and Dukler [16] map, developed in 1976, is the first developed where the transition mechanisms are based on physically sound concepts. The map was developed with the assumption that the flow initially exists in the stratified regime and subsequently transition into other regimes. Assuming the flow is initially stratified, a momentum balance is carried out on each phase, and two nondimensional groups were uncovered that influence transition. These groups were defined as follows: x, dPd (2.3) Xt dP dx) (2.3) (p, pg)gsiny Y= (dP / dx) I I l  100  50  20  10 5 2 0.21 0.1 0.5 66 0.05 40.2 0.020.1  o kg/m's 5 blf I ]b/fts 1 10 20 50 100 200 I I I5 I I 2 5 10 20 50 500 1000 2000 5000 10000 20000 I I I I I I I I 1 I I 1 100 200 500 1000 2000 5000 G'V Figure 22. The Baker flow regime map. where the subscripts I and g denote the liquid and gase phases respectively. (dP /dx) is the pressure drop of one phase flowing within the pipe based on the mass fraction of that phase, g is the gravitational acceleration and y is the angle of inclination of the pipe with respect to the horizontal. X, is the Martinelli parameter and Y encompasses the relative forces acting on the liquid due to gravity and pressure gradient. (2.4) II III The transition between stratified and intermittent or annular flow is modeled to take place as a result of Helmholtz instability, which causes finite amplitude waves on the surface of the stratified film to grow. The instability is a result of the Bernoulli effect, for which the pressure is reduced as the gas accelerates over the crest of the wave. This provides the basis for the following transition criterion, S1 i7 uGdA,/dh, F 2 1GddJ > 1 (2.5) F is a Froude number modified by the density ratio, F= P g (2.6) (, Pg) Dgcosy and the constant C2 is given by, C2 =1 (2.7) D where A is the flow crosssectional area, 5 is the film height, D is the diameter of the pipe, u is the velocity of the respective phase, the superscript s denotes superficial for single fluid flow, and the indicates the quantity is dimensionless. The transition to intermittent or annular flow is governed by the amount of liquid available in the film. A transition to intermittent behavior occurs when the growing wave encompasses enough of the liquid films so as to form a stable plug or slug. However if there is not sufficient liquid in the film to develop a stable plug or slug, the flow assumes an annular pattern. The amount of liquid that is sufficient to form intermittent flow is seen to occur at a specific liquid film height, which is defined by a unique value of the Martinelli parameter. The transition between the stratified smooth and the stratified wavy patterns is related to the wave generation phenomenon. In order for the stratified wavy pattern to exist, the velocity of the gas must be sufficient to cause waves but not large enough to cause rapid wave growth. It was hypothesized that this occurs when the pressure and shear work on the wave is sufficient to overcome the viscous dissipation. The criterion for transition from smooth to wavy flow is given by, K> 2 (2.8) where s is the shelter coefficient defined in [16] and takes a value of 0.01 andK is the product of the modified Froude number and the square root of the superficial Reynolds number of the liquid: K2 =F2Re= F pg ,)2 Du1 (2.9) (p Pg)Dgcosy v, Here v is the viscosity of the respective phase. The transition between intermittent and dispersed bubble flow takes place when the turbulent fluctuations are larger than the buoyancy force that keeps the gas at the top of the pipe. This leads to the following criterion, 8A 2 n (2.10) T is the ratio of the turbulent force to the gravity force, T (dPdx (2.11) Pi PggCOS 7) where the subscript i denotes the liquid film interface and S is the perimeter over which stresses act. This map was the first developed that is based on physical principles and allows a regime map to be constructed that includes the dependence on the pipe diameter, as well as the pipe orientation and the fluid properties. The drawbacks of this map are the fact that it does not take into consideration phase change and it has not been calibrated with a large data set. I I I I P II I I P I P I 10 AnnularDispersed Liquid (AD) Dispersed Bubble (DB) 100 Stratified 0 102 10' Wavy (SW) S W ( Intermittent (I)  10'l 102 d, aA S ratified c. S Smooth SS) (S 100 1 I I 103 10 102 10' 100 10' 102 10 104 Xtt Figure 23. The Taitel and Dukler flow regime map. The Steiner Map The Steiner map [23] is a modified version of the Taitel and Dukler map. The transition regions have been determined using the same physical principles as those introduced by Taitel and Dukler [16]. The major improvement of this map over its counterpart is that the transition curves are adjusted slightly using more advanced models. A much broader data set was used to calibrate the map. However this map faces a similar drawback to the Taitel and Dukler map in that it does not take into account phase change. 11), I0' to' (Re, Fr, *V 101 l0 034 0 51 10.1 Fr al 101 10 , Figure 24. The Steiner flow regime map. The Wojtan et al. Map The Wojtan et al. [24] map is the one most recently developed for horizontal flow. It is a modified form of the map suggested by Kattan et al. [25] that eliminates all iterative steps. Kattan et al. [25] found that their data for two refrigerants were predicted more accurately by the Steiner map than any other they used. However the map proved difficult to use as it involved the evaluation of five different parameters in order to determine the flow pattern. To alleviate this problem and develop the map into a more useful design tool, the axes of the Steiner map were converted to mass flux, G, versus vapor quality, x. In an attempt to improve the accuracy, the transition curves were 10, IT O 10, IV toO Xtt empirically modified so that the predictions better match the experimental observations. Kattan et al. [25] were able to transform the map, which was an adiabatic map into a diabetic one, thus being able to predict partial dryout in annular flow, which was not possible with earlier maps. Kattan et al. [25] specifically mention that their flow regime map was developed for vapor qualities higher than 0.15. Wojtan et al. compensated for this limitation by modifying the transition curves in the low vapor quality (less than 0.327) and low mass flux (less than 200 kg/m2s) regime based on observations made with R22. Details of the map construction are found in the work of Wojtan et al. [24]. 400 350 300  SIntermittent Annular 250 S200 Slug 150 100 Stratifiedwavy 50 Slug & StratifiedWavy 0 Stratifiedsmogth 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x Figure 25. The Wojtan et al. flow regime map. Reviews of various flow regime transition maps are given by Frankum et al. [27] and Spedding and Spence [28]. Frankum et al. [27] suggest that most theoretical maps perform well over a wide parameter space, while the empirical maps only performed well for the data set from which it was developed. Spedding and Spence [28] used data collected from cocurrent waterair horizontal flow experiments through pipes of two different diameters to show that no one map could satisfactorily predict the flow regime for the experiments conducted. This underscores the importance of collecting experimental data on flow regimes that occur during chilldown so that current flow regime maps can be calibrated or new maps developed. Forced Convection Boiling Heat Transfer Correlations It is a widely accepted principle that the heat transfer in flow boiling is a combination of bulk turbulent convection (macroconvection) and ebullition (microconvection). This principle was first introduced by Dangler and Addoms [29] in 1956. The influence of these two mechanisms on each other and their effect on the heat transfer coefficient has been a source of dispute in the past and to date still remains unresolved. Dengler and Addoms [29] used a plot of log(h2/hit) versus log(l/XX,) to conclude that the primary mechanism for heat transfer in flow boiling is the bulk turbulent transport since the relationship is monotonic as is the case for the twophase frictional pressure drop. The twophase heat transfer coefficient is represented by h2, hl,t is the singlephase heat transfer coefficient based on the liquid fraction flowing, and X, is the Martinelli parameter, X, = 1 x)9Pv ) p1, (2.12) in which x is the vapor quality. However, Mesler [30] suggested that Dengler and Addoms misinterpreted their data. The plot of log(h2d/hit) versus log(l/X,) may be rewritten as log 1 w',2~ GA AT,,, versus log GA ) 0 q ,2 dz2 where A is the cross sectional area and qw,2i is the twophase wall heat flux. This is essentially a plot of the same quantities against each other, thus a monotonic relationship is guaranteed regardless of the physical mechanism involved. By plotting qw,2, against AT,, he suggested that the monotonic relationship was a result of the nucleate boiling phenomenon. Bergles and Rohsenow [31] incorporated the effects of both the bulk turbulent convection and nucleate boiling mechanisms by proposing a correlation that predicts the twophase wall heat flux by interpolating between the bulk turbulent convection dominated heat transfer and ebullition dominated heat transfer. The correlation takes the form, qw,20 qw,c 1 q,b l (2.13) qw,c qw,b Here the subscripts c, b, and ib denote singlephase forced convection, ebullition and the point of incipient boiling, respectively. This correlation is not utilized often since the determination of the heat flux due to ebullition is not available without experimentation. Over the past few decades, numerous correlations have been proposed for predicting the heat transfer coefficient during forced convection flow boiling. Each correlation may be classified in one of three categories: superposition, enhancement, or asymptotic. The most straightforward is the superposition model, which adds the contribution of each mechanism and accounts for the interaction of the mechanisms by the use of an amplification factor and a suppression factor. The amplification factor is used to account for the increased turbulent transport in twophase flow and the suppression factor is introduced to account for the reduced effective superheat experienced during ebullition. The second is the enhancement model, which multiplies the singlephase heat transfer coefficient for the liquid phase along flow in the pipe by the greater of the contributions between the increased turbulent transport and the ebullition process. The last model is the asymptotic model. It is termed asymptotic as the value of the twophase boiling heat transfer coefficient approaches the larger of the two components, thus assuring a smooth transition from