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Cryogenic Two-Phase Flow during Chilldown: Flow Transition and Nucleate Boiling Heat Transfer


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CRYOGENIC TWO-PHASE 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 FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Jelliffe Kevin Jackson

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This work is dedicated to my parents, Victor and Eva Jackso n. Without th eir continuous support and encouragement this work would not have been possible.

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iv ACKNOWLEDGMENTS The author would like to expr ess his sincerest gratitude to his academic advisor and PhD committee chairperson, Professor James Fr ederick Klausner. His guidance, support, encouragement and insight contributed immens ely 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 Pr ofessor 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 appreci ated. The technical assist ance provide by Mr. Christopher Velat, in the construction phase of the experi mental facility is al so greatly appreciated. This research was supported by the Nati onal Aeronautics and Space Administration Glenn Research Center, thr ough contract NAG3-270. 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 Wood-Jackson, for her unwavering support and patience throughout the course of this endeavor. She has provided the much needed encouragement in times when self-doubt wa s creeping into the author’s mind and she

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v continues to be a source of comfort and inspirat ion. Without her support, encouragement and patience, this work woul d not have been possible.

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vi TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix NOMENCLATURE........................................................................................................xiv ABSTRACT.....................................................................................................................xi x CHAPTER 1 INTRODUCTION........................................................................................................1 2 LITERATURE SURVEY.............................................................................................6 Horizontal Flow Regimes.............................................................................................6 Flow Regime Maps for Horizontal Flow......................................................................8 The Baker Map......................................................................................................8 The Taitel and Dukler Map...................................................................................9 The Steiner Map..................................................................................................13 The Wojtan et al. Map.........................................................................................14 Forced Convection Boiling Heat Transfer Correlations.............................................16 3 EXPERIMENTAL FACILITY..................................................................................31 System Overview........................................................................................................31 Visual Test Section Design.........................................................................................33 Instrumentation and Calibration.................................................................................34 Static Pressure Transducers.................................................................................34 Test Section Pressure Drop.................................................................................34 Flow Meter Calibration.......................................................................................35 Temperature Measurements................................................................................36 Data Acquisition System............................................................................................38 Digital Imaging System..............................................................................................39 Experimental Protocol................................................................................................40

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vii 4 DATA PROCESSING................................................................................................41 Vapor Quality Estimation...........................................................................................41 Vapor Volume Fraction..............................................................................................43 Extracting the Heat Transfer Coefficient....................................................................44 Computing the Temperature Field in the Pipe Wall............................................46 Iteration Process for Guessing the In ner Heat Transfer Coefficient...................50 Test for Convergence..........................................................................................50 Computational Code: Tes ting and Verification..........................................................51 Stability of Computational Code.........................................................................51 Grid Resolution...................................................................................................51 Testing the Inverse Procedure....................................................................................52 5 CHILLDOWN FLOW TRANSI TION AND HEAT TRANSFER............................57 Flow Regimes.............................................................................................................62 Experimental Observations.................................................................................64 Performance of Current Flow Regime Maps.......................................................65 Calibration of Taitel and Dukler Flow Regime Map...........................................68 Film Boiling Heat Transfer.........................................................................................75 Nucleate Flow Boiling Heat Transfer.........................................................................76 Performance of Current Flow Boiling Heat Transfer Correlations.....................78 Correlating the Nucleate Flow Boilin g Heat Transfer Coefficient......................82 6 CONCLUSIONS AND RECOMMENDATIO NS 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 LIST OF REFERENCES.................................................................................................174 BIOGRAPHICAL SKETCH...........................................................................................180

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viii LIST OF TABLES Table page 2-1 Empirical constants for the Kandlikar correlation...................................................25 4-1 Influence of grid resolution on th e computed outer wall temperature.....................52 5-1 Sample data points for cryogenic chill down. SW denotes st ratified-wavy flow; I denotes intermittent flow; A denotes annular flow..................................................70 5-3 Summary of measured average nucleate flow boiling heat transfer coefficients using inverse method for regions.............................................................................81

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ix LIST OF FIGURES Figure page 2-1 Schematic representation of flow regimes observed in horizontal two-phase flow........................................................................................................................... ..7 2-2 The Baker flow regime map.....................................................................................10 2-3 The Taitel and Dukler flow regime map..................................................................13 2-4 The Steiner flow regime map...................................................................................14 2-5 The Wojtan et al. flow regime map..........................................................................15 2-6 Flow structures used to evaluate stratified flow liquid film thickness and stratified angle..........................................................................................................28 2-7 Flow structures used to evaluate (a ) annular flow liquid film thickness, (b) annular flow liquid film thickne ss and partial-dry out angle...................................29 3-1 Schematic of chilldown experimental facility..........................................................31 3-2 Schematic of the flange assembly............................................................................33 3-3 Calibration plot of the actual velocity versus the ideal velocity (Velat [56])..........36 3-4 Thermocouple arrangement on the steel tr ansfer line prior to the visual test section.......................................................................................................................3 7 3-5 Thermocouple placement for heat transfer test section............................................38 4-1 Model used for the stratified, wavy and intermittent flow volume fraction computation..............................................................................................................44 4-2 Diagram of the model used for the annular flow volume fraction computation......44 4-3 Flow chart for transient heat transfer coefficient extraction....................................45 4-4 Coordinate system for heat conduction through the pipe wall.................................47 4-5 Calibration for determining the outer pi pe surface heat transfer coefficient...........48

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x 4-6 Assumed variation of heat transfer coe fficient on the inside surface of the pipe....50 4-7 Computation of a parabolic varying heat transfer coefficient using the inverse method......................................................................................................................55 4-8 Comparison of heat transfer coeffici ent computed using the inverse procedure and the Dittus-Boelter correlation fo r single-phase nitrogen gas flow....................56 5-1 Quenching front that marks transitio n for film boiling to nucleate boiling.............57 5-2 Temperature profile during chill down for low mass flux experiment.....................58 5-3 Temperature profile during chilldow n for moderate mass flux experiment............59 5-4 Transient mass flux for lo w mass flux experiment..................................................59 5-5 Transient mass flux for moderate mass flux experiment.........................................60 5-6 Transient vapor volume for low mass flux experiment............................................60 5-7 Transient vapor volume fraction fo r moderate mass flux experiment.....................61 5-8 Transient vapor quality for low mass flux experiment............................................61 5-9 Transient vapor quality for moderate mass flux experiment....................................62 5-10 Transient inlet pressure prof ile for low mass flux experiment.................................63 5-11 Transient inlet pressure profile for moderate mass flux experiment........................63 5-12 Comparison of Van Dresar and Si egwarth data with the Baker map.......................67 5-13 Comparison of Van Dresar and Siegwarth data with the Taitel and Dukler map....67 5-14 Comparison of Van Dresar and Siegwa rth data with the Wojtan et al. map............68 5-15 Comparison of current chilldown data with the Baker map.....................................69 5-16 Comparison of current chilldown data with the Taitel and Dukler map..................69 5-17 Comparison of current chilldown da ta with the Wojtan et al. map..........................71 5-18 Liquid-vapor 2-D channe l flow configuration.........................................................72 5-19 Comparison of current chilldown data with the modified Taitel and Dukler map..75 5-20 Heat transfer coefficients for each re gion in the film boiling regime of the low mass flux experiment...............................................................................................77

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xi 5-21 Heat transfer coefficients for each region in the film boiling regime of the moderate mass flux experiment................................................................................77 5-22 Average two-phase heat transfer coefficient variation with time.............................79 5-23 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using G ungor and Winterton correlation.................................83 5-24 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients us ing Kandlikar correlation.....................................................83 5-25 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using Mller-Steinhagen correlation.......................................84 5-26 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using Wojtan et al correlation.................................................84 5-27 Method for assigning the heat transfer coefficient on the inside surface of the pipe........................................................................................................................... 85 5-28 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................87 5-29 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................87 5-30 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................88 5-31 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................88 5-32 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................89 5-33 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................89 5-34 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................90 5-35 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................90 5-36 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................91 5-37 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................91

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xii 5-38 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................92 5-39 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................92 5-40 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................93 5-41 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................93 5-42 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................94 5-43 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................94 5-44 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................95 5-45 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................95 5-46 Comparison of the predicted and meas ured temperatures using both the MllerSteinhagen and Jamialahmadi correla tion and the modified version.......................96 5-47 Comparison of predicted and measured average nucleate flow boiling heat transfer coefficients using modifi ed Mller-Steinhagen correlation........................97

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xiv NOMENCLATURE A cross-sectional area (m2) a constant in the Mller-Steinhagen and Jamialahmadi correlation B o Boiling number 0C empirical constant in Zuber Findlay correlation 15CC constants in the Kandlikar correlation 2C coefficient dependent on the size of disturbance Co Convection number c interface wave speed (m/s) pc specific heat capacity (J/kgK) D inner diameter of pipe (m) d pipe wall thickness (m) E enhancement factor F modified Froude number kF fluid property enhancement f actor for nucleate boiling in the Kandlikar correlation pF pressure function Fr Froude number G mass flux (kg/m2s) g gravitational acceleration (m/s2)

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xv h heat transfer coefficient (W/m2K) f gh latent heat of vaporization (J/kg) K wavy flow dimensionless parameter k thermal conductivity (W/mK) M molecular weight M a 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 p R surface roughness (m) r radial coordinate S suppression factor also slip velocity (m/s) 1S modified suppression factor s shelter coefficient T dispersed bubble floe dimensi onless parameter also temperature (K) t time (s) vjU empirical constant in Zuber-Findlay correlation

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xvi u fluid velocity (m/s) V voltage output (V) tt X Martinelli parameter x vapor quality Y parameter encompassing relative forces acting on the fluid due to Gravity and pressure z axial coordinate Greek Symbols 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 (Pa-s) kinematic viscosity (m2/s) angle film occupies (rad.) density (kg/m3) surface tension (N/m) s enhancement factor of Shah

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xvii fluid property correction factor for liquid mass flux in the Baker Map Subscripts 0 denotes reference quantity 1t denotes single-phase 2 denotes two-phase quantity denotes far field condition a denotes air actual denotes actual quantity b denotes nucleate boiling bottom denotes bottom of the pipe c denotes single-phase convection crit denotes critical quantity dry denotes dry perimeter of pipe f l denotes fluid inside pipe f o 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 l denotes liquid phase

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xviii new denotes new quantity ONB denotes onset of nucleate boiling out denotes outer surface of pipe p res denotes present quantity p rev denotes previous quantity r denotes reduce sat denotes saturation condition side denotes side of the pipe top denotes top of the pipe w denotes quantity is evaluated at the pipe inner wall wa denotes water wet denotes wetted area of inner pipe wall Superscripts s denotes superficial quantity ~ denotes dimensionless quantity

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xix Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CRYOGENIC TWO-PHASE FLOW DURING CHILLDOWN: FLOW TRANSITION AND NUCLEATE BOILING HEAT TRANSFER By Jelliffe Kevin Jackson August 2006 Chair: James F. Klausner Major Department: Mechanic al and Aerospace Engineering The recent interest in space exploration has placed a renewed focus on rocket propulsion technology. Cryogenic pr opellants are the preferred fuel for rocket propulsion since they are more energetic and environmen tally friendly compared with other storable fuels. Voracious evaporation occurs while tran sferring these fluids th rough a pipeline that is initially in thermal equilibrium with the environment. This phenomenon is referred to as line chilldown. Large temperature differen ces, rapid transients, pr essure 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 ha ve been fair at best. A major shortcoming of these models is the use of correlations that were de veloped for steady, non-cryogenic flows. The

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xx development of reliable correlations for cr yogenic chilldown has been hindered by the lack of experimental data. An experimental facility was constructe d that allows the flow structure, the temperature history and the pr essure history to be record ed during the line chilldown process. The temperature history is then ut ilized in conjunction w ith an inverse heat conduction procedure that was developed, wh ich 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 nucle ate boiling heat transfer. It is found that by calibrating the transition between the stratified-wavy and the intermittent/annular regimes of the Taitel and Dukler flow regime map, satisfactory predictions ar e obtained. It is also found that by utilizing a simple model that in cludes the effect of flow structure and incorporating the enhancement provided by th e local heat flux, significant improvement in the predictive capabilities of the Mller-S teinhagen and Jamialahmadi correlation for nucleate flow boiling is achieved.

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1 CHAPTER 1 INTRODUCTION Cryogenic fluids have been used in various applications over the past century. One application that has continuously been gett ing attention has been the use of cryogenic propellants for rocket propulsion. This in terest has been sparked by the fact that cryogenic propellants yield more energy and ar e more environmentally friendly, when compared to non-cryogenic propellants [1] and the storage systems for these cryogenic propellants are lighter than those required for their non-cryogenic counterparts [1]. Before these propellants can be used for propul sion in space they must first be filled in their respective storage contai ners 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 “cool-down”. 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 ma terial used for the transfer lines, and the heat transfer rate determines the type and thickness of in sulation to be used. Other important factors that must be considered when dealing with chilldown are the quantity of liquid propellant vaporized, the time it take s 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

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2 chilldown process would allow for more ec onomical 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 si mulations. 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 ex perimental 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 m odel of Burke for chilldown time and a model for estimating the frequency of pressure oscillat ions. It was determined that these models gave an acceptable prediction of chilldown tim e. Bronson et al. were able to highlight the existence of circumferent ial 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 computati onal technology available at the time to solve the continuity, moment um and energy equations. With the aid of numerous assumptions, they were able to investigate pressure variations, estimate chilldown time and predict temp erature profiles. It was conc luded that pressure surges are exacerbated by a high degrees of subcooli ng of the inlet fluid, long transfer lines, dense fluids and rapid open ing of the inlet valve.