the convective boiling regime to the nucleate boiling regime. Many correlations have been developed for horizontal and vertical flows; however in this study the focus is placed on the horizontal correlations. The most cited superposition model in the literature is the Chen correlation [32], originally proposed for vertical flow. In this correlation, the twophase heat transfer coefficient is given as, h2 = Eh, + Shb, (2.14) where E is the amplification or enhancement factor and S is the suppression factor. The singlephase liquid heat transfer coefficient is evaluated using the wellknown Dittus Boelter equation [33] for turbulent flow, h = 0.023 (')Re Pr4, (2.15) where k is the thermal conductivity and the Reynolds number is based on the liquid fraction flowing, Re G( x)D (2.16) /l The nucleate boiling heat transfer coefficient is evaluated using the Forster and Zuber [34] correlation for pool boiling, k 79 045 049 hb = 0.00122 05 O24 T Tat( ] 024 [t T~ 07 (2.17) o0 I 29hfg 24Pg where c, is the specific heat capacity, P is the pressure and the subscript w denotes the quantity is to be evaluated at the pipe wall. Chen argued that the amplification factor is a function of the Martinelli parameter and the suppression factor is a function of the two phase Reynolds number (Re2,), and through a regression analysis he determined the correlation curves for E and S. These correlations were presented graphically and much later Collier [35] proposed the following curve fits to the graphical correlations for E and S Eqs. 2.18 2.20, E = 1 for X' < 0.1 (2.18a) E =2.35 0.213 + 1 for X,' >0.1 (2.18b) S= (1+2.56 x106Re2 7)1 (2.19) where the twophase Reynolds number is determined by, Re2 = Re (E)125. (2.20) A more modem superposition model is the Gungor and Winterton correlation [36]. This correlation has the same form as the Chen [32] correlation, however, a different model is used for the nucleate boiling heat transfer coefficient and the enhancement factor is taken as a function of both the Martinelli parameter and the Boiling number. The Boiling number, Bo is defined as, Bo =q (2.21) hfgG where q" is the heat flux and hf, is the latent heat. The nucleate boiling heat transfer coefficient, hb, is modeled using the pool boiling correlation of Cooper [37], hb = 55PO12 ( log1 P)055M 05q07, (2.22) where M is the molecular weight and PI is the reduced pressure and is equal to the ratio between the system pressure and the critical pressure. The amplification factor and suppression factor were determined to be, 0 86 E = 1+ 24000Bol16 +1.37 (2.23) X,) and S = (2.24) 1+1.15x106E2 Re)17 For horizontal flow with Froude number less than 0.05 the amplification factor must be multiplied by the following factor, E = Fr(0 12Fr) (2.25) and the suppression factor should be multiplied by the following factor, S, = Fr (2.26) where Fr, is the Froude number is, Fr, = (2.27) pgD By incorporating the heat flux into the enhancement factor it is implied that the nucleate boiling process further enhances the bulk turbulent convection. This is consistent with the enhanced frictional pressure drop with increasing heat flux reported by Klausner et al. [38]. The correlation of MtllerSteinhagen and Jamialahmadi [39] uses a superposition technique that accounts for the interaction of the convective and nucleate boiling mechanisms by employing an enhancement factor and a suppression factor. This formulation absorbs the enhancement factor into the computation of the convective heat transfer contribution, and the correlation takes the form, h29 =h, + Shb. (2.28) This correlation employs the correlation of Petukov and Popov [40], for the liquid phase convective heat transfer coefficient, k (fj) Re29 Pr( h,= (2.29) D 1+12.7 f (Prl2/3 ) where the friction factor is given by Filonenko [41], f = (1.821og Re2 1.64) 2. (2.30) The twophase Reynolds number is defined as in Eq. (2.20) and the enhancement factor, E is given by Eq. (2.18). For flow through annular tubes Eq. (2.29) is multiplied by a factor ,6 (016 D=0.860 D'" (2.31) DoJ The suppression factor is computed by Eq. (2.19). In order to compute the nucleate boiling contribution to heat transfer, the pool boiling correlation developed by Gorenflo [42] is used, b t / p 0113 =~F, (2.32) he q" R, where Rp is the surface roughness of the pipe. The pressure function, FP and the exponent n are calculated using the reduced pressure P,, + + 0.68p2 (2.33) F =1.731<+ 6.1+ p 2. (2.33) Equation (2.33) pertains to water and other low boiling point liquids and is used here; for the computation of Fp for organic liquids reference [39] should be consulted. The exponent is calculated from n = 0.9 0.3Pr"2, (2.34) with a = 0.15 for water and other low boiling point liquids including nitrogen. The reference heat transfer coefficient ho, reference heat flux q", and reference surface W W roughness Rpo for nitrogen are found in [43], and are q" = 10000 h = 4380 and m m K R =lxl 06m. One of the most popular enhancement models is the Shah correlation, which was first developed in graphical form [44] and was later reestablished in equation form [45]. Shah proposed that the twophase heat transfer coefficient might be determined as follows, h2 = 'Phl. (2.35) The liquid convective heat transfer coefficient, h,, is evaluated using the DittusBoelter [33] equation, Eq. (2.15), as in the previous models. However, the evaluation of Y, is more complicated. N, = Co for Fr, > 0.04 (2.36a) N, = 0.38Fr,0 3Co for FrI < 0.04 (2.36b) F = 14.7 for Bo>lx104 (2.37a) F, =15.43 for Bo <11x104 (2.37b) where Bo is the boiling number defined previously and Co is the Convection number given by, Co =Clx P (2.38) x Ap Hence the contribution from the bulk turbulent transport is, 1.8 c = (2.39) and the contribution from the ebullition process is determined as follows, for N, >1.0 ,b = 230Bo05 for Bo > 3x105 (2.40a) or Yb = 1+ 46Bo5 for Bo < 3x10 5 (2.40b) for N, <1.0 Yb =]FBoo exp(2.74N;o1) for 0.1 b = rBo"5 exp(2.74N 15) for N < 0.1 (2.41b) Thus Y, is calculated as, S= max(Yc, b). (2.42) Shah [45] indicates that the equations agree with the graphical representation to within +6% over most of the chart except in two regions: 1) near Co = 0.004 and Bo = 50x104, and 2) for horizontal tubes at Fr, < 0.04 and Bo < xl104 He notes that the equations overpredict h by approximately 11% in region 1, but should not pose a problem since these conditions are in the postdryout region. The inaccuracy in region 2 of approximately 20% is inconsequential since values below Bo < 1x104 are rarely encountered in practice. This correlation uses the larger of the two effects in determining the heat transfer coefficient, thus some of the physics is inevitably lost in the process. Another enhancement model was developed by Kandlikar [46]. This correlation expands on the work of Shah [45] with the major advancement being the determination of a suppression factor and an enhancement factor that depend on not only the boiling number (Bo) but also the convection number (Co), the Froude number (Fr,) and a fluid dependent parameter. The twophase heat transfer coefficient is predicted as follows, h2 = ( CCoC2 (25FrN)c + CBo4 Fk, I. (2.43) h, is evaluated using the DittusBoelter [33] Eq. (2.15). The coefficients C, through C5 take different values depending on whether or not the heat transfer is determined to be in the convective region or the nucleate boiling region, and Fk is a parameter that enhances the nucleate boiling term and represents the fluidsurface combination effect. The values of these coefficients may be determined from Table 21 below. Table 21. Empirical constants for the Kandlikar correlation. Co < 0.65 convectivee region) Co > 0.65 nucleatee boiling region) C, 1.1360 0.6683 C2 0.9 0.2 C3 667.2 1058 C4 0.7 0.7 C5 0.3 0.3 Fk 0.74 0.74 The Kandlikar correlation has the added advantage of being much simpler to implement than the Shah [45] correlation. The asymptotic model was first introduced by Kutateladze [47] in 1961 while he was describing the influence of forced convection on heat transfer with nucleate boiling in tubes. He proposed that the heat transfer coefficient is a function of the ratio of the heat transfer coefficient due to convection and that due to nucleate boiling. This may be represented as, h,= f h^ (2.44) where the following conditions hold true, k =0 fn=l f= 0; (2.45a) hi S ,c fn fn 1. (2.45b) hi h, The most basic interpolation formula that satisfies these conditions is h n L +hb (2.46) hi h )h It was determined from experiments that an acceptable value of n is 2. However, this correlation does not account for either the enhancement effect or the suppression effect and thus was modified by a number of investigators to take these effects into account. A widely cited asymptotic model in the literature is that of Liu and Winterton [48]. This correlation models the twophase heat transfer coefficient in the following manner, h2 = (Eh)2(Shb). (2.47) They observed that previous correlations, which use the superposition principle, overpredict the heat transfer coefficient in the high quality region and under predict it in the low quality region. As a result they selected the asymptotic approach that has the property of further suppressing nucleate boiling once Eh, is appreciably larger than Shb . As with the previous correlations h, is evaluated using the DittusBoelter [33] equation, Eq. (2.15), however, the Reynolds number in this case is defined as GD Ref GD (2.48) The nucleate boiling heat transfer coefficient, hb, is evaluated using the Cooper model [37] for nucleate pool boiling, Eq. (2.22). The enhancement factor and the suppression factors are calculated as follows, 035 E= 1+xPr, Pl 1 (2.49) and S= (1+ 0.055Eo 1 Re, 16) . (2.50) For horizontal flow, the enhancement factor and the suppression factor are modified as previously mentioned in Gungor and Winterton [36]. Liu and Winterton claimed that this correlation performs better than those developed previously. However, the improvement is seen to be marginal. One correlation developed that cannot be placed explicitly into one of these three categories is the most recent one developed by Thome [49] and his colleagues. This correlation is best described as a flow pattern based model, since it is the first to use the flow structure to determine the portion of the pipe that is in contact with the liquid and the portion in contact with the vapor and apply a suitable model to the respective region for horizontal flow. The heat transfer coefficient is thus determined as follows, ROd, h + R(2; )hwe h = (2.51) where R is the internal radius of the pipe, 0d is the portion of the pipe circumference that is in contact with the vapor phase and the subscript wet indicates regions in contact with the liquid. The dry perimeter, Od,, is determined using a simplified geometric model for the flow structure. The vapor convective heat transfer coefficient, hg, is determined using the DittusBoelter correlation assuming tubular flow over the dry perimeter of the pipe, k h = 0.023Re08 Pr04 kg (2.52) g g D where the Reynolds number with respect to the vapor is GxD Reg (2.53) a'Ug and a is the void fraction. In calculating the void fraction, the Steiner [23] version of the Rouhani and Axelsson [50] drift flux void fraction model was adopted: 1. X )[go( p ,_01 25 1 x x 1x 1.18(1x) go )T2g a= (1+0.12(1x)) + +i +l'o8( GP5 (2.54) Pg g I P AGP The heat transfer coefficient, hw,, on the wetted perimeter of the pipe is calculated using an asymptotic equation of the form, hhe= (h +hJ)3, (2.55) where hb is modeled using the Cooper correlation [37] mentioned previously and h, is computed using a correlation developed by Kattan et al.[51], h=0.0133Re69 Pr4 (2.56) Here 3 is the simplified film thickness and the Reynolds number is 4G(1 x)3 Re, = x) (2.56) The simplified film thickness, 3, is determined based on the flow structure shown in Figs. 2.6 and 2.7. Vapr "''Uquld Figure 26. Flow structures used to evaluate stratified flow liquid film thickness and stratified angle. dry0 ,,str.tilrNd (a) (b) (c) Figure 27. Flow structures used to evaluate (a) annular flow liquid film thickness, (b) annular flow liquid film thickness and partialdry out angle, and (c) stratified liquid film with partial dryout angle. In order to better model the physical process that occurs in twophase with heat transfer, an expression for the onset of nucleate boiling, qoB was added; the expression gives the value below which the contribution due to nucleate boiling is not significant. The criterion employed was developed by Zurcher and coworkers [52], 2oT,,h, qo =2c (2.57) rcntPghg in which r,, is the critical nucleation radius, and is assigned the value 0.38x106 m. This correlation does not utilize the enhancement factor and the suppression factor as in other models. Using the asymptotic method for hwt, weighs the relative importance of the two effects, however, it is not proven that it correctly accounts for the enhancement and suppression effects. The existence of such a large number of predictive models for forced convection boiling heat transfer highlights the fact that a reliable model that may be applied universally has not yet been developed. This is clearly illustrated in three recent studies, each of which identifies a different model as giving the best predictions for the heat transfer coefficient. Greco and Vanoli [53] compared their data for HFC mixtures in smooth horizontal tubes with a number of correlations including the correlations of Chen [32], Gungor and Winterton [36], Shah [45], Kandlikar [46], and Thome and coworkers [49, 51]. They concluded that the best performance was achieved by using the Kandlikar correlation. Zhang, Hibiki, and Mishima [54] used their data for water, R11, R12 and R13, and evaluated the correlations of Chen [32], Shah [45], Gungor and Winterton [36], Kandlikar [46] and Liu and Winterton [48]. The best predictive model for their data proved to be the Chen correlation. In 2003, Qu and Mudawar [55] carried out experiments with water in microchannels and compared the heat transfer data obtained against the predictive models of Chen [32], Shah [45], Gungor and Winterton [36], Liu and Winterton [48], and Kandlikar [46]. The correlation of Liu and Winterton out performed the others. The predictive models reviewed all agree that the salient factors that influence the heat transfer in flow boiling is the bulk turbulent convection and ebullition. However, the manner in which they interact with each other is unclear, hence the existence for such a large number of correlations. These models have been developed using steady, non cryogenic flows, but neither of these conditions applies to the chilldown process. Since the chilldown process is characterized by rapid transients, pressure fluctuations, voracious evaporation and large temperature differences, which makes it very difficult to determine how the two effects responsible for the heat transfer interact. CHAPTER 3 EXPERIMENTAL FACILITY System Overview The experimental facility was developed so that the flow structure, the temperature profile, and the pressure drop may be measured simultaneously. It is illustrated schematically in Fig. 31 below. Collection Tank 1 CCD Vented to environment Nitrogen Supply Tanks FdP1 rnB Heat Element Ball Valve Temperature Pressure Differential Prenure Venturi Heat Exchanger Heat Transfer Section Figure 31. Schematic of chilldown experimental facility. Liquid nitrogen was selected as the working fluid for this investigation since it is chemically inert, colorless, odorless, noncorrosive, nonflammable, relatively inexpensive, readily available, and poses no significant environmental hazards; the physical and thermal properties of nitrogen are also well documented. The liquid nitrogen is stored in highpressure vacuum jacketed cylinders (at 1587 kPa), the tank pressure that provides the driving potential for the flow. Once the fluid exits the tank it is directed through a JouleThompson heat exchanger that cools the liquid to ensure that the nitrogen is in the subcooled state before entering the facility. Upon entering the facility the flow passes through a 304stainless steel section (I.D. 12.7 mm, O.D. 15.9 mm, approximate thermal conductivity 16.3 W/mC and specific heat 0.46 kJ/kgC), which is fitted with a series of external type E (ChromelConstantan) thermocouples (3 on the top of the pipe, and 3 at the bottom of the pipe), an internal type E thermocouple and pressure tap. This allows the inlet flow conditions, and the outer wall temperature profile to be determined. Following this section, the fluid then enters a vacuum jacketed visual test section fabricated from pyrex. Here the flow structure is captured via a CCD (ChargeCoupled Device) camera with appropriate image capturing software. The nitrogen then passes through another section of piping which contains an internal thermocouple and a pressure tap, which are used to record the exit conditions at the exit of the visual test section as well as the pressure drop across it. Once past this measuring station the fluid enters the heat transfer section of the facility. The section is 38 cm in length between the inlet and outlet; inline thermocouples record the fluid temperature at these points. A series of thermocouples are placed circumferentially around the pipe wall and the outer surface for the insulation, which are used to extract the unsteady heat transfer coefficient information (the details of this procedure is given in a later section). A cryogenic ball valve is located after the heat transfer section that allows the flow to be throttled; thus a wider range of flow rates is attainable. Once through the ball valve, two heaters vaporize any remaining liquid before the flow enters the venturi flow meter. Then nitrogen is collected in an expansion tank before being vented to the atmosphere via a ventilation system. In performing the experiments, the ball valve is set to the desired position, and the data acquisition system is activated just prior to opening the nitrogen cylinder. All the measurements, including image capturing, are made electronically and the data are recorded and displayed in near real time, allowing for immediate experiment feedback, and determination of the completion of chilldown. Visual Test Section Design One of the most vital components of the cryogenic facility is the visual test section. The visual section consists of a vacuum insulated pyrex tube that is designed to operate under high pressure (maximum of 1400 kPa) and low temperature conditions (180 C) that exist during chilldown. In order to connect the to the stainless steel tubing pyrex tube a flange assembly was designed that ensures leakfree operation, see Fig. 32. Hex Nut Teflon Oring ...... ...... .... ::::::...... ............ .. .... Test Sectio .... *:* .... ....... S. .....Teflo nGor Goretex Gasket Figure 32. Schematic of the flange assembly. Instrumentation and Calibration One of the most vital components of the cryogenic facility is the visual test section. The visual consists of a vacuum insulated pyrex tube that is designed to operate under the high pressure (maximum of 1400 kPa) and low temperature conditions (180 C) that exist during chilldown. In order to connect the to the stainless steel tubing, a pyrex tube flange assembly was designed that ensured leakfree operation, see Fig. 32. Static Pressure Transducers Two Validyne P2200V pressure transducers are installed in the facility. One is installed at the inlet to the visual test section so that the inlet pressure (P,) of the fluid may be determined, while the second on is installed at the inlet to the venturi flow meter to measure the pressure (P ), which allows for corrections to be made for compressibility effects. The transducers are rated for 1340 kPa and are independently calibrated using a mercury manometer. The equation of the calibration curves are given by, P = 27.712 + 274.937 V (3.1) and P2 = 30.709 + 276.479 V (3.2) where P1 and P2 are in kPa and V is the voltage output in volts. The plots of the calibration curves are given in the work of Velat [56]. Test Section Pressure Drop The pressure drop (AP) across the visual test section is recorded using a Validyne model DP215 variable reluctance differential pressure transducer equipped with a dash 30 diaphragm (rated for 0.0 to 8.6 kPa). A carrier demodulator device converts the transducer signal to an analog voltage, and allows the span to be adjusted and signal to be zeroed. The calibration of the transducer was carried out using a manometer with R 827 manometer oil. The equation of the calibration curve is given by, AP= 1.2788 V (3.3) where AP is in kPa and V is in volts; the upper limit on the calibration is 8.2 kPa (the curve may be seen in the work of Velat [56]). The standard deviation of the calibration is 0.12%, which is within the 0.25% fullscale accuracy listed by the manufacturer. Flow Meter Calibration The nitrogen flow rate is measured using a Presco venturi flow meter that has an inner diameter of 13.9 mm and a throat diameter of 8.73 mm. Proper performance of the flow meter demands that only nitrogen vapor pass through the instrument; to ensure that this is the case two 1kilowatt coil heaters are positioned prior to the flow meter so that any liquid nitrogen is vaporized before entering the venturi. A Validyne variable reluctance DP 15 differential pressure transducer with a dash 40 diaphragm (rated for 0.0 to 86.0 kPa) was used to measure the pressure drop across the venturi; this diaphragm maximizes the sensor output response while providing moderate overload protection. The differential pressure transducer is coupled to a carrier demodulator device. The transducer and demodulator device were calibrated using a mercury monometer, see Velat [56] for calibration curve. The standard deviation of the differential pressure transducer calibration was 0.17%, which was within the 0.25% full scale accuracy claimed by the manufacturer. Once the transducer was calibrated, the venturi flow meter was calibrated with an Omega vortex flow meter with compressed air. The actual velocity measured with the vortex flow meter was plotted against the ideal velocity (see Fig. 3.3) computed with the measured pressure drop and a modified Bernoulli relation [57], which accounted for compressibility, P0 =P+ Ipu2 +Ma2+ Ma4 +... (3.4) where is the Mach number and y is the ratio of specific heats. where Ma is the Mach number and 2 is the ratio of specific heats. 