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3 In the mid 1970’s a series of studies [5-7] on the cool-down of short transfer lines were performed. These studies utilized an en ergy 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 thos e developed for steady, non-cry ogenic systems. Thus there was poor agreement between the results of th eir analytical model and the experimental data. With the rapid advancement of computi ng technology during the past two decades, more sophisticated numerical simulations of the chilldown process were attempted. Papadimitriou and Skorek [8] developed a thermohydraulic code fo r the calculation of system variables for both steady state and transient processes for two-phase cryogenic flows. They utilized the conservation equations for both the liquid and vapor phases coupled with various correlations for heat tran sfer coefficient and pressure drop, none of which were developed for unstea dy flow or cryogenic fluids. They were able to predict the temperature and pressure history of the cooldown pro cess; however their predicted results consistently under-predicted the temperature and pressure. In 2002 Cross et al. [9] developed a numeri cal procedure that utilizes the unsteady conservation equations in conjunction w ith a thermodynamic equation of state and correlations for boiling heat transfer. These co rrelations for boiling h eat transfer were not developed for two-phase 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 fl uid enter as a superheated vapor.

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4 The chilldown process is physically similar to the re-wetting phenomenon encountered in the nuclear i ndustry when re-establishing no rmal 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 failu re 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 proceed s in a similar manner to that of cryogenic chilldown as it goes from the film boiling regi me to the nucleate flow boiling regime and eventually to the single phase convective heat transfer regime. Research in the area of rewetting usually focuses on the prediction of the quenching velocity [10-12]. Chan and Banerjee [13-15] used a two-fl uid numerical model to invest igate the re-wetting and refilling 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 proce ss that the focus has been on predicting chilldown time and simulatin g the flow so as to obtain the pressure history, the temperature histor y and the fluid expenditure. Ho wever, all models to date use empirical correlations for determining the heat transfer coefficient and the pressure gradient that were developed steady n on-cryogenic flows. The agreement with experimental data has been fair at best.

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5 Hence the purpose of this research investig ation is to develop a database of flow regime and heat transfer coefficient for cryoge nic chilldown in horizon tal transfer lines. Techniques are also provided to predict fl ow 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 horizo ntal once through chilldown facility utilizing nitrogen as the working fluid was constructed. The facility allows for the flow structure to be observed while simultaneously meas uring and recording the mass flow rate, temperature, and pressure within the test sect ions. At present, ther e is no database that exists that includes a compilation of data for temperature, pressure, mass flow rate and flow regimes that occur duri ng chilldown. Hence the first step is to compile a large database of temperature, pressure, mass fl ow 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 calib rated for use in chilldown models. A literature survey of flow structure and h eat transfer predictions is given in the next chapter. This is followed by a detailed description of the expe rimental facility in chapter 3 that has been de veloped to compile the required database for cryogenic chilldown. Chapter 4 describe s the methods used to regre ss the experimental data and extract the heat transfer coefficient. Chap ter 5 compares the experimental data with existing models or correlations and the modifications required to fit the data.

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6 CHAPTER 2 LITERATURE SURVEY In order to reliably predict the therma l 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 re gime and heat transfer in two-phase flow. The intent of this review is to examine th e 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 tw o-phase flow is more comple x than single-phase flows. Apart from the inertia, viscous, and pressure forces experienced in single-phase flow, two-phase 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 two-phase 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 geomet ry and orientation. The two-phase flow regimes that are typically encountered for horizontal flow are illu strated in Fig. 2-1.

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7 Figure 2-1. Schematic represen tation of flow regimes obser ved in horizontal two-phase 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 pr oducing larger plug-type bubbles, this is referred to as plug flow. At low mass flow rate s and higher qualities, stratified flow is observed; as the flow rate and/or quality are increased the liquid-vapor interface becomes unstable (due to Helmholtz instability), result ing in stratified-wavy flow. At high liquid flow rates the amplitude of the waves may gr ow until the crest spans the cross-section of the pipe forming large vapor slugs. This is re ferred to as slug flow. At higher vapor velocities and moderate liquid flow rates the flow structur e is observed to be annular, with liquid film covering the entire circumferenc e of the pipe with an inner vapor core. If

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8 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 existi ng in two-phase flows is essential for developing phenomenological models for mass, momentum and energy transport within those flow systems. Throughout the past deca des numerous flow regi me maps have been developed for horizontal and vertical fl ows. 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 ma p was developed by an empirical correlation method, which is comprised of plotting th e observed flow pattern for air-water and steam-water flows on a chart of liquid mass flux (lG) versus gas mass flux (gG). The transition lines were then simply drawn onto th e chart in such a manner as to divide the area into regions associated with the flow pa ttern that was observed in that particular area. In order to create maps for two-phase flow with fluids ot her than air-water and steam-water, fluid property corr ection factors were introduced. Thus th e coordinates of the map are modified by the factors and 2 1 wa l a g (2.1)

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9 3 1 2 l wa wa l wa (2.2) where the subscripts g l, a, and wa represent the gas, the liquid, air and water respectively. is the fluid density of the respective fluid, is the fluid viscosity of the respective fluid, is the surface tension between the liquid and the gas and wa is the surface tension between water and air. The new coordinates of the map become lG versus gG This map has been used in studies invol ving cryogenic fluids [3, 22] with some success. However this map has a severe shor tcoming, which is the fact that the map cannot take into account variations in pipe diam eter 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 in itially 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 non-dimensional groups were uncovered that influence tr ansition. These groups were defined as follows: 2/ / s l tt s g dPdx X dPdx (2.3)

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10 sin /lg s gg Y dPdx (2.4) Figure 2-2. The Baker flow regime map. where the subscripts l and g denote the liquid and gase phases respectively. sdx dP / is the pressure drop of one phase flowing wi thin the pipe based on the mass fraction of that phase, g is the gravitati onal acceleration and is the angle of inclination of the pipe with respect to the horizontal. tt X is the Martinelli parameter and Y encompasses the relative forces acting on th e liquid due to gravity and pressure gradient.

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11 The transition between stratified and interm ittent or annular flow is modeled to take place as a result of Helmholtz instability, wh ich causes finite amplitude waves on the surface of the stratified film to grow. The instability is a resu lt of the Bernoulli effect, for which the pressure is reduced as the gas acce lerates over the crest of the wave. This provides the basis for the fo llowing transition criterion, 2 2/ 1 1Gll gudAdh F C A (2.5) F is a Froude number modifi ed by the density ratio, coss gg lgu F Dg (2.6) and the constant 2C is given by, 21lC D (2.7) where A is the flow cross-sectional area, 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 ~ indicate s 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 interm ittent 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 de velop 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 hei ght, which is defined by a unique value of the Martinelli parameter.

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12 The transition between the stratified sm ooth and the stratified wavy patterns is related to the wave generati on phenomenon. In order for th e stratified wa vy pattern to exist, the velocity of the gas must be suff icient 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 ove rcome the viscous dissipa tion. The criterion for transition from smooth to wavy flow is given by, 2glK uus (2.8) where s is the shelter coefficient defined in [16] and takes a value of 0.01 and K is the product of the modified Froude number and the square root of the superficial Reynolds number of the liquid: 2 22Re. coss s gg s l l l lgu Du KF Dg (2.9) Here 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 buoya ncy force that keeps the gas at the top of the pipe. This leads to the following criterion, 2 28 .g n illlA T SuuD (2.10) T is the ratio of the turbulen t force to the gravity force, 1 2/ coss l lgdPdx T g (2.11)

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13 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 prin ciples 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 propertie s. The drawbacks of this map are the fact that it does not take into cons ideration phase change and it has not been calibrated with a large data set. tt X Figure 2-3. The Taitel and Dukler flow regime map. The Steiner Map The Steiner map [23] is a modified vers ion of the Taitel and Dukler map. The transition regions have been determined us ing the same physical principles as those introduced by Taitel and Dukl er [16]. The major improvement of this map over its counterpart is that the transition curves ar e adjusted slightly using more advanced models. A much broader data set was used to calibrate the map. However this map faces

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14 a similar drawback to the Taitel and Dukler map in that it does not take into account phase change. ttX Figure 2-4. The Steine r 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 th is 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

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15 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 diabatic one, thus being able to predict pa rtial 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 cu rves in the low vapor quality (less than 0.327) and low mass flux (less than 200 kg/m2-s) regime based on observations made with R-22. Details of the map construction are found in the work of Wojtan et al. [24]. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 50 100 150 200 250 300 350 400 Annular Stratified-wavy Slug Slug & Stratified-Wavy Intermittent Stratified-smooth x G (kg/m2s) Figure 2-5. 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, wh ile the empirical maps only performed well for the data set from which it was devel oped. Spedding and Spence [28] used data

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16 collected from co-current water-air horizo ntal flow experiment s through pipes of two different diameters to show that no one map c ould 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 calibrat ed or new maps developed. Forced Convection Boiling Heat Transfer Correlations It is a widely accepted principle that th e 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 pa st and to date still remains unresolved. Dengler and Addoms [29] used a plot of log(h2 /hl,t) versus log(1/ttX ) to conclude that the primary mechanism for heat transf er in flow boiling is the bulk turbulent transport since the relationship is monotonic as is the case for the two-phase frictional pressure drop. The two-phase heat tr ansfer coefficient is represented by h2 hl,t is the single-phase heat transfer coefficient based on the liquid fraction flowing, and ttX is the Martinelli parameter, 0.50.1 0.91 ,vl tt lvx X x (2.12) in which x is the vapor quality.

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17 However, Mesler [30] sugge sted that Dengler and Addo ms misinterpreted their data. The plot of log(h2 /hl,t) versus log(1/ttX ) may be rewritten as log sat wT q GA2 ,1 versus log z wdz q GA0 2 ,1, where A is the cross sectional area and 2 ,wq is the two-phase wall heat flux. This is essentia lly a plot of the same quantities against each other, thus a monotonic relati onship is guaranteed regardle ss of the physical mechanism involved. By plotting 2 ,wq against satT he suggested that th e monotonic relationship was a result of the nucleate boiling phenomenon. Bergles and Rohsenow [31] incorporated the effects of bot h the bulk turbulent convection and nucleate boiling mechanisms by proposing a correlation that predicts the two-phase wall heat flux by interpolati ng between the bulk tu rbulent convection dominated heat transfer and e bullition dominated heat transf er. The correlation takes the form, 1 2 2 ,, ,2, ,,11.wbwib wwc wcwbqq qq qq (2.13) Here the subscripts c, b, and ib denote single-phase forced convection, ebullition and the point of incipient boiling, respectively. This correlation is not ut ilized often since the determination of the heat flux due to ebullition is not availa ble without experimentation. Over the past few decades, numerous correlations have been proposed for predicting the heat transfer coefficient dur ing forced convection flow boiling. Each correlation may be classified in one of three categories: superpositi on, enhancement, or asymptotic. The most straightforward is the superposition model, which adds the

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18 contribution of each mechanism and accounts for the interaction of the mechanisms by the use of an amplification f actor and a suppression factor. The amplification factor is used to account for the increased turbul ent transport in twophase flow and the suppression factor is introduced to acc ount for the reduced effective superheat experienced during ebullition. The second is the enhancement model, which multiplies the single-phase heat transfer coefficient for the liquid phase along flow in the pipe by the greater of the contributions between the incr eased turbulent trans port and the ebullition process. The last model is the asymptotic model. It is termed asymptotic as the value of the two-phase boiling heat transfer coeffi cient 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 develope d 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 two-phase heat transfer coefficient is given as, b lSh Eh h 2, (2.14) where E is the amplification or enhancement factor and S is the suppression factor. The single-phase liquid heat transfer coefficien t is evaluated using the well-known DittusBoelter equation [33] for turbulent flow, 0.80.40.023RePr,l lllk h D (2.15) where k is the thermal conductivity and the Reynolds number is based on the liquid fraction flowing,

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19 l lD x G 1 Re. (2.16) The nucleate boiling heat transfer coefficien t is evaluated using the Forster and Zuber [34] correlation for pool boiling, 0.790.450.49 0.240.75 0.50.290.240.240.00122,lpll bwsatlsatwl lfggkc hTTPPTP h (2.17) where pc 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 twophase Reynolds number (2Re ), and through a regression an alysis 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 th e graphical correlations for E and S Eqs. 2.18 – 2.20, 1 0 11 ttX for E (2.18a) 1 0 1 213 0 35 21 736 0 tt ttX for X E (2.18b) 1 61.17 212.5610Re S (2.19) where the two-phase Reynolds number is determined by, 1.25 2ReRelE (2.20) A more modern 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

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20 factor is taken as a function of both the Ma rtinelli parameter and the Boiling number. The Boiling number, Bo is defined as, fgq Bo hG (2.21) where q is the heat flux and f gh is the latent heat. The nucleate boiling heat transfer coefficient, bh is modeled using the pool boi ling correlation of Cooper [37], 67 0 5 0 55 0 10 12 0log 55 q M P P hr r b (2.22) where M is the molecular weight and rP 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, 86 0 16 11 37 1 24000 1 ttX Bo E (2.23) and 17 1 2 6Re 10 15 1 1 1lE x S (2.24) For horizontal flow with Froude number less than 0.05 the am plification factor must be multiplied by the following factor, lFr lFr E2 1 0 1 (2.25) and the suppression factor should be multiplied by the following factor, lFr S 1 (2.26) where lFr is the Froude number is, gD G Frl l 2 2. (2.27)