160 140 120 g 100 80 73 > 80 < 60 40 20 0 50 100 150 200 250 300 Ideal Velocity (m/sec) Figure 33. Calibration plot of the actual velocity versus the ideal velocity (Velat [56]). A polynomial curve, shown in Eq. (3.5), was then fit to the calibration data and used to correlate the ideal velocity with the actual velocity. actu= (1 107)uea (5*105)* deal +0.0076 deall +0.5653 ideall (3.5) Temperature Measurements Measuring the temperature at various locations in the experimental facility was vital in understanding and analyzing the chilldown process. The temperature at the inlet and exit of the visual test section were measured using two 1/16inch type E (Chromel Constantan) thermocouple probes from Omega Engineering. These probes were placed through precisiondrilled holes in line with the fluid and sealed with a combination of A Compressible Velocity 0 Incompressible Velocity / Curve Fit brass compression fittings. In order to monitor the chilldown process, a series of 6 (laboratory manufactured) type E (ChromelConstantan) thermocouples were placed along the top and bottom of the 304stainless steel tube prior to the test section, see Fig. 34. Temp3 Temp2 Tempi .... TestSection 32 mmr *  Temp 6 Temp 5 Temp 4 Figure 34. Thermocouple arrangement on the steel transfer line prior to the visual test section. These temperature measurements were used to determine the end of the chilldown process, which is the point at which the transfer line temperature reaches the saturation temperature of the liquid nitrogen. The heat transfer section of the facility is located downstream of the visual test section and is instrumented with 16 type E (laboratory manufactured) thermocouples. These were symmetrically positioned around the exterior of the pipe wall and insulation as shown in Fig. 35. The thermocouples were placed in such a manner that the exterior thermocouples that were secured to the insulation were exactly at the same angular positions as the interior thermocouples that were secured to the pipe wall. Each group of thermocouples is separated by an axial distance of 9.0 cm and is secured to the insulation and the pipe wall with 0.25inch Teflon tape, to ensure proper thermal contact. At the inlet and exit of the heat transfer section, thermocouple probes, separated by an axial distance of 35.5 cm, were used to evaluate the change in fluid temperature as it passed through the section. The temperature data obtained were used to calculate the unsteady heat transfer coefficient. ... .: .. .. .. ..... .... ..... .... .......... .. ... .. ... ........ . Figure 35. Thermocouple placement for heat transfer test section. Once through the heat transfer test section the flow passes through the venturi flow meter, which is instrumented with an inline type E thermocouple. The temperature and pressure information at this location are used to correct for any compressibility effects. The temperature readings were accurate to +1.70C over the large temperature range experienced in these experiments. Data Acquisition System A digital data acquisition system was assembled to record and process the analogue output of the instrumentation. The system consists of a personal computer outfitted with an analog to digital data acquisition board and accompanying data acquisition software. The computer is equipped with an AMD Athlon XP 2200 MHz processor board in combination with 15 Gigabits of random access memory. The analogtodigital board was a Measurement Computing PCIMDAS 1602/16 with 8 channels and 16 bit resolution and was connected to two Measurement Computing CIOEXP32 multiplexer boards. These two multiplexer boards allow for 64 analog inputs/channels. Each board is divided into two banks of 16 channels each. The gain for each bank of 16 may be set independently, and as such the gain for the thermocouple signals was set to 100 while the gain for the pressure transducers was set to 1. The reference temperature for thermocouple readings was obtained from an on board junction temperature that was input to the analogtodigital board through a selected channel. All channels through which thermocouple measurements are taken are provided with a 1 [F capacitor across the high and low inputs forming a lowpass filter having a 7 Hz filtered cutoff. Open thermocouple detect, and a reference to ground through a 100 kohm resistor are also provided. The analogtodigital board and each multiplexer board were calibrated to the manufacture's specifications using the supplied software, InstaCal. A computer program was developed, using Softwire, to measure and record the experimental data. The program sampled each channel at a frequency of 50 Hz, and compiled these readings in a series of distinct arrays. At the completion of the 50th recording, the arrays were time averaged, and transferred to an Excel spreadsheet where further data processing was carried out. In the Excel spreadsheet, the temperature and pressure data were processed to obtain the mass flux, Mach number, vapor and liquid velocities, vapor and liquid densities, and vapor and liquid Reynolds numbers. Digital Imaging System A digital imaging facility was constructed to capture the flow structure as it passed through the visual test section. The imaging system was comprised of a Pulnix TM 1400CL progressive scan CCD (capable of capturing images with 1392 x 1040 pixel resolution), with a 50 mm Canon magnification lens, connected to a Data Translation DT3145 framegrabber board via a Camera Link cable. Images were captured using the Global Imaging Lab software provided by Data Translation, which not only records the images but also allows for the image to be calibrated so that accurate length measurements may be made. The visual data allowed for the flow regime and vapor volume fraction to be determined. Experimental Protocol Once the experimental facility was constructed it was used to investigate the cryogenic chilldown process. Experiments are carried out in the following manner: * The data acquisition program is activated so that it may commence recording at the push of a button. * The imaging program is activated so that it may begin capturing the flow structure at the push of a button. * The nitrogen tank connected to the heat exchanger shellside is opened. * The nitrogen tank connected to the facility is opened to a predetermined position and the data acquisition program and imaging program are started. * Liquid nitrogen is allowed to flow through the facility until all thermocouples that are in contact with the pipe wall read the saturation temperature of the liquid nitrogen; at that point it is concluded that the chilldown process is complete. * The temperature, pressure and mass flow rate are recorded as described prior. * The flow structure images are recorded as described prior. The liquid film thickness is measured from the flow structure images using the Global Imaging Lab software from the information recorded. * The above steps are repeated with the throttling valve in different positions so that a wide parameter range may be investigated. In the following chapter the data reduction method will be presented. CHAPTER 4 DATA PROCESSING Vapor Quality Estimation The direct computation of the vapor quality using an energy conservation approach was not employed because there is a substantial amount of energy transfer into the nitrogen that is not easily quantified. In order to obtain an approximation for the vapor quality, a correlation between the vapor volume fraction and the vapor quality is utilized. One of the simplest models that correlates vapor quality and vapor volume fraction is the slip velocity model. The slip velocity, S, is the ratio of the mean vapor velocity to the mean liquid velocity and can be expressed as, S=lf P (4.1) The above expression may be rearranged to express vapor volume fraction as a function of quality and slip velocity, as in Eq. (4.2), or it may be rearranged to express the quality as a function of the vapor volume fraction and the slip velocity, as in Eq. (4.3). a =, (4.2) x+S(1x) P x = aS (4.3) aS+(1 a) P\ \P,) The slip velocity model is limited to situations in which the slip velocity remains relatively constant, and this is not the case for the chilldown process. Instead a different correlation for relating the vapor volume fraction to the vapor quality is employed. In 1965, Zuber and Findlay [59] developed a more practical model to correlate the vapor quality and the vapor volume fraction. The model was derived by considering the local volumetric fluxes of the liquid and vapor phases together with the mass continuity equations of the two phases. It was determined that the vapor volume fraction and the vapor quality are related by, =Co 1+1 + ,U (4.4) a x P, Gx where Co and are empirical constants. The distribution parameter, Co, which accounts for nonuniform flow and concentration profiles, and 0U accounts for the effect of the local relative velocity. Eq. (4.4) may be rearranged to give, x= a(pgU +CoG) (4.5) G 1Co+Coa^ It was demonstrated by Klausner [60] that assigning values of Co = 1.0 and U = 0.6 for horizontal flow, give excellent agreement: within + 5% for over 90% of the horizontal twophase flow data with R113 as the working fluid. Due to the excellent agreement with the horizontal flow experiments of Klausner [60] using R1 13, Eq. (4.5) was used to estimate the vapor quality from the measured vapor volume fraction. Vapor Volume Fraction The vapor volume fraction a is an important parameter that must be determined when analyzing twophase flows. This is underscored by the fact that many different experimental methods have been developed to compute this quantity. Methods vary from using gamma radiation absorption and laser dispersion techniques to visual techniques. For this study, digital images of the flow structure were recorded; thus a visual technique is adopted. In order to compute the vapor volume fraction, the flow regime must first be identified. Researchers have used a number of different conventions to describe the various flow structures observed in horizontal twophase flows; the convention used here is the one described by Carey [58] and is illustrated in Fig. 2.1. Once the regime is determined one of the following approaches is used to compute the vapor volume fraction. If the flow regime is classified as stratified, wavy or intermittent the liquid height is measured using the Global Imaging Lab software from the images as shown in Fig. 4.1. The vapor volume fraction is calculated, a=r 1 2 2 (4.6) For the case of annular, and plug flow, the flow structure is modeled as shown in Fig. 42. The liquid film thickness at the top, 8top, and bottom, bottom, of the tube are measured and the vapor volume fraction is calculated as a= 1 bottom 2r 2rtop 2r Figure 41. Model used for the stratified, wavy and intermittent flow volume fraction computation. Figure 42. Diagram of the model used for the annular flow volume fraction computation. Extracting the Heat Transfer Coefficient In order to extract the heat transfer coefficient from the temporal profile of wall temperature; an inverse procedure is employed which varies from that of traditional inverse heat conduction methods. It does not require a system of leastsquare equations to be solved. Some of these traditional methods are reviewed by Ozisik [61]. (4.7) The process used here for extracting the transient heat transfer coefficient on the inside of the pipe involves a number of iterative procedures, which are reported here as three major steps. These steps are illustrated in Fig. 43 and are carried out for each instance of time. These steps include (1) guess the heat transfer coefficient on the inside of the pipe, (2) knowing the heat transfer coefficient on the outside of the pipe via calibration, the temperature field is calculated, and (3) the temperatures calculated at the outer wall are then compared with those measured. If the temperatures match, the guessed heat transfer coefficient is taken as the actual heat transfer coefficient, otherwise a new guess is made and the process is repeated until the computed and measured temperatures match. Guess the heat transfer coefficient inside the pipe Solve the heat conduction equation in the pipe wall Check if computed temperatures and measured temperatures at the outer surface match Do temperatures no match? yes Record the heat transfer coefficient Figure 43. Flow chart for transient heat transfer coefficient extraction. Computing the Temperature Field in the Pipe Wall The unsteady 3D form of the heat conduction equation in cylindrical coordinates, see Fig. 44, is written as follows: aT 8 ( aT\ 1 8( aT\ 1 8 (k T\ cp= k +I rk +  (4.8) a t 8z 8z r ar ar) r 8Cr 8o) where p is the density of the material, cp is the specific heat capacity, t is the time variable, T is the temperature, r is the radial coordinate, z is the axial coordinate and 0 is the azimuthal coordinate. This equation is nondimensionalized using the following parameters: T T z r k p ) T, Ta, d; d; crp k/ Po, where T,, is the saturation temperature of the fluid within the pipe, 7T is the temperature on the outer wall of the pipe, d is the pipe wall thickness, and the subscript 0 denotes the property is to be evaluated at the initial temperature, To. Thus the original equation is transformed to Pocod2 o= + kI + (4.10) The temperature variations experienced by the pipe during the chilldown process are significant, and thus the thermal properties (k and c) of the pipe material vary significantly. These variations are taken into account by assigning the thermal properties as a function of the temperature at any given point. A finite volume formulation is used to disceritize Eq. (4.10); a backward Euler scheme is employed for the temporal term and a central difference scheme is used for the spatial terms. The system of equations that result are solved using the Alternating Direction Implicit (ADI) method described in [62]. In order to solve the system of equations, the energy entering the system from the ambient must be known; hence the heat transfer coefficient for the outside surface of the r I I  \m z P Din Dout I   Figure 44. Coordinate system for heat conduction through the pipe wall. pipe insulation must be determined. This is accomplished through a steadystate calibration process in which cool nitrogen vapor is passed through the heat transfer section at various mass flow rates. A relationship between heat flux through the pipe insulation versus temperature difference (ambient temperature less the insulation surface temperature) is determined. A constant heat transfer coefficient is approximated as shown in Fig. 45. The slope of the line is the heat transfer coefficient for the outer pipe ft surface. The measurement of the heat flux into the pipe, q, is quite difficult to measure due to the small temperature rise in the cryogenic vapor; thus there is some scatter in Fig. 45. However, the measured heat transfer coefficient, 4.38 W/m2K, is quite small, compared with convective heat transfer on the inner pipe wall. The errors in the calibration have a negligible impact on the computed thermal field in the pipe wall. The boundary condition for the outer pipe surface is written, fT k = hoU, (ToU, T), (4.11) ar 60 Measured q," 50 Linearfit 4 40 30 20 10 0 2 4 6 8 10 12 AT (K) Figure 45. Calibration for determining the outer pipe surface heat transfer coefficient. which is nondimensionalized to give, = hd h+ T, h T (4.12) ar' ko k T,T at Here subscripts out and oo denote the outer surface of the pipe, and the outer insulation surface, respectively. The inner pipe boundary condition is written as, aT k r=h,(Tl, (4.13) ar which is then nondimensionalized to give, _~ = h,,d d h,,t h,jl ( kk k+0 T (4.14) ar k, ki T, T^ Here the subscripts i and fl denote the inner surface of the pipe and the fluid flowing through the pipe, respectively. The fluid temperature is determined using an internal thermocouple that measures the temperature at the inlet of the heat transfer section. The heat transfer coefficient on the inside of the pipe, h,, is the quantity that is guessed during the calculation. The twophase flow structure present for much of the experiment is stratified, and there is a significant difference between the temperature at the top of the pipe and the temperature at the bottom the pipe. This must be due to circumferential variations in the heat transfer coefficient. This problem is dealt with adequately by dividing the interior surface of the pipe into three distinct sections within which the heat transfer coefficient is assumed constant. Region 1 is such that 0 a << a, and h,, = htop, region 2 is such that a, < < a and h,, = h,,, and region 3 is such that a2 allow all three regions to be equal in size, hence, a, = a 1 a, = r a2. However in the nucleate boiling regime, where the temperature at the bottom changes suddenly by a significant amount very high heat transfer coefficients are present. Hence it is important not to overestimate the size of the region in which nucleate boiling occurs. If the region is overestimated then the amount of energy removed from the pipe would be too large in the adjacent region (in this case region 2) making it impossible to match the outer wall temperature. This is handled adequately by reducing the size of region 3 by increasing the value of a2. When necessary, it is sufficient to reduce the size of region 3 by a factor of 2. For modeling purposes, a more systematic approach to describing different regions during nucleate boiling is desirable. However, the present approach is sufficient to match the measured and computed wall temperature variations. Iteration Process for Guessing the Inner Heat Transfer Coefficient Any number of methods may be used to obtain a new guess for the inner heat transfer coefficient; a systematic method for iterating is recommended. In this work after the initial guess is made subsequent guesses are determined using linear interpolation or a Region 1 hIln=htop Region 2 hin=hside Region 3 hln=hbottom Figure 46. Assumed variation of heat transfer coefficient on the inside surface of the pipe. linear extrapolation. Hence the new guess for inner heat transfer coefficient is given by, h h res hrev Tpre )+hprev, (4.15) Tpres prev where s is a scaling factor that reduces oscillations and takes the value 0.3 in this work. The subscripts pres, prey, new, and known denote the present, previous, new, and known quantities respectively. Test for Convergence The final step in the process is checking the computed temperature against the measured temperature. This is done using the temperatures at the top, side and bottom of the pipe. Once the computed temperature is within +lxl108 K, the temperatures are considered a match. Care must be taken when determining the limit within which to consider the temperatures to be matched; if the value selected is too small the computation time increases significantly and the marginal improvement in accuracy does not justify the increased computational cost. Computational Code: Testing and Verification Stability of Computational Code For simplicity the stability criterion is developed using the Von Neumann analysis of the ID heat conduction equation, au 2U aa (4.15) at x2 where u is the dependent variable, t is the time, x is the spatial parameter and alpha is the thermal diffusion. Eq. (4.15 ) is discretized using a backward in time and central in space scheme.gives un+l un At (Ax)2 n+1 2 +u (4.16) where n is the index representing time, and j is the index representing space. The stability analysis of this scheme may be found in any classical numerical methods text, and proves that the scheme is unconditionally stable. This is also true for the 2D and 3D schemes. Grid Resolution The grid resolution is as an important factor when considering the accuracy of the solution obtained from numerical computations. Thus, the influence of grid resolution on the computed heat transfer coefficient is assessed by examining the average percentage error obtained when various size grids are utilized. A singlephase flow simulation with a constant heat transfer coefficient is used to compute the outer wall surface temperature for a series of 50 time steps. The physical parameters are as follows: 1) pipe density = 8000 kg/m3, 2) pipe specific heat capacity = 500 J/kgK, 3) pipe thermal conductivity = 16.2 W/mK, 4) inner diameter of pipe = 12.5mm, 5) thickness of pipe = 1.65 mm, and 6) time step size = 0.1 sec. The inverse procedure is then applied to this series of temperature