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21 By incorporating the heat flux into the enhan cement 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 in creasing heat flux reporte d by Klausner et al. [38]. The correlation of Mller-Steinhagen and Ja mialahmadi [39] uses a superposition technique that accounts for the interac tion of the convective and nucleate boiling mechanisms by employing an enhancement factor and a suppression factor. This formulation absorbs the enhancement factor in to the computation of the convective heat transfer contribution, and th e correlation takes the form, 2.lbhhSh (2.28) This correlation employs the correlati on of Petukov and Popov [40], for the liquid phase convective heat tr ansfer coefficient, 2 23RePr 8 112.7Pr1 8ll l lf k h f D (2.29) where the friction factor is given by Filonenko [41], 2 2(1.82logRe1.64). f (2.30) The two-phase 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 0.160.86.in outD D (2.31)

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22 The suppression factor is computed by Eq. (2 .19). In order to compute the nucleate boiling contribution to heat tr ansfer, the pool boiling correl ation developed by Gorenflo [42] is used, 0.113,n p b p oopoR h q F hqR (2.32) where p R is the surface roughness of the pipe. The pressure function, p F and the exponent n are calculated us ing the reduced pressure rP, 22 20.68 1.736.1. 1prr r F PP P (2.33) Equation (2.33) pertains to wa ter and other low boiling point li quids and is used here; for the computation of p F for organic liquids reference [ 39] should be consulted. The exponent is calculated from 20.90.3,a rnP (2.34) with 0.15a for water and other low boiling point liquids including nitrogen. The reference heat transfer coefficient oh, reference heat flux oq and reference surface roughness po R for nitrogen are found in [43], and are 210000oW q m 24380oW h mK, and 6110po R m. One of the most popular enhancement models is the Shah correlation, which was first developed in graphical form [44] and wa s later re-established in equation form [45]. Shah proposed that the two-phase heat tran sfer coefficient might be determined as follows, l sh h 2. (2.35)

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23 The liquid convective heat transfer coefficient, lh, is evaluated using the Dittus-Boelter [33] equation, Eq. (2.15), as in the prev ious models. However, the evaluation of s is more complicated. 04 0 l sFr for Co N (2.36a) 04 0 38 03 0 l l sFr for Co Fr N (2.36b) 410 11 7 14 x Bo for Fs (2.37a) 410 11 43 15 x Bo for Fs (2.37b) where Bo is the boiling number defined previously and Co is the Convection number given by, 5 0 8 01 l gx x Co (2.38) Hence the contribution from th e bulk turbulent transport is, 0.81.8c sN (2.39) and the contribution from the ebulliti on process is determined as follows, for 0 1 sN 0.55230310bBoforBox (2.40a) or 0.55146310bBoforBox (2.40b) for 0 1 sN 0.50.1exp2.740.11.0bsssFBoNforN (2.41a) or

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24 0.50.15exp2.740.1bsssFBoNforN (2.41b) Thus s is calculated as, max, s cb. (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 004 0 Co and 410 50x Bo, and 2) for horizontal tubes at 04 0 lFr and 410 1 x Bo. 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 post-dryout region. The inaccuracy in region 2 of approximately 20% is inconse quential since values below 410 1x Bo 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 in evitably lost in the process. Another enhancement model was develope d 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 (lFr) and a fluid dependent parameter. The two-phase heat tran sfer coefficient is predicted as follows, l k C C l Ch F Bo C Fr Co C h4 5 23 1 225 (2.43) lh is evaluated using the Dittus-Boelter [33] Eq. (2.15). The coefficients 1C through 5C 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 kF is a parameter that enhances the nucleate boiling term and represents the fl uid-surface combination effect. The values of these coefficients may be determined from Table 2-1 below.

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25 Table 2-1. Empirical constants for the Kandlikar correlation. 65 0Co (convective region) 65 0Co (nucleate boiling region) 1C 1.1360 0.6683 2C -0.9 -0.2 3C 667.2 1058 4C 0.7 0.7 5C 0.3 0.3 kF 0.74 0.74 The Kandlikar correlation has the added adva ntage 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 convect ion on heat transfer with nucleate boiling in tubes. He proposed that th e 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, l b lh h fn h h2, (2.44) where the following conditions hold true, ; 0 1 0 n f fn h hl b (2.45a) 1 , n f h h fn h hl b l b (2.45b) The most basic interpolation formula that satisfies these conditions is n n l b lh h h h 12. (2.46)

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26 It was determined from experiments that an acceptable value of n is 2. However, this correlation does not account for either the en hancement effect or the suppression effect and thus was modified by a number of investig ators to take these effects into account. A widely cited asymptotic model in the litera ture is that of Liu and Winterton [48]. This correlation models the two-phase heat transfer coefficient in the following manner, 2 2 2b lSh Eh h (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 se lected the asymptotic approach that has the property of further suppr essing nucleate boiling once lEh is appreciably larger than bSh. As with the previous correlations lh is evaluated using the Di ttus-Boelter [33] equation, Eq. (2.15), however, the Reynolds num ber in this case is defined as l foGDRe. (2.48) The nucleate boiling heat transfer coefficient, bh, 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, 35 01 Pr 1 g l lx E (2.49) and 1 16 0 1 0Re 055 0 1 foE S. (2.50)

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27 For horizontal flow, the enhancement factor and the suppression fact or are modified as previously mentioned in Gungor and Winterton [36]. Liu and Winterton claimed that this correlation performs better than those devel oped previously. However, the improvement is seen to be marginal. One correlation developed that cannot be pla ced 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 th e vapor and apply a suitable mo del to the respective region for horizontal flow. The heat transfer coe fficient is thus determined as follows, 22 2drygdrywet R hRh h R (2.51) where R is the internal radius of the pipe, dry 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, dry is determined using a simplified geometric model for the flow structure. The vapor convective heat tran sfer coefficient, gh, is determined using the DittusBoelter correlation assuming tubular flow over the dry perimeter of the pipe, D k hg g g g 4 0 8 0Pr Re 023 0 (2.52) where the Reynolds number with respect to the vapor is g gGxD Re (2.53)

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28 and is the void fraction. In calculating the voi d fraction, the Steiner [23] version of the Rouhani and Axelsson [50] drift fl ux void fraction model was adopted: 1 0.25 0.51.181 1 10.121.lg ggllxg xxx x G (2.54) The heat transfer coefficient, weth, on the wetted perimeter of th e pipe is calculated using an asymptotic equation of the form, 1 33 3,wetblhhh (2.55) where bh is modeled using the Cooper correla tion [37] mentioned previously and lh is computed using a correlation developed by Kattan et al.[51], 0.690.40.0133RePr.l lllk h (2.56) Here is the simplified film thickness and the Reynolds number is l lx x G 1 ) 1 ( 4 Re. (2.56) The simplified film thickness, is determined based on the flow structure shown in Figs. 2.6 and 2.7. Figure 2-6. Flow structures us ed to evaluate stratified flow liquid film thickness and stratified angle.

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29 ( a ) ( b ) ( c ) Figure 2-7. Flow structures us ed to evaluate (a) annular fl ow liquid film thickness, (b) annular flow liquid film thickness and pa rtial-dry out angle, and (c) stratified liquid film with par tial dry-out angle. In order to better model the physical process th at occurs in two-phase with heat transfer, an expression for the onset of nucleate boiling, ONBq was added; the e xpression gives the value below which the contribution due to nucleate boiling is not significant. The criterion employed was developed by Zurcher and coworkers [52], 2 s atl ONB critgfgTh q rh (2.57) in which critr is the critical nucleation radius and is assigned the value 0.38x10-6 m. This correlation does not utilize the enhancement f actor and the suppression factor as in other models. Using the asymptotic method for wethweighs 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 th at 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

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30 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 pe rformance 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 Wi nterton [48]. The best pred ictive model for their data proved to be the Chen correlation. In 2003, Qu and Mudawar [55] carried out experiments with water in micro-channels a nd compared the heat transfer data obtained against the predictive models of Chen [32] Shah [45], Gungor a nd Winterton [36], Liu and Winterton [48], and Kand likar [46]. The correlati on of Liu and Winterton out performed the others. The predictive models reviewed all agree th at the salient factors that influence the heat transfer in flow boiling is the bulk turb ulent convection and ebullition. However, the manner in which they interact with each othe r is unclear, hence the existence for such a large number of correlations. These models have been developed using steady, noncryogenic flows, but neither of these conditions applies to the chilldown process. Since the chilldown process is characterized by rapid transients, pre ssure fluctuations, voracious evaporation and large temperature di fferences, which makes it very difficult to determine how the two effects responsi ble for the heat transfer interact.

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31 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 meas ured simultaneously. It is illustrated schematically in Fig. 3-1 below. Figure 3-1. Schematic of chill down experimental facility. Liquid nitrogen was selected as the working fluid for this investigation since it is chemically inert, colorless, odorless, non-corrosive, nonflammable, relatively inexpensive, readily available, and pose s no significant environmental hazards; the physical and thermal properties of nitroge n are also well documented. The liquid T T T P dP dP Vented to environment Visual Test Section Nitrogen Supply Tanks CCD Collection Tank Heat Element Ball Valve Temperature Pressure Differential Pressure Venturi Heat Exchan g e r Heat Transfer Section P dP T P

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32 nitrogen is stored in high -pressure vacuum jacketed cy linders (at 1587 kPa), the tank pressure that provides the driv ing potential for the flow. Once the fluid exits the tank it is directed through a Joule-Thompson heat exchanger that cools th e liquid to ensure that the nitrogen is in the subcooled st ate before entering the facility. Upon entering the facility the flow passes through a 304-stainless steel section (I.D. 12.7 mm, O.D. 15.9 mm, approximate therma l conductivity 16.3 W/m-C and specific heat 0.46 kJ/kg-C), which is fitted with a se ries of external type E (Chromel-Constantan) 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 allo ws 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 fabricat ed from pyrex. Here the flow structure is captured via a CCD (Charge-Coupled Device) camera with appropriate image capturing software. The nitrogen then passes through a nother section of pipi ng which contains an internal thermocouple and a pressure tap, whic h 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 tran sfer section of the fac ility. The section is 38 cm in length between the inlet and outle t; 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 (t he details of this pr ocedure is given in a later section). A cryogenic ball valve is located after the heat transfer s ection that allows the flow to be throttled; thus a wider ra nge of flow rates is attainable Once through the ball valve,

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33 two heaters vaporize any remaining liquid before the flow enters the venturi flow meter. Then nitrogen is collected in an expansion ta nk before being vented to the atmosphere via a ventilation system. In performing the experiments, the ball valv e is set to the desired position, and the data acquisition system is activated just prio r to opening the nitrogen cylinder. All the measurements, including image capturing, ar e 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 cryogen ic facility is the vi sual test section. The visual section consists of a vacuum insula ted pyrex tube that is designed to operate under high pressure (maximum of 1400 kP a) and low temperature conditions (-180 C) that exist during chilldown. In order to c onnect the to the stainl ess steel tubing pyrex tube a flange assembly was designed that en sures leak-free operation, see Fig. 3-2. Figure 3-2. Schematic of the flange assembly. Goretex Gasket Teflon O-ring Test Sectio n Teflo n T Hex Nut

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34 Instrumentation and Calibration One of the most vital components of the cryogen ic facility is the vi sual test section. The visual consists of a vacuum insulated py rex 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 orde r to connect the to the stainl ess steel tubing, a pyrex tube flange assembly was designed that ensu red leak-free operation, see Fig. 3-2. Static Pressure Transducers Two Validyne P2-200V pressure transducers are installed in the facility. One is installed at the inlet to the visual test section so that the inlet pressure (1P) of the fluid may be determined, while the second on is installed at the inlet to the venturi flow meter to measure the pressure (2P), 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, V P 937 274 712 271 (3.1) and V P 479 276 709 302 (3.2) where 1P and 2P 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 ( P ) across the visual test sectio n is recorded using a Validyne model DP215 variable reluctan ce differential pressure transducer equipped with a dash30 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

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35 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, V P 2788 1 (3.3) where P 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 deviati on of the calibration is 0.12%, which is within the 0.25% full-scale 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 diam eter of 8.73 mm. Proper performance of the flow meter demands that only nitrogen vapor pa ss through the instrume nt; to ensure that this is the case two 1-kilowatt coil heaters are positioned prior to the flow meter so that any liquid nitrogen is vaporized before entering the venturi. A Validyne variable reluctance DP15 differe ntial pressure transducer with a dash40 diaphragm (rated for 0.0 to 86.0 kPa) was us ed to measure the pressure drop across the venturi; this diaphragm maximizes the sensor output response while providing moderate overload protection. The diffe rential pressure transducer is coupled to a carrier demodulator device. The transducer and de modulator device were calibrated using a mercury monometer, see Velat [56] for calibra tion curve. The standard deviation of the differential pressure transducer calibrati on was 0.17%, which was within the 0.25% fullscale accuracy claimed by the manufacturer. Once the transducer was calibrated, the ve nturi 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

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36 measured pressure drop and a modified Bernoulli relation [57], which accounted for compressibility, ... 24 2 4 1 1 2 14 2 2 0Ma Ma u P P (3.4) where Ma is the Mach number and is the ratio of specific heats. Ideal Velocity (m/sec) 050100150200250300 Actual Velocity (m/sec) 20 40 60 80 100 120 140 160 Compressible Velocity Incompressible Velocity Curve Fit Figure 3-3. Calibration plot of th e 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. ideal 2 ideal 3 ideal -5 4 -7u 0.5653 + u 0.0076 + u ) 10 (5 )u 10 (1 ideal actualu (3.5) Temperature Measurements Measuring the temperature at various loca tions in the experimental facility was vital in understanding and analyz ing the chilldown process. The temperature at the inlet and exit of the visual test section were m easured using two 1/16-inch type E (ChromelConstantan) thermocouple probes from Omega Engineering. These probes were placed through precision-drilled holes in line with the fluid and seal ed with a combination of

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37 brass compression fittings. In order to mon itor the chilldown process, a series of 6 (laboratory manufactured) t ype E (Chromel-Constantan) th ermocouples were placed along the top and bottom of the 304stainless steel tube prior to the test section, see Fig. 3-4. Figure 3-4. Thermocouple arrange ment 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 tran sfer 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. 3-5. The thermocouples we re placed in such a manner that the exterior thermocouples that were secured to the in sulation were exactly at the same angular positions as the interior thermocouples that we re 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

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38 and the pipe wall with 0.25-inch Teflon tape, to ensure proper thermal contact. At the inlet and exit of the heat tr ansfer 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 ob tained were used to calculate the unsteady heat transfer coefficient. Figure 3-5. Thermocouple placement for heat transfer test section. Once through the heat transfer test secti on the flow passes thr ough the venturi flow meter, which is instrumented with an inlin e 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 1.7C over the large temperature range experienced in these experiments. Data Acquisition System A digital data acquisition system was asse mbled to record and process the analogue output of the instrumentation. The system consists of a personal computer outfitted with an analog to digital data ac quisition 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 analog-to-digital board

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39 was a Measurement Computing PCIMDAS1602/16 with 8 channels and 16 bit resolution and was connected to two Meas urement Computing CIO-EXP32 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 analog-to-digital board through a selected channe l. All chan nels through which thermocouple measurements are taken are provided with a 1F capacitor across the high and low inputs forming a low-pass f ilter having a 7 Hz filtered cutoff. Open thermocouple detect, and a reference to ground through a 100 k-ohm resistor are also provided. The analog-to-digital board and each multiplexer board were calibrated to the manufacture’s specifications usi ng the supplied software, InstaCal. A computer program was developed, usi ng 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, a nd transferred to an Excel spreadsheet where further data processing was car ried out. In the Excel spre adsheet, the temperature and pressure data were processed to obtain th e 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 st ructure as it passed through the visual test secti on. The imaging system was comprised of a Pulnix TM-

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40 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 DT-3145 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 da ta allowed for the flow regime and vapor volume fraction to be determined. Experimental Protocol Once the experimental facility was cons tructed 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 h eat exchanger shell-side is opened. The nitrogen tank connected to the facil ity is opened to a predetermined position and the data acquisition program a nd 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 stru cture 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.

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41 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 substa ntial 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 fr action and the vapor qu ality 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, 1 1l gx S x (4.1) The above expression may be rearranged to e xpress 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 a nd the slip velocity, as in Eq. (4.3). 1g lx xSx (4.2) 1g lS x S (4.3)

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42 The slip velocity model is limited to situa tions in which the slip velocity remains relatively constant, and this is not the case fo r 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 determ ined that the vapor volume fraction and the vapor quality are related by, 011 1gg vj lx CU xGx (4.4) where 0C and vjU are empirical constants. The distribution parameter, 0C, which accounts for non-uniform flow and concentration profiles, and vjU accounts for the effect of the local relative velocity. Eq (4.4) may be rearranged to give, 0 001gvj g lUCG x GCC (4.5) It was demonstrated by Klausner [ 60] that assigning values of 0 10 C and 0.6vjU for horizontal flow, give excellent agreement: within 5% for over 90% of the horizontal two-phase flow data with R113 as the worki ng fluid. Due to the excellent agreement with the horizontal flow expe riments of Klausner [60] usi ng R113, Eq. (4.5) was used to estimate the vapor quality from the measured vapor volume fraction.

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43 Vapor Volume Fraction The vapor volume fraction is an important parameter that must be determined when analyzing two-phase 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 di spersion techniques to visual techniques. For this study, digital images of the flow st ructure were recorded; thus a visual technique is adopted. In order to compute the vapor volume frac tion, the flow regime must first be identified. Researchers have used a number of different conventions to describe the various flow structures observed in horizont al two-phase flows; th e convention used here is the one described by Carey [58] and is illu strated 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 stratifie d, 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, 22 2cos2 1 r rArhr r r (4.6) For the case of annular, and plug flow, the flow structure is modeled as shown in Fig. 4-2. The liquid film thickness at the top, top and bottom, bottom of the tube are measured and the vapor volume fraction is calculated as

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44 22 2 1 r rtop bottom (4.7) Figure 4-1. Model used for the stratified, wavy and intermittent flow volume fraction computation. Figure 4-2. Diagram of the model used for th e annular flow volume fraction computation. Extracting the Heat Transfer Coefficient In order to extract the heat transfer co efficient from the temporal profile of wall temperature; an inverse procedure is empl oyed which varies from that of traditional inverse heat conduction methods. It does not re quire a system of l east-square equations to be solved. Some of these traditiona l methods are reviewed by Ozisik [61].

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45 The process used here for extracting the tr ansient heat transfer coefficient on the inside of the pipe involves a number of itera tive procedures, which are reported here as three major steps. These steps are illustra ted in Fig. 4-3 and ar e 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 tr ansfer 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 match? Record the heat transfer coefficient yes no Figure 4-3. Flow chart for transient h eat transfer coefficient extraction.

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46 Computing the Temperature Field in the Pipe Wall The unsteady 3-D form of the heat conducti on equation in cylindr ical coordinates, see Fig. 4-4, is written as follows: 11pTTTkT c krk tzzrrrrr (4.8) where is the density of the material, pcis the specific heat capacity, t is the time variable, T is the temperature, r is the radial coordinate, z is the axial coordinate and is the azimuthal coordinate. This equati on is non-dimensionalized using the following parameters: s at wsatTT TT ; z z d ; r r d ; 0p p pc c c ; 0k k k ; 0, (4.9) where s atT is the saturation temperature of the fluid within the pipe, wT is the temperature on the outer wall of the pipe, d is the pipe wall thickness, a nd the subscript 0 denotes the property is to be evaluated at the initial temperature, 0T. Thus the original equation is transformed to 2 00 011 cd k ckrk ktzzrrrrr (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 a ssigning 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

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47 spatial terms. The system of equations th at result are solved using the Alternating Direction Implicit (ADI) me thod 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 transf er coefficient for the outside surface of the z r do di Din Dout Figure 4-4. Coordinate system for heat conduction through the pipe wall. pipe insulation must be determined. Th is is accomplished through a steady-state calibration process in which cool nitrogen vapor is passed through the heat transfer section at various mass flow rates. A rela tionship between heat flux through the pipe insulation versus temperature difference (amb ient temperature less the insulation surface temperature) is determined. A constant heat transfer coefficient is approximated as shown in Fig. 4-5. The slope of the line is th e heat transfer coefficient for the outer pipe surface. The measurement of the heat flux into the pipe, wq is quite difficult to measure due to the small temperature rise in the cryogen ic vapor; thus there is some scatter in Fig. 4-5. However, the measured heat transfer coefficient, 4.38 W/m2-K, is quite small,

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48 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, ,outoutT khTT r (4.11) T (K) qw”(W/m2) Figure 4-5. Calibration for determining the outer pipe surface heat transfer coefficient. which is non-dimensionalized to give, 00.outoutsatout wsathdhThT d k rkkTT (4.12) Here subscripts out and denote the outer surface of the pipe, and the outer insulation surface, respectively. The inner pi pe boundary condition is written as, ,ininflT khTT r (4.13) which is then non-dimensionalized to give, 00 insatinfl in wsathThT hd d k rkkTT (4.14)

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49 Here the subscripts i and f l denote the inner surface of th e pipe and the fluid flowing through the pipe, respectively. The fluid temp erature is determined using an internal thermocouple that measures the temperature at the inlet of the heat transfer section. The heat transfer coefficien t on the inside of the pipe, inh, is the quantity that is guessed during the calculation. The two-phase flow structure present for much of the experiment is stratified, and there is a signi ficant 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 interi or surface of the pipe into th ree distinct sections within which the heat transfer coefficient is a ssumed constant. Region 1 is such that 10 and intophh, region 2 is such that 12 and insidehh and region 3 is such that 23 and ibottomhh (see Fig. 4-6). In the film boiling regime it is adequate to allow all three regions to be equal in size, hence, 1212 However in the nucleate boiling regime, where the temperat ure at the bottom changes suddenly by a significant amount very high heat transfer coefficients are pres ent. 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 re moved 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 2 When necessary, it is sufficient to reduce the size of re gion 3 by a factor of 2. For modeling purposes, a more systematic approach to describing diffe rent regions during nucleate boiling is desirabl e. However, the present approach is sufficient to match the measured and computed wall temperature variations.

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50 Iteration Process for Guessing th e Inner Heat Transfer Coefficient Any number of methods may be used to obt ain 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 ar e determined using linear interpolation or 1 2 Region 1 hin=htopRegion 2 hin=hsideRegion 3 hin=hbottom Figure 4-6. Assumed variation of heat transfer coefficient on the inside surface of the pipe. linear extrapolation. Hence the new guess for in ner heat transfer coefficient is given by, ,presprev newknownprevprev presprevhh hTTh TT (4.15) where is a scaling factor that reduces oscillati ons and takes the value 0.3 in this work. The subscripts p res, p rev, 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 t op, side and bottom of the pipe. Once the computed temperature is within 1x10-8 K, the temperatures are

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51 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 th e marginal improvement in accuracy does not justify the increased computational cost. Computational Code: Test ing and Verification Stability of Computational Code For simplicity the stability criterion is de veloped using the Von Neumann analysis of the 1D heat conduction equation, 2 2 x u t u (4.15) 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 1 111 11 22nn jj nnn jjjuu uuu t x (4.16) where n is the index representing time, a nd j is the index representing space. The stability analysis of this scheme may be found in any classical nu merical methods text, and proves that the scheme is unconditionally stab le. This is also true for the 2D and 3D schemes. Grid Resolution The grid resolution is as an important f actor 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 ut ilized. A single-phase flow simulation with

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52 a constant heat transfer coefficient is used to compute the outer wall surface temperature for a series of 50 time steps. The physical pa rameters 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 = 12.5 mm, 5) thickness of pi pe = 1.65 mm, and 6) time step size = 0.1 sec. The inverse proce dure 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, 11 100,N actualextracted i actualabshh Averagepercentageerror Nh (4.17) where N is the number of time steps. The results are given in Table 4-1. Table 4-1. Influence of grid resolution on the computed heat tr ansfer coefficient. Nx Ny Average percentage error (%) 120 64 0.000729 60 32 0.003904 30 16 0.01681 From Table 4-1 we see that the refinement of 60x32 or better gives an error of less than 4 x 10-3%. 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 additiona l computational cost. From Fig. 4-7 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 valid ity of this inverse method, it is first used to calculate the heat tran sfer coefficients for a single-phase 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 sing le-phase nitrogen gas flowing through the

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53 y = -2.2636x + 3.6496 -7.5 -7 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 33.23.43.63.844.24.44.64.85 LN(Grid Size)LN(Average Error) Figure 4-7. Ln(Error) vs ln(grid size) for the inverse technique. experimental facility, with th e results being compared with the predictions of the DittusBoelter correlation for cooling. Finally, it is used to calculate the he at transfer coefficient for a single phase flow simulation undergoing a step change in heat transfer coefficient. In the first test case, the heat transfer coe fficient follows a parabolic path with time. A comparison of the specified heat transfer coe fficient with that extr acted using the inverse method is shown in Fig. 4-8 (the time step si ze used in this test is 0.1 sec; all other parameters are as specified previously). In Fi g. 4-8 it is seen that a parabolic varying heat transfer coefficient is captured quite reliabl y with the inverse appr oach. The difference between the exact and the extracted heat transf er coefficients for this case are shown in Fig. 4-9. It is seen that erro r 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 single-phase heat transfer coefficient with the DittusBeoelter correlation for flowing nitrogen gas is shown in Fig. 4-10 (the time step size used in this test is 1 sec since that is the smallest time interval for which reliable data

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54 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/m2-s. Figure 4-11 illustrates the performance of the inverse procedure in a case where there is a step change in the heat transfer coeffi cient (the time step size used in this test is 0.1 sec; all other parameters are as specified previously). It is obs erved that the inverse procedure is capable of handling a step change in heat transf er coefficient satisfactorily. In order to assess the sensitivity of the pr ocedure to errors in the experimental measurements of pipe wall temperature, 0.2oC errors were artificially added to the measured data, and the heat transfer coeffi cient extraction procedure is applied. The value 0.2oC is the repeatability of the thermocouple measurements, and since the extracted heat transfer coefficients de pend 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 0.2oC resulted in a maximum deviation of 6% in the value of the heat transfer coeffi cient extracted. Hence the inherent variations in thermocouple meas urements 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 extr acted over regions 1, 2, and 3.