values to extract the heat transfer coefficient. This is done using various size grids. The average percentage error is computed as, 1 abs (hoct ol h xt)ed) Average percentage error = as ( actual acted x 100, (4.17) N= actual where N is the number of time steps. The results are given in Table 41. Table 41. Influence of grid resolution on the computed heat transfer coefficient. Nx Ny Average percentage error (%) 120 64 0.000729 60 32 0.003904 30 16 0.01681 From Table 41 we see that the refinement of 60x32 or better gives an error of less than 4 x 103%. Hence no significant error is introduced once the grid resolution is better than 60x32. For this study we have chosen to use a refinement of 60x32 as it is gives good results with little additional computational cost. From Fig. 47 we observe that the approach s second order accurate, which is consistent with the numerical scheme employed. Testing the Inverse Procedure In order to assess the performance and validity of this inverse method, it is first used to calculate the heat transfer coefficients for a singlephase flow simulation in which the heat transfer coefficient is known and varies in time. Second it is used to calculate the actual heat transfer coefficient for singlephase nitrogen gas flowing through the 32 34 36 38 4 42 44 46 48 35 4 45 y = 2 2636x + 3 6496 2 w 5 > 5 5 z 6 65 7 75 LN(Grid Size) Figure 47. Ln(Error) vs In(grid size) for the inverse technique. experimental facility, with the results being compared with the predictions of the Dittus Boelter correlation for cooling. Finally, it is used to calculate the heat transfer coefficient for a single phase flow simulation undergoing a step change in heat transfer coefficient. In the first test case, the heat transfer coefficient follows a parabolic path with time. A comparison of the specified heat transfer coefficient with that extracted using the inverse method is shown in Fig. 48 (the time step size used in this test is 0.1 sec; all other parameters are as specified previously). In Fig. 48 it is seen that a parabolic varying heat transfer coefficient is captured quite reliably with the inverse approach. The difference between the exact and the extracted heat transfer coefficients for this case are shown in Fig. 49. It is seen that error is not significant and it is of interest to note that the error is largest in regions where the rate of change of temperature with time are largest. A comparison of the extracted singlephase heat transfer coefficient with the Dittus Beoelter correlation for flowing nitrogen gas is shown in Fig. 410 (the time step size used in this test is 1 sec since that is the smallest time interval for which reliable data could be obtained; all other parameters are as specified previously). The comparison is quite good. The heat transfer coefficient is not constant with time since the mass flux fluctuates around a mean of 196 kg/m2s. Figure 411 illustrates the performance of the inverse procedure in a case where there is a step change in the heat transfer coefficient (the time step size used in this test is 0.1 sec; all other parameters are as specified previously). It is observed that the inverse procedure is capable of handling a step change in heat transfer coefficient satisfactorily. In order to assess the sensitivity of the procedure to errors in the experimental measurements of pipe wall temperature, 0.2C errors were artificially added to the measured data, and the heat transfer coefficient extraction procedure is applied. The value 0.2C is the repeatability of the thermocouple measurements, and since the extracted heat transfer coefficients depend on the temperature difference between successive time instances, the error associated the temperature difference is also expected to be of this order. It was found that the perturbation of 0.2C resulted in a maximum deviation of 6% in the value of the heat transfer coefficient extracted. Hence the inherent variations in thermocouple measurements do not significantly affect the extracted heat transfer coefficients. The inverse technique is next applied to the experimental data for the chilldown process in the nucleate boiling regime. The unsteady heat transfer coefficients on the inner surface of the pipe are extracted over regions 1, 2, and 3. 0 2 4 6 8 10 12 14 16 18 20 Time (sec.) Figure 48. Computation of a parabolic varying heat transfer coefficient using the inverse method. 0004 00031 0002 0001 " oool E 0 S0 001 0 002 0 003 0 004 Time (sec.) Figure 49. Difference between the exact heat transfer coefficient and the heat transfer coefficient extracted using the inverse technique for the parabolic varying heat transfer coefficient simulation given in Fig 48. ) 2 4 6 8 10 12 14 16 18 4+ 4 4 *4 *4 * ^ 400 0emoe 0 o o oo 0 00 f 300 ,E Tbulk =174 K 200 = 196 kg/m2s DittusBoelter correlation 100 a o Inverse model 0  0 5 10 15 20 25 30 35 Time (sec) Figure 410. Comparison of heat transfer coefficient computed using the inverse procedure and the DittusBoelter correlation for singlephase nitrogen gas flow. 2500 2000 E ' 1500 .2 0  S1000 I 500 500  0 05 1 15 2 25 3 35 4 Time (sec.) Figure 411. Computation of a step change in heat transfer coefficient using the inverse method.  Actual Heat Transfer Coefficient A Extracted Heat Transfer Coefficient CHAPTER 5 CHILLDOWN FLOW TRANSITION AND HEAT TRANSFER Upon introducing the liquid nitrogen into the facility, heat stored in the pipe walls vaporizes the incoming fluid. As more liquid enters the facility a liquid film is observed to travel through the pipe supported on top of a vapor layer. This is the film boiling regime. As the pipe wall cools it eventually reaches the Leidenfrost temperature at which point nucleate boiling ensues resulting in a much higher heat transfer rate. This transition between the film boiling regime and the nucleate boiling regime is marked by the quenching front which is shown in Fig. 5.1. Figure 51. Quenching front that marks transition for film boiling to nucleate boiling The data from two experiments are shown in Figs. 5.2 and 5.3, for various circumferential positions on the outer wall of the pipe (the top, the bottom, and the left and right sides). These measurements are recorded on the outer wall of the pipe in the first station of the heat transfer section, which is located approximately one meter down stream of the visual test section. Fig. 52 gives the temperature profile for a low mass flux experiment, 75 kg/m2s (the actual mass flux data is shown in Fig. 54); while Fig. 5 3 gives the temperature profile for a moderate mass flux experiment, 210 kg/m2s (the actual mass flux data is shown in Fig. 55). By examining Figs. 52 and 53 it is seen that the heat transfer process passes through two distinct regimes, which are the film boiling regime and the nucleate boiling regime. The film boiling regime is seen to have a lower heat transfer rate than for the nucleate boiling regime, which is illustrated by different temperature gradients in the two regions. It is also observed that at higher mass flow rates the chilldown time is shorter, which is expected since there is a higher rate of thermal transport. 50.00 1 0.00 50.00 E 100.00 150.00 200.00 0 20 40 60 80 100 120 140 160 180 Time (sec) Figure 52. Temperature profile during chilldown for low mass flux experiment. Temp 1 (Top) M * Temp 2 (Left)  Temp 3 (Bottom) S <Temp 4 (Right) ______ Stratified /V avy_____ 50.00 oTemp 1 (Top) Temp 2 (Left) 0.00 ' Temp 3 (Bottom) Temp 4 (Right) 35 VStratifie d/ Wavy S50.00 a Slug Plug E 100.00 I 150.00 200.00 0 20 40 60 80 100 1: Time (sec) Figure 53. Temperature profile during chilldown for moderate mass flux experiment. 120.00 100.00 c 80.00 E S60.00 x 40.00 20.00 0 20 40 60 80 100 Time (sec) 120 140 160 180 Figure 54. Transient mass flux for low mass flux experiment. 300.00 250.00 S200.00 E S150.00 L S100.00 50.00 0.00 Figure 55. Transient mass flux for moderate mass flux experiment. 1.2 1.0 Stratified/Wavy 0 0.8 E 0.6 C 0.4 0.2 0.0 0 20 40 60 80 100 120 Time (sec) Figure 56. Transient vapor volume for low mass flux experiment. 140 160 180 Stratified r Wavy Slug Plug 0 20 40 60 80 100 12 Time (sec) 1.2 Stratified/Wavy Slug Plug 1.0  .0 0.8 U E 0.6 0.4 0.2 0.0 0 20 40 60 80 100 12( Time (sec) Figure 57. Transient vapor volume fraction for moderate mass flux experiment. 1.2 1.0 Stratified/Wavy 0.8 S0.6 0.4 0.2  0.0 0 20 40 60 80 100 120 140 160 180 Time (sec) Figure 58. Transient vapor quality for low mass flux experiment. 1.2 Stratified/Wavy Slug Plug 1.0 0.8 c0.6 0.4 0.2 0.0 0 20 40 60 80 100 120 Time (sec) Figure 59. Transient vapor quality for moderate mass flux experiment. It must be noted that the mass flux data collected at the start of the experiment may not be reliable. In the instances when the storage tank pressure is high a shock is generated when the valve is initially opened. This causes large pressure oscillations which leads to erroneous mass flux readings from the venture flow meter, which uses pressure to determine the mass flux. This is evident in Fig. 510, which displays the inlet pressure profile for the low mass flux experiment. The moderate mass flux experiment also exhibits this behavior, however it is more mild than the low mass flux case, which is evident from Fig. 511. Flow Regimes The detailed momentum and heat transfer processes that evolve during transient chilldown are not well understood, which limits the development of advanced hydrodynamic and thermal models. Knowledge of the flow structure is essential to 63 predicting the nonuniform temperature fields encountered during the film and nucleate boiling heat transfer regimes. A satisfactory flow regime transition map has yet to be 1400 1200 1000 800 600 400 200 0 Figure 1000 900 800 700 . 600 500 S400 300 200 100 0 0 20 40 60 80 100 Time (sec) 120 140 160 180 510. Transient inlet pressure profile for low mass flux experiment. 