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55 0 50 100 150 200 250 300 350 02468101214161820 Time (sec.)Heat Transfer Coefficient (W/m2K) Actual heat transfer coefficient Extracted heat transfer coefficient Figure 4-8. Computation of a pa rabolic varying heat transfer coefficient using the inverse method. -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 02468101214161820 Time (sec.)Difference Between Actual and Extracted Heat Transfer Coefficient (W/m2K) Figure 4-9. Difference between th e exact heat transfer coeffi cient and the heat transfer coefficient extracted using the inverse t echnique for the parabolic varying heat transfer coefficient simu lation given in Fig 4-8.

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56 Dittus-Boeltercorrelation Inverse model Tbulk= 174 oK G = 196 kg/m2-s G Figure 4-10. Comparison of heat transfer coefficient computed using the inverse procedure and the Dittus-Boelter corre lation for single-phase nitrogen gas flow. 0 500 1000 1500 2000 2500 00.511.522.533.54Time (sec.)Heat Transfer Coefficient (W/m2K) Actual Heat Transfer Coefficient Extracted Heat Transfer Coefficient Figure 4-11. Computation of a step change in heat transfer coefficient using the inverse method.

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57 CHAPTER 5 CHILLDOWN FLOW TRANSITI ON AND HEAT TRANSFER Upon introducing the liquid nitr ogen into the facility, heat stored in the pipe walls vaporizes the in-coming 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 resu lting 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 5-1. Quenching front that marks tr ansition 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 th e pipe (the top, the bottom, and the left and right sides). These measurements are reco rded on the outer wall of the pipe in the

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58 first station of the heat tran sfer section, which is located approximately one meter down stream of the visual test section. Fig. 5-2 gives the temperature profile for a low mass flux experiment, 75 kg/m2s (the actual mass flux data is shown in Fig. 5-4); while Fig. 53 gives the temperature profile for a moderate mass flux experiment, 210 kg/m2s (the actual mass flux data is shown in Fig. 5-5). By examining Figs. 5-2 and 5-3 it is seen that the heat transfer process passe s through two distinct regime s, which are the film boiling regime and the nucleate boiling regime. The f ilm 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 expect ed since there is a hi gher rate of thermal transport. -200.00 -150.00 -100.00 -50.00 0.00 50.00 020406080100120140160180 Time (sec)Temperature (C) Temp 1 (Top) Temp 2 (Left) Temp 3 (Bottom) Temp 4 (Right) Stratified / Wavy Figure 5-2. Temperature profile during chilldown for low mass flux experiment.

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59 -200.00 -150.00 -100.00 -50.00 0.00 50.00 020406080100120 Time (sec)Temperature (C) Temp 1 (Top) Temp 2 (Left) Temp 3 (Bottom) Temp 4 (Right) Stratified / Wavy SlugPlug Figure 5-3. Temperature profile during chil ldown for moderate mass flux experiment. 0.00 20.00 40.00 60.00 80.00 100.00 120.00 020406080100120140160180 Time (sec)Mass Flux (kg*m^2/sec) Stratified / Wavy Figure 5-4. Transient mass flux for low mass flux experiment.

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60 0.00 50.00 100.00 150.00 200.00 250.00 300.00 020406080100120 Time (sec)Mass Flux (kg*m^2/sec) Stratified / WavySlug Plug Figure 5-5. Transient mass flux fo r moderate mass flux experiment. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 020406080100120140160180 Time (sec)Vapor Volume Fraction Stratified/Wavy Figure 5-6. Transient vapor volum e for low mass flux experiment.

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61 0.0 0.2 0.4 0.6 0.8 1.0 1.2 020406080100120Time (sec)Vapor Volume Fraction Stratified/WavySlugPlug Figure 5-7. Transient vapor volume frac tion for moderate mass flux experiment. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 020406080100120140160180 Time (sec)Qualtiy Stratified/Wavy Figure 5-8. Transient vapor qual ity for low mass flux experiment.

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62 0.0 0.2 0.4 0.6 0.8 1.0 1.2 02040608010012 0 Time (sec) Q ua lti y Stratified/WavySlugPlug Figure 5-9. Transient vapor quality for moderate mass flux experiment. It must be noted that the mass flux data co llected at the start of the experiment may not be reliable. In the instances when th e storage tank pressure is high a shock is generated when the valve is in itially 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. 5-10, which displays the inlet pressure profile for the low mass flux expe riment. The moderate mass flux experiment also exhibits this behavior, however it is mo re mild than the low mass flux case, which is evident from Fig. 5-11. Flow Regimes The detailed momentum and heat transfer processes that evolve during transient chilldown are not well understood, whic h limits the development of advanced hydrodynamic and thermal models. Knowledge of the flow structure is essential to

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63 predicting the non-uniform temp erature fields encountered during the film and nucleate boiling heat transfer regimes. A satisfactory flow regime transition map has yet to be 0 200 400 600 800 1000 1200 1400 020406080100120140160180 Time (sec)Pressure ( kPa ) Figure 5-10. Transient inlet pressure profile for low mass flux experiment. 0 100 200 300 400 500 600 700 800 900 1000 020406080100120 Time (sec)Pressure (kPa) Figure 5-11. Transient inlet pressure profile for modera te mass flux experiment.

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64 developed that address the cryogenic chilldow n process. The experiments carried out allow the flow regime transitions encounter ed during transient cryogenic chilldown in a horizontal pipeline to be obser ved 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. 2-1. Experiments are carr ied out for mass fluxes that range from 66 to 625 kg/m2-s; 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 pr oduces voracious evaporation accompanied by a high velocity vapor front trav ersing 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. 5-4 and 5-5. At lo w to moderate mass fluxes (usually below 350 kg/m2-s), a stratified-wavy 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 character ized by the sudden and steep increase in the slope of the wall temper ature history profile s hown in Figs. 5-2 and

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65 5-3. This transition to nucleate flow boiling is observed visually as a quenching front that propagates through the pipeline. As the pipe co ols further, the flow structure transitions from the stratified-wavy regime to the intermittent regime. Once the pipe wall temperature reaches the saturation temperature of the nitrogen, the flow transitions to single-phase liquid flow. At higher mass fluxes (usually above 350 kg/m2-s), the initial mist flow structure transitions into annular flow following th e passage of the film boiling front. The later flow transitions include intermittent and single-phase liquid flow. The mass flux, shown in Figs. 5-4 and 55, and vapor volume fraction profiles, shown in Figs. 5-6 and 5-7, highlight the inherent unsteady natu re of the chilldown process. The vapor volume fraction was com puted from the digital images of the flow structure and smoothed by findi ng the best smooth curve fit to the measurements, as outlined in Chapter 4. The computed vapor qu ality profile is illustrated in Figs. 5-8 and 5-9. Performance of Current Flow Regime Maps Modern 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 experimental ly observed flow regimes for horizontal cryogenic flow chilldown. These include fl ow regime maps proposed by Baker [19], Taitel and Dukler [16], and Wo jtan et al. [24]. All of th ese flow regime maps were developed for quasi-steady two-phase flow. They do not attempt to account for the transients encountered during chilldown. Van Dresar and Siegwarth [63] reported flow patter ns for low mass flux (97-346 kg/m2s) steady two-phase flow of nitrogen thro ugh a horizontal pipeline. The data of Van Dresar and Siegwarth [63] are compared against the flow regime predictions from

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66 the three maps discussed. Only turbulent flow data are considered. Comparisons with the Baker map, shown in Fig. 5-12, are rather fortuitous, as it is observed that the flow patterns are correctly predicted with the excep tion of 2 points, wh ich lie close to the correct flow pattern regime. It is observed in Fig. 5-13 that the Taitel and Dukler map performs reasonably well, as all the data point s 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 pred ict the annular data, as shown in Fig. 5-14. 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 en tire database consists of 2625 data points. Table 5-1 provides a samp le 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 repr esentative set of data consisting of 400 data points. These 400 data points cover the enti re range of flow parameters and flow structures. They are chosen to avoid excessi ve 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. 5-15. It is observed that the intermittent data are predicted reas onably well, but neither the annular nor the stratified-wavy predictions give satisfactory agreement with th e data. Fig. 5-16 shows a comparison of the experimentally observed fl ow regimes with those predicted using the Taitel and Dukler map. Although, many obs erved 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. 5-17. While the stratified-wavy and the

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67 Wavy Annular Dispersed Bubbly Slug Plug = intermittent = annular = stratified-wavy Figure 5-12. Comparison of Van Dresar a nd Siegwarth data with the Baker map. 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 Stratified-wavy Stratified-smooth Intermittent Bubbly Annular = intermittent = annular = stratified-wavy XttT F K x 10-3 Figure 5-13. Comparison of Van Dresar and Si egwarth data with the Taitel and Dukler map.

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68 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 50 100 150 200 250 300 350 400 Annular Stratified-wavy Slug Slug & Stratified-Wavy Intermittent Stratified-smooth x G (kg/m2s) = intermittent = annular = stratified-wavy Figure 5-14. Comparison of Van Dresar and Si egwarth data with the Wojtan et al. map. intermittent regime data are pred icted well, the annular regime data are not. This is likely due to the low vapor quality encountered for an nular flow during the chilldown process. The modifications to Kattan et al. map only consider mass fluxes below 200 kg/m2-s; thus the annular regime data lie outside the m odified 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 Dukl er [16], the transition between the stratified and the intermittent or annular regimes is governed by the Kelvin-Helmholtz stability criterion for wave propagation (Milne-Thompson [64]). Kordyban and Ranov [65] and Wallis and Dobson [66] also utilized the Kelvin-Helm holtz stability criterion to analyze the transition to slug flow. Lin a nd Hanratty [67] carried out a similar analysis and included the viscous effects which were neglected in the earlier works, however no significant

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69 Wavy Annular = intermittent = annular = stratified-wavy Slug Plug Bubbly Dispersed Figure 5-15. Comparison of current ch illdown data with the Baker map. 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 Annular Bubbly Stratified-wavy Intermittent Stratified-smooth = intermittent = annular = stratified-wavy T F K x 10-3Xtt Figure 5-16. Comparison of cu rrent chilldown data with the Taitel and Dukler map.

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70 Table 5-1. Sample data points for cryogeni c chilldown. SW denot es stratified-wavy flow; I denotes intermittent flow; A denotes annular flow Mass Flux kg/m2-s Quality Saturation Temperature K Flow Structure Observed 61 0.04 103.2 SW 60 0.04 103.0 SW 64 0.04 103.0 SW 72 0.03 103.3 SW 75 0.03 103.5 SW 74 0.03 103.9 SW 83 0.03 104.4 SW 84 0.03 104.7 SW 79 0.03 104.6 SW 80 0.03 104.6 SW 89 0.02 104.6 SW 86 0.02 104.4 SW 79 0.02 104.3 SW 390 0.03 90.8 I 399 0.03 91.3 I 394 0.03 90.5 I 355 0.04 90.7 I 376 0.06 90.5 I 366 0.04 89.8 I 351 0.05 90.0 I 346 0.04 90.0 I 336 0.03 90.0 I 378 0.06 90.0 I 330 0.04 89.9 I 273 0.04 89.1 I 291 0.06 88.9 I 295 0.08 89.1 I 323 0.03 89.2 I 301 0.06 89.2 I 502 0.13 97.6 A 583 0.10 97.7 A 600 0.06 96.9 A 569 0.08 96.2 A 603 0.04 96.3 A 612 0.11 96.1 A 575 0.09 95.6 A 588 0.12 95.5 A 606 0.07 94.6 A 572 0.07 94.8 A 537 0.17 95.3 A

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71 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 600 Intermittent Slug Slug & Stratified-Wavy Stratified-smooth Annular Stratified-wavy = intermittent = annular = stratified-wavy G (kg/m2s) x Figure 5-17. Comparison of current chill down 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 2-D planar geometry with vapor flow on top of a stationary liquid film with very large thickne ss compared to the size of any disturbances; it was determined that the instability criterion takes the following form 1 2 1 lgg g gg uC (5.1) where 1C is a constant to be determined. A number of simplifying arguments were presented to estimate a value of 1C that is less than unity. The analysis was extended to an inclined pipe geometry to arri ve at Eq. (2.5). The constant, 2C, 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 in terface between the liquid and vapor phases in a

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72 2-D planar configuration with in a confined channel, with both fluids moving. The configuration is illust rated in Fig. 5-18. g l g uluO g l cxy Figure 5-18. Liquid-vapor 2-D ch annel flow configuration. As determined by Milne-Thompson the equatio n that governs the wave speed is given by 2 2cothcoth.lllggglgmucmmucmg (5.2) Here m is the wave number, c is the wave speed, is the fluid height and all other parameter are as define in the previous secti ons. The condition for st ability 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 2 42A AD B B c (5.3) here. A B and D are constants given by Eq. (5.4), cothcothllggAmmmm (5.4a) 2cothcothlllgggBummumm (5.4b) 22cothcoth.lllggglgDmummumg (5.4c)

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73 For the onset of wave instability the value of c must be imaginary thus we have the condition, 0 42 AD B (5.5) After further simplification it is found that th e Kelvin-Helmholtz instability is triggered when 1 1 1 2 2 2 1 211 coshcoshlgg g l g gggllg lgg u u mmmm g .(5.6) Comparison of Eqs, (5.1) and (5.2) yield the following form for 1C, 1 1 2 2 1 1 211 coshcoshg l gggll lgu C mmmm g (5.7) The value of 1C easily exceeds unity for small values of liquid film velocity and low and moderate wave number. A liquid film velocity of 0.01m/s and wave number of yields a value of 1C greater than 3, while a wave number of 1 gives a value of 1C greater than 10. Hence it is expected that 2C in Eq. (2.5) may exceed unity for horizontal and inclined pipe geometries. In order to achieve better pred ictive capabilities, an attemp t is made to calibrate the Taitel and Dukler map. The transition bounda ry that demarcates the transition from stratified-wavy to either annular or inte rmittent flow requires modification. As previously discussed, the transition boundary depends on the value of the constant 2C. For the present data a better fitting transiti on boundary is obtained when the functional form of 2C is calibrated so as to best fit the data. The calibrated value of 2C is given by

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74 1 2 2 -2 2 0.72 tt1.49 4.516 XC (5.8) Hence 2C ranges from 0 to 4.516. This is consistent with Eq. (5.6). The demarcation line for the transition between th e 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 he ight 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 1.6ttX to 4.0ttX which represents a small change physically. Instead of transition to intermittent flow if the liquid film height is gr eater 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. 5-19. The flow regime transitions are significantly improved with th e calibration to the Tait el and Dukler [16] flow regime map. The annular flow regime is typically ch aracterized by thin liquid films with moderate velocities. The overs implified assumptions used by Taitel and Dukler [16] to arrive at Eq. (5.1) severely limits the pa rameter 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 veloci ty can play an important role in KelvinHelmholtz instability. The experimentally observed stratified to annular flow regime transitions in this work clea rly support the notion that the liquid film height and liquid velocity are important parameters in the flow regime transition.

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75 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 Annular Bubbly Stratified-smooth T F K x 10-3XttStratified-wavy = intermittent = annular = stratified-wavy Intermittent Figure 5-19. Comparison of curre nt chilldown data with the modified Taitel and Dukler map. Film Boiling Heat Transfer This section focuses on measuring the heat tr ansfer 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 investigati on 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 5-20 and 5-21 show the film boiling heat transf er coefficients extracted from the experimental data of the low (75 kg/m2s) and moderate mass flux (210 kg/m2s)

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76 experiments highlighted at the beginning of the chapter, resp ectively. It is observed from both Figs.5-20 and 5-21 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. 5-20 to 5-21 it is seen that the higher the mass flux the larger the heat transfer coe fficient. This is also as expected since convective heat transfer increases with increasi ng mass flux. It is in teresting 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 possibl e reason for this is that the circumferential conduction heat to the lowe r region (region 3) is larger for lower mass fluxes, since the convective h eat 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 predic ting the heat transfer rates associated with the complex, unsteady, nucleate flow boiling heat transfer that occurs during cryogenic chilldown. The inverse technique desc ribed 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 te mperature of the pipeline coupled with numerical simulations of the unsteady heat tr ansfer through the wall of the pipeline to

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77 determine the heat transfer coefficients. Th ese experimentally determined heat transfer coefficients are compared against the nucle ate flow boiling heat transfer correlations 0 100 200 300 400 500 600 0102030405060708090 Time (sec.)Heat Transfer Coefficient (W/m2K) Region 1 (Top) Region 2 (Side) Region 3 (Bottom) 275 Gkgms Figure 5-20. Heat transfer coefficients for each region in the film boiling regime of the low mass flux experiment. 0 100 200 300 400 500 600 051015202530354045 Time (sec.)Heat Transfer Coefficient (W/m2K) Region 1 (Top) Region 2 (Side) Region 3 (Bottom) 2210 Gkgms Figure 5-21. Heat transfer coefficients for each region in the film boiling regime of the moderate mass flux experiment.

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78 of Gungor and Winterton [30], Kandlikar [40], Mller-Steinha gen 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 correlati ons, an average heat transfer coefficient must be computed. This is done by integrati ng the heat transfer co efficients assigned on the inner surface over the perimeter of the inne r surface. This approach is also employed by Thome [43]. Hence the average two-phase heat transfer coefficient, 2h is computed as 212 1 2.topsidebottomhhhh (5.9) Fig. 5-22 illustrates the vari ation of the average two-phase heat transfer coefficient extracted from the experimental data with tim e 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 two-phase heat transfer coefficient. The robust nature of the computa tional method is demonstrated in that it is able to handle the step change in heat tr ansfer coefficient from the film to nucleate boiling regime. The nucleate flow boiling heat transfer coefficients extracted from the experimental data are presented in Table 5-3. 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, a nd the contribution to the two-phase heat transfer in each region are tabulated. It is observed that the influence of region 1 on the

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79 average two-phase heat transfer coefficient in the nucleate flow boiling regime is small when compared to the infl uence of regions 2 and 3. 0 500 1000 1500 2000 2500 3000 3500 0102030405060Time (sec.)Heat Transfer Coefficient (W/m2K) 2102,239satkg TKG ms Nucleate Boiling Regime Film Boiling Regime Figure 5-22. Average two-phase heat tran sfer 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 cont ribution than region 3. This occurs because of the unsteady nature of the flow whic h results in instances where region 2 is periodically wetted resulting in a thinner liqui d 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 assi gned to each region it is evident that the flow structure influences the size of each re gion. For annular flow and stratified-wavy

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80 flow in which the liquid film height is great er than the radius of the pipe, the three regions may be constructed such that they ar e of equal size. While in the intermittent flow regime the size of each regi on is adjusted slightly. However, when the flow is in the stratified-wavy regime, a significant difference in the size of regions is observed. This results from the inability to determine the ac tual wetted area of the pipe. If the size of region 3 is overestimated the energy removed from the pipe wall w ould 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 ma inly in the stratified-wavy 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 si ze 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 th e regions sizes were chosen to maintain as much symmetry as possible while ensuring th at the size of the wetted region is not overestimated. The database of cryogenic nuc leate flow boiling heat transfer coefficient for chilldown presented in Table 5-3 is the only one we are aware of. In Table 5-3, SW (0.5+) denotes stratified wavy flow where the height of the liquid film greater than 2id; I denotes intermittent flow; SW (0.5-) denotes stratified wavy flow where the height of the liquid film less than 2id; A denotes annular flow.

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81 Table 5-3. Summary of measur ed average nucleate flow boiling heat transfer coefficients using inverse method for regions. Flow Regime Mass Flux x Sat. Temp. Fraction of area & Avg. Wall Temp for Region 1 Fraction of area & Avg. Wall Temp for Region 2 Fraction of area & Avg. Wall Temp for Region 3 tph kg/m2s K 1 K 1 2 K 2 K W/m2K SW (0.5+) 61 0.04 103.2 0.33151.5 0.33 131.0 0.33 105.3 2203 SW (0.5+) 60 0.04 103.0 0.33153.8 0.33 130.8 0.33 109.4 1561 SW (0.5+) 64 0.04 103.0 0.33151.2 0.33 125.2 0.33 110.1 1852 SW (0.5+) 72 0.03 103.3 0.33156.8 0.33 141.8 0.33 116.0 1265 SW (0.5+) 75 0.03 103.5 0.33155.2 0.33 136.6 0.33 106.9 2211 SW (0.5+) 74 0.03 103.9 0.33152.9 0.33 131.0 0.33 107.8 2508 SW (0.5+) 83 0.03 104.4 0.33151.0 0.33 127.3 0.33 112.1 1881 SW (0.5+) 84 0.03 104.7 0.33145.3 0.33 111.5 0.33 108.8 2888 SW (0.5+) 79 0.03 104.6 0.33139.6 0.33 111.2 0.33 108.2 2787 SW (0.5+) 80 0.03 104.6 0.33134.2 0.33 110.0 0.33 107.1 2429 SW (0.5+) 89 0.02 104.6 0.33138.9 0.33 122.6 0.33 107.8 1514 SW (0.5+) 86 0.02 104.4 0.33135.3 0.33 107.7 0.33 102.2 2374 SW (0.5+) 79 0.02 104.3 0.33132.6 0.33 105.3 0.33 103.2 1588 SW (0.5+) 390 0.03 90.8 0.33145.6 0.33 122.9 0.33 108.1 1967 SW (0.5+) 399 0.03 91.3 0.33142.0 0.33 111.4 0.33 107.5 2381 I 394 0.03 90.5 0.42126.7 0.29 99.4 0.29 100.3 1790 I 355 0.04 90.7 0.42152.1 0.29 131.6 0.29 115.1 1300 I 376 0.06 90.5 0.42148.6 0.29 118.1 0.29 111.3 1880 I 366 0.04 89.8 0.42145.7 0.29 113.8 0.29 111.6 1554 I 351 0.05 90.0 0.42142.9 0.29 113.1 0.29 110.6 1345 I 346 0.04 90.0 0.42140.1 0.29 112.3 0.29 108.4 1631 I 336 0.03 90.0 0.42137.2 0.29 110.1 0.29 108.0 1932 SW (0.5-) 378 0.06 90.0 0.42121.0 0.42 107.2 0.16 93.1 1247 SW (0.5-) 330 0.04 89.9 0.42119.5 0.42 93.0 0.16 90.2 5097 SW (0.5-) 273 0.04 89.1 0.42117.9 0.42 101.0 0.16 89.2 1848 SW (0.5-) 291 0.06 88.9 0.42124.3 0.42 110.6 0.16 97.5 1103 SW (0.5-) 295 0.08 89.1 0.42118.6 0.42 91.8 0.16 92.8 2255 SW (0.5-) 323 0.03 89.2 0.42120.2 0.42 100.9 0.16 94.6 2103 SW (0.5-) 301 0.06 89.2 0.42118.1 0.42 105.4 0.16 97.2 1330 SW (0.5-) 502 0.13 97.6 0.42115.4 0.42 90.4 0.16 94.4 3806 SW (0.5-) 583 0.10 97.7 0.42115.5 0.42 99.4 0.16 96.3 1904 SW (0.5-) 600 0.06 96.9 0.42119.7 0.42 96.4 0.16 96.0 2264 SW (0.5-) 569 0.08 96.2 0.42119.1 0.42 97.2 0.16 96.0 2218 SW (0.5-) 603 0.04 96.3 0.42140.1 0.42 120.5 0.16 101.3 1342 SW (0.5-) 612 0.11 96.1 0.42138.9 0.42 114.7 0.16 103.7 1081 SW (0.5-) 575 0.09 95.6 0.42124.0 0.42 107.1 0.16 105.5 1706 A 588 0.12 95.5 0.33130.8 0.33 114.7 0.33 108.4 1654 A 606 0.07 94.6 0.33128.3 0.33 104.8 0.33 104.4 2149 A 572 0.07 94.8 0.33127.3 0.33 110.4 0.33 104.6 2225 A 537 0.17 95.3 0.33124.9 0.33 104.7 0.33 106.0 2203 A 352 0.039 95.2 0.33127.4 0.33 111.2 0.33 106.5 1682 A 415 0.053 95.0 0.33124.9 0.33 104.0 0.33 105.7 1808

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82 Comparisons of the computed average flow boiling heat transfer coefficients with those determined experimentally are shown in Figs 5-23, 5-24, 5-25 and 5-26. Figs 5-23, 5-24, 5-25 and 5-26 show comparisons with the Gungor and Winterton, Kandlikar, Mller-Steinhagen and Jamialahmadi, and Thom e correlations, respectively. It is observed that the Mller-Stei nhagen and Jamialahmadi corre lation performs the best, predicting 47.6% of the data within the 25% error band. This is followed by the Gungor and Winterton correlation with 38.1%, then th e Thome correlation with 21.4% and finally the Kandlikar carrleation with 9.5%. The Kandlikar correlation and Gungor and Winterton correlation both over predict the heat transfer coefficient. Thus in appl ying these correlations care must be taken in order to account for the region that is actually wetted during the flow boiling process. The Thome correlation under predicts the heat transfer coefficient. Although this correlation is the only one tested that takes into account the flow stru cture, it has not been extensively tested within the low quality range encountered during the chilldown experiments. The Mller-Steinhagen and Jami alahmadi perfoms the best for the present data, however this correlati on does not account for the flow structure. This information gives a reasonable starting point for the development of a re liable correlation for nucleate flow boiling during cryogenic chilldown. Correlating the Nucleate Flow Boiling Heat Transfer Coefficient Many of the current flow boiling heat transfer coefficient correlations ignore the flow structure in their predictions. Of the correlations considered here only the correlation of Thome [43] takes in to account the structure of the flow, however it is seen from Fig. 5-26 that this particular co rrelation under-predicts the data. Since the

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83 0.00 1000.00 2000.00 3000.00 4000.00 5000.00 6000.00 0100020003000400050006000 Measured Heat Transfer Coefficient (W/m2K)Predicted Heat Transfer Coefficien t (W/m2K)+25% -25% Figure 5-23. Comparison of predicted and m easured average nucleate flow boiling heat transfer coefficients using G ungor and Winterton correlation. 0 1000 2000 3000 4000 5000 6000 0100020003000400050006000 Measured Heat Transfer Coefficient ( W/m2K ) Predicted Heat Transfer Coefficient (W/m2K)+25% -25% Figure 5-24. Comparison of predicted and m easured average nucleate flow boiling heat transfer coefficients using Kandlikar correlation.