0 20 40 60 80 100 Time (sec) Figure 511. Transient inlet pressure profile for moderate mass flux experiment. developed that address the cryogenic chilldown process. The experiments carried out allow the flow regime transitions encountered during transient cryogenic chilldown in a horizontal pipeline to be observed and recorded. The observations are compared with well known flow regime maps described in chapter 2. Experimental Observations The flow pattern names and corresponding flow structures observed during this investigation are shown in Fig. 21. Experiments are carried out for mass fluxes that range from 66 to 625 kg/m2s; and vapor qualities vary from 0.004 to 1. The entire database consists of 2625 data points and is available in Excel format from the author. When the liquid nitrogen first enters the flow facility a film boiling front is positioned at the entrance to the facility. This film boiling front produces voracious evaporation accompanied by a high velocity vapor front traversing down the test section. The vapor flow is typically entrained with a very fine mist of liquid to produce a mist flow. The mass flux through the system rises very rapidly, but is constrained by the fact that the flow becomes choked due to the high velocity vapor flow. Typical profiles of the mass flux are shown in Figs. 54 and 55. At low to moderate mass fluxes (usually below 350 kg/m2s), a stratifiedwavy flow structure with a thin liquid film is seen to flow through the pipe once the film boiling front has passed through the test section. At this point the flow is in the film boiling regime, and a thin layer of vapor exists between the liquid film and the pipe wall; hence the heat transfer is mainly the result of thermal conduction through the vapor layer. As the pipe chills, the liquid film thickness grows. The flow transitions from film boiling to nucleate flow boiling when the pipe wall temperature falls below the Leindenfrost temperature. This transition is characterized by the sudden and steep increase in the slope of the wall temperature history profile shown in Figs. 52 and 53. This transition to nucleate flow boiling is observed visually as a quenching front that propagates through the pipeline. As the pipe cools further, the flow structure transitions from the stratifiedwavy regime to the intermittent regime. Once the pipe wall temperature reaches the saturation temperature of the nitrogen, the flow transitions to singlephase liquid flow. At higher mass fluxes (usually above 350 kg/m2s), the initial mist flow structure transitions into annular flow following the passage of the film boiling front. The later flow transitions include intermittent and singlephase liquid flow. The mass flux, shown in Figs. 54 and 55, and vapor volume fraction profiles, shown in Figs. 56 and 57, highlight the inherent unsteady nature of the chilldown process. The vapor volume fraction was computed from the digital images of the flow structure and smoothed by finding the best smooth curve fit to the measurements, as outlined in Chapter 4. The computed vapor quality profile is illustrated in Figs. 58 and 59. Performance of Current Flow Regime Maps Modem phenomenological twophase flow models rely on knowledge of the flow structure for a prescribed operating condition. Three different well known flow pattern maps are tested against the experimentally observed flow regimes for horizontal cryogenic flow chilldown. These include flow regime maps proposed by Baker [19], Taitel and Dukler [16], and Wojtan et al. [24]. All of these flow regime maps were developed for quasisteady twophase flow. They do not attempt to account for the transients encountered during chilldown. Van Dresar and Siegwarth [63] reported flow patterns for low mass flux (97346 kg/m2s) steady twophase flow of nitrogen through a horizontal pipeline. The data of Van Dresar and Siegwarth [63] are compared against the flow regime predictions from the three maps discussed. Only turbulent flow data are considered. Comparisons with the Baker map, shown in Fig. 512, are rather fortuitous, as it is observed that the flow patterns are correctly predicted with the exception of 2 points, which lie close to the correct flow pattern regime. It is observed in Fig. 513 that the Taitel and Dukler map performs reasonably well, as all the data points lay within or close to the predicted flow pattern. The Wojtan et al. map is able to predict slug flow which is considered to be intermittent flow; however it is unable to predict the annular data, as shown in Fig. 514. The flow regime transition maps are now applied to the data obtained for the chilldown process, which at times may have significantly larger mass fluxes than the experiments reported by Van Dresar and Siegwarth [63]. The entire database consists of 2625 data points. Table 51 provides a sample of 40 data points from the assembled database, which covers the entire range of parameters. For the purpose of clarity, the flow regime maps are compared against a representative set of data consisting of 400 data points. These 400 data points cover the entire range of flow parameters and flow structures. They are chosen to avoid excessive clustering of points in the flow regime maps that occur when the entire database is used. A comparison of the data with the Baker map is shown in Fig. 515. It is observed that the intermittent data are predicted reasonably well, but neither the annular nor the stratifiedwavy predictions give satisfactory agreement with the data. Fig. 516 shows a comparison of the experimentally observed flow regimes with those predicted using the Taitel and Dukler map. Although, many observed flow regimes differ from those predicted, the agreement could be greatly improved with calibration. A comparison of the data with Wojtan et al. map is shown in Fig. 517. While the stratifiedwavy and the 67 I l I I I I l I I I I 20 100 2 10 0.2hi 0,1 0.5 0.1 0.05 x = interrr 0. 0.2 = annul + = stratifi 0.02 0.1 kg/fms 5 10 20 D kgr s 50 100 200 500 1000 2000 I 1 I 1 I 1 I I I I I I I lb/fls 1 2 5 10 20 50 100 oyu 5000 10000 20000 I I I I I I I I 200 500 1000 2000 5000 Figure 512. Comparison of Van Dresar and Siegwarth data with the Baker map. 101 Annular Bubbly 0 o__7 x = intermittent O = annular 10 + = stratifiedwavy Kx 103 103 102 x Intermittent xxx Stratifiedwavy Stratifiedsmooth 100 Xtt Figure 513. Comparison of Van Dresar and Siegwarth data with the Taitel and Dukler map.  400 350 300 Intermittent Annular 250 E 2 x = intermittent Z 200 Slug 0= annular 0 1 + = stratifiedwavy 150  1oo:000 0 (O0 0 Stratifiedwavy 50 Slug & StratifiedWavy Stratifiedsmo9th 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x Figure 514. Comparison of Van Dresar and Siegwarth data with the Wojtan et al. map. intermittent regime data are predicted well, the annular regime data are not. This is likely due to the low vapor quality encountered for annular flow during the chilldown process. The modifications to Kattan et al. map only consider mass fluxes below 200 kg/m2s; thus the annular regime data lie outside the modified region, and the Kattan et al. map is only valid for vapor qualities greater than 0.15. Calibration of Taitel and Dukler Flow Regime Map According to Taitel and Dukler [16], the transition between the stratified and the intermittent or annular regimes is governed by the KelvinHelmholtz stability criterion for wave propagation (MilneThompson [64]). Kordyban and Ranov [65] and Wallis and Dobson [66] also utilized the KelvinHelmholtz stability criterion to analyze the transition to slug flow. Lin and Hanratty [67] carried out a similar analysis and included the viscous effects which were neglected in the earlier works, however no significant I I I I I I I 10 20 50 100 200 500 1000 2000 1 I I I I I 1 5 10 20 50 100 Gow I I I 5000 10000 20000 1 1 1 I I I 0 200 500 1000 2000 5000 Figure 515. Comparison of current chilldown data with the Baker map. 101 Annular Bubbly Intermittent x = intermittent 10 0 = annular + = stratifiedwavy Stratifiedwavy Kx 103 Stratifiedsmooth S100 Figure 516. Comparison of current chilldown data with the Taitel and Dukler map. 20 100 10 50 0.2  b kg/mbs5 Ib/f's 1 I I I I Table 51. Sample data points for cryogenic chilldown. flow; I denotes intermittent flow; A denotes Saturation Mass Flux Temperature kg/m2s Quality OK 61 0.04 103.2 60 0.04 103.0 64 0.04 103.0 72 0.03 103.3 75 0.03 103.5 74 0.03 103.9 83 0.03 104.4 84 0.03 104.7 79 0.03 104.6 80 0.03 104.6 89 0.02 104.6 86 0.02 104.4 79 0.02 104.3 390 0.03 90.8 399 0.03 91.3 394 0.03 90.5 355 0.04 90.7 376 0.06 90.5 366 0.04 89.8 351 0.05 90.0 346 0.04 90.0 336 0.03 90.0 378 0.06 90.0 330 0.04 89.9 273 0.04 89.1 291 0.06 88.9 295 0.08 89.1 323 0.03 89.2 301 0.06 89.2 502 0.13 97.6 583 0.10 97.7 600 0.06 96.9 569 0.08 96.2 603 0.04 96.3 612 0.11 96.1 575 0.09 95.6 588 0.12 95.5 606 0.07 94.6 572 0.07 94.8 537 0.17 95.3 SW denotes stratifiedwavy annular flow Flow Structure Observed SW SW SW SW SW SW SW SW SW SW SW SW SW I I I I I I I I I I I I I I I I A A A A A A A A A A A 600 P Q ,o 0o oo 500 D O 400 Intermittent Annular E l 300 0 x = intermittent x 0 = annular 200 Slug + = stratifiedwavy +++ + + 100 + Slug & StratifiedWavy Stratifiedwavy 0 Stratifie smooth 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x Figure 517. Comparison of current chilldown data with the Wojtan et al. map. difference was observed when compared to the work of Taitel and Dukler [16]. Taitel and Dukler [16] assumed a 2D planar geometry with vapor flow on top of a stationary liquid film with very large thickness compared to the size of any disturbances; it was determined that the instability criterion takes the following form l (PI P g g 2 u > Cp (5.1) Pg ) where C, is a constant to be determined. A number of simplifying arguments were presented to estimate a value of C, that is less than unity. The analysis was extended to an inclined pipe geometry to arrive at Eq. (2.5). The constant, C2, in Eq. (2.5) is again determined to be less than or equal to unity as revealed by Eq. (2.7). Here we consider the stability analysis for a wave at the interface between the liquid and vapor phases in a 2D planar configuration within a confined channel, with both fluids moving. The configuration is illustrated in Fig. 518. Y, pgg Pg Ug c Ix 81 p1 U, Figure 518. Liquidvapor 2D channel flow configuration. As determined by MilneThompson the equation that governs the wave speed is given by mp1 (u, c)2 coth m, +mpg (U )2 coth mSg = g ( pg ). (5.2) Here m is the wave number, c is the wave speed, 3 is the fluid height and all other parameter are as define in the previous sections. The condition for stability dictates that the wave speed, c, must be real. Equation (5.2) is a quadratic equation in c and thus can be solved for c by utilizing the quadratic formula, hence we have B+ B2 4AD c = (5.3) 2A here. A, B and D are constants given by Eq. (5.4), A = mp1 coth m5, + mpg coth mg (5.4a) B = 2 (u,mp, coth m5, + Ugmpg coth m ) (5.4b) D = mpu2 coth mg + mpgu coth mg g( P Pg). (5.4c) For the onset of wave instability the value of c must be imaginary thus we have the condition, B2 4AD < 0. (5.5) After further simplification it is found that the KelvinHelmholtz instability is triggered when u > + +_ .