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84 0.00 1000.00 2000.00 3000.00 4000.00 5000.00 6000.00 0100020003000400050006000 Measured Heat Transfer Coefficient (W/m2K)Predicted Heat Transfer Coefficient (W/m2K)+25% -25% Figure 5-25. Comparison of predicted and m easured average nucleate flow boiling heat transfer coefficients using Mller-Steinhagen correlation. 0 1000 2000 3000 4000 5000 6000 0100020003000400050006000 Measured Heat Transfer Coefficient (W/m2K)Predicted Heat Transfer Coefficient (W/m2K)+25% -25% Figure 5-26. Comparison of predicted and m easured average nucleate flow boiling heat transfer coefficients using Wojtan et al. correlation. Mller-Steinhagen and Jamialahmadi correla tion performs best for the average heat transfer coefficient it is proposed that a be tter result may be obtained by applying a single

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85 phase convective correlation fo r the dry perimeter of the pipe. Here the case the DittusBoelter correlation is used. The Mller-Stei nhagen and Jamialahmadi correlation is used for the wetted perimeter of the pipe. This is shown pictorially in Fig. 5-27. Liquid Phase Vapor Phase Dittus-Boelter correlation for single phase vapor Muller-Steinhagen and Jamoalahmadi correlation for flow boiling in liquid phase Figure 5-27. Method for assigning the heat transfer coeffici ent on the inside surface of the pipe. In order to assess the effectiveness of th is approach, the outer wall temperatures will be computed using this approach of a ssigning the heat transfer coefficient on the inner surface of the pipe, in the nucleate boiling regime. The wetted area is determined using the measured liquid heights from the digi tal images of the flow structure. Once the temperatures are computed they are then comp ared to the measured wall temperatures at the corresponding time instance. It was observed that the temperature values predicted for the dry region of the pipe, i.e. the region that is in contact with the vapor, agree well with the measured temperatures. However, the temperatures pred icted at the side and at the bottom of the pipe do not match well with the measured temp eratures in those locations. In examining the Mller-Steinhagen and Jamialahmadi correl ation, it is seen that the enhancement of

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86 the convective contribution to the heat transf er correlation does not account for the heat flux into the system. The correlation of Gungor and Winterton [ 30] incorporates the effect of the heat flux in the conv ective term by including a Boiling number, Bo, term, as expressed in Eq. (2.23). The Boiling number is defined in Eq (2.21). Following the lead of Gungor and Winterton [30], the effect of the heat fl ux is incorporated through the use of the Boiling number in the enhancement factor for the convective term of the heat transfer coefficient. Thus the modified correlation for the nucleate flow boiling heat transfer coefficient applied to the wetted perimeter takes the form 2.lnbhEhSh (5.10) Here lh is defined in Eq. (2.29), nbh is defined in Eq (2.32), S is defined in Eq. (2.19) and the enhancement factor, E is given by 0.86 31.291 15101.37 1.5ttEBo X (5.11) where Bo is defined in Eq. (2.21), and the Martinelli parameter, ttX, is given in Eq. (2.12). Employing this modified correlation signi ficantly improves the prediction of the temperature at the bottom of the pipe wall. This is illustrated in Figs. 5-28 to 5-46, which compare the predicted outer wall temperatures to the measured outer wall temperatures with the original Mller-Steinhagen and Ja mialahmadi correlation and the modified version. It is of interest to note that the temperature on th e side is not well predicted using either correlation in the wetted region. The primary reason for this is the inability to accurately determine the actual area that is wetted by the liquid phase in the side wall

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87 region. Periodic liquid wetting re sults in very high heat transfer coefficients, and such behavior is not accounted for using this simple model. -180 -170 -160 -150 -140 -130 -120 58.85959.259.459.659.86060.2Time ( sec. ) Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-28. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 140 kg/m2s. -180 -170 -160 -150 -140 -130 -120 86.88787.287.487.687.88888.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-29. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 76 kg/m2s.

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88 -180 -170 -160 -150 -140 -130 -120 104.8105105.2105.4105.6105.8106106.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-30. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 62 kg/m2s. -180 -170 -160 -150 -140 -130 -120 40.54141.54242.54343.5Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-31. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 211 kg/m2s.

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89 -180 -170 -160 -150 -140 -130 45.54646.54747.54848.5Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-32. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 292 kg/m2s. -180 -170 -160 -150 -140 -130 -120 47.84848.248.448.648.84949.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-33. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 279 kg/m2s.

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90 -180 -170 -160 -150 -140 -130 -120 61.86262.262.462.662.86363.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-34. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 210 kg/m2s. -180 -170 -160 -150 -140 -130 -120 83.58484.58585.58686.58787.58888.5Time (sec.) Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-35. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 186 kg/m2s.

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91 -190 -180 -170 -160 -150 120.8121121.2121.4121.6121.8122122.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-36. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 95 kg/m2s. -190 -180 -170 -160 -150 108.8109109.2109.4109.6109.8110110.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-37. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 113 kg/m2s.

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92 -190 -180 -170 -160 -150 86.88787.287.487.687.88888.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-38. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 93 kg/m2s. -190 -180 -170 -160 -150 135.8136136.2136.4136.6136.8137137.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-39. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 134 kg/m2s.

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93 -190 -180 -170 -160 -150 105.8106106.2106.4106.6106.8107107.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-40. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 127 kg/m2s. -190 -180 -170 -160 -150 105.8106106.2106.4106.6106.8107107.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-41. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 132 kg/m2s.

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94 -190 -180 -170 -160 -150 92.89393.293.493.693.89494.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-42. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 162 kg/m2s. -185 -175 -165 -155 68.86969.269.469.669.87070.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-43. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 165 kg/m2s.

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95 -190 -180 -170 -160 -150 87.88888.288.488.688.88989.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-44. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 153 kg/m2s. -180 -170 -160 -150 -140 -130 132.8133133.2133.4133.6133.8134134.2Time (sec.)Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-45 Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 94 kg/m2s.

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96 -180 -170 -160 -150 -140 -130 114.8115115.2115.4115.6115.8116116.2Time ( sec. ) Temperature (oC) Top: Measured Side: Measured Bottom: Measured Top: Muller-Steinhagen Side: Muller-Steinhagen Bottom: Muller-Steinhagen Top: Modified with Bo Number Side: Modified with Bo Number Bottom: Modified with Bo Number Figure 5-46. Comparison of the predicted a nd measured temperatures using both the Mller-Steinhagen and Jamialahmadi corr elation and the modified version. Average mass flux 94 kg/m2s. In order to better compare th e performance of this modified version of the MllerSteinhagen and Jamialahmadi co rrelation, the predicted averag e heat transfer coefficient is computed and then compared to the measur ed average heat transfer coefficient. The results are shown in Fig. 5-47. It is seen fr om Fig. 5-47 that the prediction of the average heat transfer coefficient is significantly impr oved, with 75.6% of the data lying within the 25% error band. This clearly demonstrates that the Boiling number is an important parameter when considering the enhancement of the convective cont ribution to the heat transfer coefficient. This observation is consistent with the findi ngs of Klausner [60] who observed that at with increasing heat fluxes, the two-phase friction pressure drop increases in horizontal flows compared with adiabatic flow at the same vapor quality and vapor volume fraction. This suggests that the bulk turbulent conv ection increases as a result of increasing

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97 0 1000 2000 3000 4000 5000 6000 0100020003000400050006000 Measured Heat Transfer Coefficient (W/m2K)Predicted Heat Transfer Coefficient (W/m2K)+25 -25 Figure 5-47. Comparison of predicted and m easured average nucleate flow boiling heat transfer coefficients using modified Mller-Steinhagen and Jamialahmadi correlation. transverse vapor momentum at higher heat fl uxes. In the current work, the local heat fluxes are seen to range from 10.4 kW/m2 to 103.6 kW/m2, which are consistent with the heat flux ranges investigated by Klausner [60].

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98 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH The process of cryogenic chilldown is ve ry complex and although attempts have been made to simulate the momentum and energy interactions, prior attempts have been fair at best. One of the major reasons is th e lack of reliable data and correlations that encompass the parameter space associated with cryogenic fluids. This work has taken the much needed first step in compiling a database of flow structures, mass flow rates, pressure drop and heat transfer coefficients in both the film boili ng and nucleate boiling regimes. In order to extract the unst eady heat transfer coefficien ts from the experimental temperature data, a novel inverse approach has been developed th at utilizes finite volume computations to deduce the heat transfer coefficients based on the measured temperatures. The technique assumes a give n heat transfer coefficient on the inner surface of the pipe and computes the unsteady te mperature field within the pipe wall then checks whether the computed temperature fiel d matches the measured temperature values at specified locations. If a match is achieved then the assumed heat transfer coefficient is considered to be the actual heat transfer coe fficient at that location. If a match is not obtained a different heat transfer coefficient is assumed and the process is repeated until a match is obtained. The inverse technique is s een to perform well for singl e phase flow structures; however, for two-phase flow structures a suit able approach must be employed to account for circumferential variations in the heat transfer coefficient. This work uses a simple

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99 model that divides the inner perimeter into th ree regions, and the heat transfer coefficient is assumed constant in each region. The actual variation of the heat transfer coefficient is more complicated, although the approach used pr oved to be adequate and robust. This is one of the areas where further work is require d. Better models are desired to account for the circumferential variations of the heat transfer coefficient. As a result more detailed studies must be conducted to gain a better unde rstanding of the fluid interaction with the wall, as these interactions greatly affect the magnitude of the heat transfer rates, especially in the nucleate flow boiling regime. The experimental data gathered were used to calibrate existing models for predicting flow regime transitions and the nucleate flow boiling heat transfer coefficients. It was highlighted that even though the Taitel and Dukler [16] flow regime map is the map best suited to predict chilldown flow regi me transitions, it utilizes assumptions that oversimplify the transition boundary be tween the stratified-wavy and the intermittent/annular regimes. The transition wa s calibrated to give a significantly better performance. For future studies, a more mechanistic approach for modifying the transition boundary is desired so that the modified map may be applied to a wider range of operating parameters and operating fluids. The flow boiling heat transf er correlation of Mller-Ste inhagen and Jamialahmadi [39] performs best of the co rrelations tested here, but it lacks two major features necessary for it to be utilized for correlating the flow boiling heat transfer coefficient in cryogenic chilldown. The most obvious shortcom ing is that it ignores the flow structure, which plays a major role in determining th e heat transfer. Secondly, it ignores the influence of local heat flux on the enhancemen t of the convective component of the heat

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100 transfer coefficient. A simple model that includes the effect of flow structure and the enhancement provided by the local heat fl ux, significantly improves the predictive capabilities of the correlation. To achieve even better perf ormance detailed knowledge of the wetting phenomena on the inne r surface of the pipe must be known. This is another area that requires further work. This work has provided a database th at will aid in the development and improvement of models and correlations that are useful to predic t the thermal hydraulic transport for the chilldown process. A us eful inverse technique for extracting the unsteady heat transfer coefficients in both the film and the nucleate boiling regimes has been developed. A modified Taitel and D ukler map is given that is applicable to cryogenic chilldown with liquid nitrogen. And a flow boiling heat transfer correlation is proposed that gives better performan ce than those currently available.

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101 APPENDIX A PHYSICAL PROPERTIES OF NITROGEN The physical properties for nitrogen ma y be obtained by utilizing the following curve fit equations: T is in C. l = -0.202330 x 104 0.251212 x 102 *T 0.546161 x 10-1 T2 (kg/m3) v = 0.925489 x 101 0.859076 x 10-1 *T 0.454727 x 10-3 T2 (kg/m3) l = -0.954068 x 10-4 0.103000 x 10-5 T + 0.678184 x 10-8 T2 + 0.642683 x 10-10 T3 0.229346 x 10-12*T4 0.211157 x 10-14*T5 (Ns/m2) v = 0.607870 x 10-4 + 0.509473 x 10-6 T + 0.116164 x 10-8 T2 (Ns/m2) cpl = 2.2956 x 104 + 1.49146 x 10*T 0.602354 T2 + 0.289989 x 10-2 T3 -0.166225 x 10-4 T4 0.704924 x 10-6 T5 + 0.115665 x 10-8 T6-0.125146 x 10-11 T7-0.222653 x 10-13*T8 (kJ/kgK) cpv = 0.44248 x 1014*EXP(0.253474 T + 0.659959 x10-3 T2) (kJ/kgK)

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102 kl = -0.135374 0.879867 x10-3 T + 0.242658 x 10-5 *T2 0.207528 x 10-8 *T3 (W/mK) kv = 0.140406 + 0.79933 x 10-4 T -0 .36289 x 10-5 T2 + 0.18728 x 10-7 T3 -0.99885 x 10-10 T4 0.407198 x 10-12 T5 +7 .02725 x 10-15 T6 -7.14345 x 10-18 T71.31179 x 10-19 T8 (W/mK) hf = 6.62495 x 105 + 6.13878 x 103 T+ 1.09164 x 10 T2 (J/kg) hg = -1.74503 x x105 – 7.49609 x 102 *T + 4.93291 T2-0.113927 x 10-1 T3 +0.299316 x 10-3 T4+0.360372 x 10-7 T5-0.172519 x 10-7 T6 +0.238447 x 10-10 T7+0.29486x 10-12 T8 (J/kg) hfg = hg-hf (J/kg) Psat = 0.380945 x 102 + 0.310646 T + 0.177896 x 10-3 T2 0.214602 x10-5 T3 (MPa) = -0.488624 x 10-2 + 0.398741 x 10-4 T + 0.160255 x 10-6 T2 -0.203075.179123E-13 x10-8 T3 + 0.365340 x 10-11 T4 + 0.179123E x 10-13 T5 (N/m)