(5.6) [g /2 1 2 1Pg 6 mpg coshm$ mp cosh m6 Pg Comparison of Eqs, (5.1) and (5.2) yield the following form for C,, 1 1 p2 2 1 6 = g U + mp cosh mg mp, cosh md, The value of C, easily exceeds unity for small values of liquid film velocity and low and moderate wave number. A liquid film velocity of O.Olm/s and wave number of yields a value of C, greater than 3, while a wave number of 1 gives a value of C, greater than 10. Hence it is expected that C2 in Eq. (2.5) may exceed unity for horizontal and inclined pipe geometries. In order to achieve better predictive capabilities, an attempt is made to calibrate the Taitel and Dukler map. The transition boundary that demarcates the transition from stratifiedwavy to either annular or intermittent flow requires modification. As previously discussed, the transition boundary depends on the value of the constant C2. For the present data a better fitting transition boundary is obtained when the functional form of C2 is calibrated so as to best fit the data. The calibrated value of C2 is given by r4.5162+i1.49 C2= 4.5162 072 (5.8) Hence C2 ranges from 0 to 4.516. This is consistent with Eq. (5.6). The demarcation line for the transition between the annular and the intermittent flow regimes must also be shifted to the right; this transition line was set based on the assumption that intermittent flow can only be present if the height of the liquid film is greater than the pipe radius, which may not necessarily be correct. The transition boundary between the annular and intermittent flow regimes is shifted from X, =1.6 to X, = 4.0, which represents a small change physically. Instead of transition to intermittent flow if the liquid film height is greater than the radius of the pipe, the shift corresponds to transition to intermittent flow if the liquid film height greater than 0.55D. The resulting flow map is compared with the chilldown data and is presented in Fig. 519. The flow regime transitions are significantly improved with the calibration to the Taitel and Dukler [16] flow regime map. The annular flow regime is typically characterized by thin liquid films with moderate velocities. The oversimplified assumptions used by Taitel and Dukler [16] to arrive at Eq. (5.1) severely limits the parameter space for which their flow regime transition from stratified to annular flow or intermittent flow is valid. Indeed, Eq. (5.6) shows that the liquid height and liquid velocity can play an important role in Kelvin Helmholtz instability. The experimentally observed stratified to annular flow regime transitions in this work clearly support the notion that the liquid film height and liquid velocity are important parameters in the flow regime transition. 101 F ~ Annular Bubbly 100 T x = intermittent Ko Intermittent 101 = annular + = stratifiedwavy Stratifiedwavy 102 10 Kx 103 Stratifiedsmooth 103 102 101 100 101 102 Xtt Figure 519. Comparison of current chilldown data with the modified Taitel and Dukler map. Film Boiling Heat Transfer This section focuses on measuring the heat transfer coefficients associated with the complex, unsteady, film flow boiling heat transfer that occurs during cryogenic chilldown; the prediction and modeling of the film boiling heat transfer coefficients is currently under investigation by a fellow graduate student. The inverse technique described in chapter 4 is used to extract the heat transfer coefficient from time dependent measurements of wall temperature. Using knowledge of the local temperature of the pipeline coupled with numerical simulations of the unsteady heat conduction through the wall of the pipe to determine the heat transfer coefficients. Figures 520 and 521 show the film boiling heat transfer coefficients extracted from the experimental data of the low (75 kg/m2s) and moderate mass flux (210 kg/m2s) experiments highlighted at the beginning of the chapter, respectively. It is observed from both Figs.520 and 521 that the heat transfer coefficient in the lower portion of the pipe (region 3) is at least double in magnitude to the heat transfer coefficient in the other two regions. This is as expected since the liquid film resides in the lower region of the pipe and due to gravitational effects the vapor film that separates the liquid film from the pipe wall is thinnest at the bottom. By comparing Fig. 520 to 521 it is seen that the higher the mass flux the larger the heat transfer coefficient. This is also as expected since convective heat transfer increases with increasing mass flux. It is interesting to note that for the low mass flux experiment it is observed that the heat transfer coefficient at the side of the pipe (region 2) is slightly smaller than the heat transfer coefficient at the top of the pipe (region 1). This trend was observed for experiment where the average mass flux was below 120 kg/m2s, in experiments. One possible reason for this is that the circumferential conduction heat to the lower region (region 3) is larger for lower mass fluxes, since the convective heat transfer is reduced. The heat transfer coefficients for the film boiling regime are available in tabulated form in appendix B. Nucleate Flow Boiling Heat Transfer This section focuses on measuring and predicting the heat transfer rates associated with the complex, unsteady, nucleate flow boiling heat transfer that occurs during cryogenic chilldown. The inverse technique described in chapter 4 is used to extract the heat transfer coefficient from time dependent measurements of wall temperature. This technique utilizes knowledge of the local temperature of the pipeline coupled with numerical simulations of the unsteady heat transfer through the wall of the pipeline to 77 determine the heat transfer coefficients. These experimentally determined heat transfer coefficients are compared against the nucleate flow boiling heat transfer correlations eRegion 1 (Top)  Region 2 (Side) Region 3 (Bottom) 0 10 20 30 40 50 Time (sec.) G= 75kg/m2s 60 70 80 90 Figure 520. Heat transfer coefficients for each region in the film boiling regime of the low mass flux experiment. 600  E 500 S400  o 300 C S200 i S100 0  0 5 20 25 Time (sec.) Figure 521. Heat transfer coefficients for each region in the film boiling regime of the moderate mass flux experiment. 600 E 500 " 400 a. ao . I 6 300  S200 I 1 S 100 0 o Region 1 (Top)  Region 2 (Side)  Re nin 3 (Rnttnm G = 210kg/m2s :l i IL ll l ik . > r . W A / of Gungor and Winterton [30], Kandlikar [40], MillerSteinhagen and Jamialahmadi [33] and Thome [43]. Performance of Current Flow Boiling Heat Transfer Correlations In determining the heat transfer coefficients using the inverse procedure outlined in chapter 4, it is sometimes necessary to change the size of the various regions. In order to compare the results obtained to existing correlations, an average heat transfer coefficient must be computed. This is done by integrating the heat transfer coefficients assigned on the inner surface over the perimeter of the inner surface. This approach is also employed by Thome [43]. Hence the average twophase heat transfer coefficient, k, is computed as k2 htop ) hsde ( bottom. (5.9) Fig. 522 illustrates the variation of the average twophase heat transfer coefficient extracted from the experimental data with time for the chilldown process. It is clearly seen that the transition from the film boiling regime to the nucleate flow boiling regime is accompanied by an order of magnitude increase in the average twophase heat transfer coefficient. The robust nature of the computational method is demonstrated in that it is able to handle the step change in heat transfer coefficient from the film to nucleate boiling regime. The nucleate flow boiling heat transfer coefficients extracted from the experimental data are presented in Table 53. The mass flux, vapor quality, flow regime, and saturation temperature are shown. In addition, the fraction of the perimeter occupied by each region, the average wall temperature, and the contribution to the twophase heat transfer in each region are tabulated. It is observed that the influence of region 1 on the average twophase heat transfer coefficient in the nucleate flow boiling regime is small when compared to the influence of regions 2 and 3. 3500 Nucleate Boiling 3000 Regime ET, =102 K, G=239 kg 2500 ms c 2000 0 1500 Film Boiling Regime 2 1000  I S 500 0 0 10 20 30 40 50 60 Time (sec.) Figure 522. Average twophase heat transfer coefficient variation with time. This is as a result of the stratified nature for the flow structure, in which the liquid resides in the lower regions of the pipe while the vapor resides in the upper region. By examining the contributions from each region to the total heat transfer, it is observed that in some instances region 2 has a larger contribution than region 3. This occurs because of the unsteady nature of the flow which results in instances where region 2 is periodically wetted resulting in a thinner liquid film than in region 3. Hence the heat transfer rate in region 2 will be greater as a result of the lower thermal resistance of the liquid film. In examining the fraction of the area assigned to each region it is evident that the flow structure influences the size of each region. For annular flow and stratifiedwavy flow in which the liquid film height is greater than the radius of the pipe, the three regions may be constructed such that they are of equal size. While in the intermittent flow regime the size of each region is adjusted slightly. However, when the flow is in the stratifiedwavy regime, a significant difference in the size of regions is observed. This results from the inability to determine the actual wetted area of the pipe. If the size of region 3 is overestimated the energy removed from the pipe wall would be too large in the adjacent region (in this case region 2) making it impossible to match the outer wall temperature. This problem is encountered mainly in the stratifiedwavy regime, in which the height of the liquid film is less than the pipe radius. It is not encountered with the other flow structures since the wetted area is not overestimated. Provided the wetted region is not overestimated, the size of regions 1, 2 and 3 may have different values, and yet suitable agreement with measured data is found. Therefore, the solution presented is not unique. Nevertheless, it is found that the average heat transfer coefficient hardly changes with variations in the size of regions 1, 2, and 3. In order to maintain consistency, these regions were taken to be of equal size, unless the solution required differently. For this work the regions sizes were chosen to maintain as much symmetry as possible while ensuring that the size of the wetted region is not overestimated. The database of cryogenic nucleate flow boiling heat transfer coefficient for chilldown presented in Table 53 is the only one we are aware of. In Table 53, SW (0.5+) denotes stratified wavy flow where the height of the liquid film greater than d,/2; I denotes intermittent flow; SW (0.5) denotes stratified wavy flow where the height of the liquid film less than d,/2; A denotes annular flow. 