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103 APPENDIX B EXPERIMENTAL DATABASE: FLOW REGIME, HEAT TRANSFER COEFFICIENT, AND PRESSURE DROP DURING CHILLDOWN A1 fraction of inner pipe perimeter occupied by region 1 A2 fraction of inner pipe perimeter occupied by region 2 A3 fraction of inner pipe perimeter occupied by region 3 FR flow regime G mass flux (kg/m2s) h1 heat transfer coefficient extracted from region 1 (W/m2K) h2 heat transfer coefficient extracted from region 2 (W/m2K) h3 heat transfer coefficient extracted from region 3 (W/m2K) P pressure drop across visual test section (kPa) Tsat saturation temperature (C) Tw,b outer wall temperature measured at the bottom of the pipe (C) Tw,i inner wall temperature in respective region (C) Tw,s outer wall temperature measured at the side of the pipe(C) Tw,t outer wall temperature measured at the top of the pipe(C) t time (s) x vapor quality liquid film height (mm) b liquid film thickness at the bottom of the pipe in annular flow (mm) t liquid film thickness at the top of the pipe in annular flow (mm)

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104EXP 1 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 73 1 -29.4 0.333 19 21 328 0.333 18.2 21.1 363 0.333 17.4 19.7 431.7 0.0 1 S 89.7 0.295 -72.2 0.333 17.1 18.3 146.1 0.333 16.1 18.3 141.9 0.333 13.4 15.1 288.5 1.6 2 S 100.5 0.248 -97.1 0.333 14.1 15.4 164.8 0.333 12.6 14.9 165 0.333 7.9 9.5 338.6 1.8 3 S 102.8 0.229 -109.6 0.333 11 12.2 166 0.333 8. 7 11.2 175.7 0.333 2.2 3.4 364.5 1.8 4 N 108.2 0.201 -116 0.333 8 9.2 154.2 0.333 4.7 7.2 172.7 0.333 -3.8 -2.9 385.8 0.0 5 S 108.8 0.192 -122.8 0.333 5.1 6. 2 110.7 0.333 0.7 3.1 126.3 0. 333 -9.4 -9.1 289.3 1.1 6 S 118 0.168 -168.3 0.333 2 3.1 110.8 0.333 -3.4 -1.3 132.6 0.333 -14.5 -14.7 265.7 1.4 7 S 123.5 0.161 -176 0.333 -1.4 -0.2 121.5 0.333 -7 .6 -5.7 138 0.333 -19.1 -19.8 251.9 1.7 8 N 113.4 0.157 -175.7 0.333 -4.6 -3.5 116.2 0.333 11.7 -9.9 135.2 0.333 -24.3 -25.1 280.5 0.0 9 S 127.8 0.132 -175.7 0.333 -7.6 -6.6 110.1 0.333 15.3 -13.8 119.8 0.333 29.1 -30.3 281.8 1.9 10 S 117.8 0.149 -175.7 0.333 -10.5 -9 .7 106.4 0.333 -18.8 -17.3 114.4 0.333 -33.1 -34.8 257.2 1.6 11 N 124.2 0.118 -175.9 0.333 -13.3 12.5 99.1 0.333 -22.4 -21 118.3 0.333 -37.4 -39.3 276.2 0.0 12 S 120.5 0.134 -174.9 0.333 -16.4 15.6 110.1 0.333 -25.6 -24.6 102.1 0.333 -41.4 -43.7 274.2 1.9 13 N 129.6 0.106 -175.6 0.333 -19.2 18.6 104.5 0.333 -28.9 -28.1 108. 5 0.333 -45 -47.6 263.6 0.0 14 S 132.8 0.117 -174.5 0.333 -22.3 21.7 113.2 0.333 -32.1 -31.5 103.5 0.333 -48.8 -51.6 279.9 1.8 15 N 132 0.103 -175.1 0.333 -25 -24.6 101.1 0.333 -35. 3 -34.9 106.2 0.333 -52.4 -55.4 276.7 0.0 16 S 125.5 0.109 -174.3 0.333 -27.9 27.6 111.2 0.333 -38.5 -38.3 102. 5 0.333 -56 -59.2 285.2 4.1 17 S 134.2 0.093 -175.1 0.333 -30.8 30.6 109.2 0.333 -41.7 -41.6 110.7 0.333 -59.2 -62.6 274.3 2.1 18 N 126.9 0.103 -173.8 0.333 -34 -33. 8 120.9 0.333 -45.1 -44.9 116.6 0.333 -62.7 -66.1 291.1 0.0 19 S 129.8 0.091 -174.6 0.333 -36.8 36.8 113.6 0.333 -48.1 -48.1 113. 3 0.333 -65.2 -69 255.4 2.5 20 S 119.4 0.098 -173.7 0.333 -40.1 40.1 128.4 0.333 -51.5 -51.4 129.9 0.333 -68.5 -72.2 283.6 1.9 21 N 130.6 0.084 -174.5 0.333 -42.9 43.1 116.1 0.333 -54.5 -54.5 123.4 0.333 -71.1 -74.9 259.4 0.0 22 S 113.1 0.096 -173.5 0.333 -45.8 46.2 119.4 0.333 -57.3 -57.5 108.2 0.333 -73.9 -77.7 273.5 2.5 23 S 129.7 0.077 -174.2 0.333 -48.4 49 109.5 0.333 -60.1 -60.3 112.6 0.333 -76.7 -80.6 280.2 2.1 24 N 136.6 0.082 -173.5 0.333 -51.2 51.9 120.9 0.333 -62.6 -63.1 98.1 0.333 -79.1 -83.2 266.7 0.0 25 S 130.3 0.082 -173.4 0.333 -53.7 54.6 107.4 0.333 -65.2 -65.9 97.5 0.333 -82.2 -86.2 308.2 3.3 26 S 148.1 0.075 -174.2 0.333 -56.4 57.5 118.4 0.333 -67.8 -68.6 106.7 0.333 -84.3 -88.5 260.4 3.3 27 S 124.6 0.087 -173 0.333 -59.2 -60. 3 124.4 0.333 -70.9 -71.6 128.7 0.333 -87.5 -91.5 321.2 4.3 28 S 150.7 0.071 -174 0.333 -61.7 -63 113.5 0.333 -73. 5 -74.2 115.2 0.333 -89.8 -94.1 290.6 2.0 29 S 146.8 0.075 -173.1 0.333 -64.3 -65.8 124 0.333 -75.9 -76.9 108 0.333 -92 -96.3 280.8 1.5 30 S 130.6 0.076 -173 0.333 -66.7 -68. 4 113.8 0.333 -78.5 -79.4 111.3 0.333 -94.9 -99.1 326.8 1.5 31 S 145.3 0.068 -174 0.333 -69 -70.8 110.4 0.333 -80. 7 -81.7 99.4 0.333 -96.7 -101.2 279.3 3.4 32 S 136.5 0.074 -172.8 0.333 -71.3 73.3 110.4 0.333 -83 -84.1 94.8 0.333 -99.2 -103.7 321.3 2.1 33 S 139.6 0.079 -172.9 0.333 -73.4 75.5 100.7 0.333 -85.2 -86.5 94. 1 0.333 -101.6 -106.2 329 4.3 34 S 156.2 0.065 -173.7 0.333 -75.7 77.9 115.1 0.333 -87.4 -88.8 106. 9 0.333 -103 -107.8 263.5 2.7 35 S 133.1 0.075 -172.5 0.333 -77.9 -80.2 111.8 0.333 -89.5 -91 90. 4 0.333 -105.3 -110 323 3.6 36 S 149.7 0.068 -173.3 0.333 -79.9 82.4 102.3 0.333 -91.5 -93 92.8 0.333 -107.5 -112.2 329.4 1.9 37 S 154.7 0.064 -173 0.333 -82 -84.6 112.8 0.333 93.5 -95.1 93.3 0.333 -109 -113.9 291.3 3.3 38

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105EXP 1 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t S 123.2 0.077 -172.5 0.333 -83.9 86.7 101 0.333 -95.6 -97.1 94.1 0.333 -111.4 -116.1 350.6 3.4 39 S 150.4 0.065 -173.8 0.333 -85.9 88.8 106.3 0.333 -97.5 -99.1 96. 1 0.333 -113 -117.9 313.5 2.6 40 S 152.1 0.07 -173 0.333 -87.9 -90. 9 112.8 0.333 -99.4 -101.1 94.2 0.333 -114.5 -119.5 304.5 2.9 41 S 113.8 0.096 -172.3 0.333 -90 -93 112.4 0.333 -101. 7 -103.4 115.8 0.333 -117.1 -121.9 390.2 5.8 42 SW 195.2 0.077 -173.9 0.333 -92.3 -95.4 134.7 0.333 -104 -105.8 132.8 0.333 -118.8 -123.7 340.3 3.8 43 SW 164.1 0.075 -173.1 0.333 -94 97.3 106.2 0.333 -105.5 -107.6 90. 4 0.333 -120 -125.1 306.1 1.9 44 SW 132.4 0.094 -172.3 0.333 -95.6 -99.1 92.5 0.333 -107.4 -109.5 92. 9 0.333 -122.4 -127.2 407.3 4.2 45 SW 194.4 0.081 -173.4 0.333 -97.4 -100.9 103 0.333 -109.2 -111.3 101.3 0.333 -123.9 -128.9 349.8 5.2 46 SW 163.5 0.068 -173.3 0.333 -99.2 -102.9 116.8 0.333 -110.6 -112.9 83. 7 0.333 -124.6 -129.9 281.6 2.5 47 SW 130.5 0.082 -172.2 0.333 -100.8 -104.6 97 0.333 -112.3 -114.7 85. 2 0.333 -126.9 -131.9 430 2.8 48 SW 151.2 0.093 -172.5 0.333 -102.3 -106.2 92.3 0.333 -113.8 -116.3 82. 1 0.333 -128.5 -133.6 385.1 4.1 49 SW 179.3 0.068 -174.1 0.333 -103.9 -107.9 106 0.333 -115.2 -117.8 78.6 0.333 -128.8 -134.2 252.3 6.1 50 SW 126 0.075 -172.4 0.333 -105.4 109.6 101.1 0.333 -116.6 -119.3 74.9 0.333 -130.8 -135.9 424.6 5.0 51 SW 133.9 0.099 -172.2 0.333 -107.3 -111.4 122.5 0.333 -118.9 -121.5 160. 9 0.333 -132.5 -137.6 413.5 2.5 52 SW 171.5 0.068 -173.8 0.333 -108.9 -113.1 110.6 0.333 -120.2 -123 96.4 0.333 -133.1 -138.4 299.4 2.8 53 SW 119.4 0.072 -172.4 0.333 -110.5 -114.8 120.4 0.333 -121.4 -124.3 69. 2 0.333 -134.4 -139.6 389.3 4.7 54 SW 126.1 0.09 -172.1 0.333 -111.9 -116.4 100.5 0.333 -123.2 -126.1 132. 1 0.333 -136.2 -141.2 433 6.2 55 SW 148.8 0.072 -173.8 0.333 -113.3 -117.9 100.2 0.333 -124.3 -127.4 77. 2 0.333 -136.9 -142.2 346.3 6.6 56 SW 137.1 0.07 -172.8 0.333 -114.8 -119.5 117.2 0.333 -125.6 -128.7 89. 9 0.333 -138 -143.2 378.9 2.2 57 SW 140.5 0.076 -172.5 0.333 -116.3 -121 111.7 0.333 -127.4 -130.5 145 0.333 -139.8 -144.8 493.3 4.8 58 SW 129.2 0.079 -172.5 0.333 -118 122.7 137.5 0.333 -131.1 -133.3 77. 1 0.333 -155.5 -158 2862.3 3.6 59 SW 143.8 0.063 -173.5 0.333 -120.7 -124.5 119.3 0.333 -141.2 -143 1006.8 0.333 -166.9 -169.1 5483.9 3.5 60 SW 121.1 0.065 -172.5 -126.8 -158.8 -169.6 2.8 61 SW 134.7 0.073 -172.4 -130.2 -165.3 -169.5 2.6 62 SW 130.1 0.067 -173.6 -135.5 -166.5 -169.8 6.0 63 SW 144.2 0.062 -173.5 -140.6 -167.5 -170.8 5.3 64 SW 144.6 0.064 -173.4 -145.7 -168.5 -170.9 2.9 65 SW 141.5 0.064 -173.1 -152.3 -169.1 -170.9 1.9 66 SW 143.4 0.057 -173.3 -157 -169.6 -170.7 8.0 67 SW 152.9 0.056 -174.1 -164.6 -169.6 -170.9 8.3 68 SW 148.9 0.057 -173.6 -169 -170.1 -171.3 7.9 69 SW 155.1 0.053 -173.6 -169.8 -170.3 -171.3 3.6 70 SW 159.1 0.052 -174.2 -170 -170.5 -171.4 2.6 71 SW 161.9 0.051 -174.4 -170.2 -170.9 -171.8 7.4 72 SW 165.9 0.049 -174.4 -170.4 -171.3 -172.2 9.8 73 SW 163.7 0.049 -174.9 -170.7 -171.6 -172.5 4.0 74 SW 161.5 0.048 -175.2 -170.8 -171.9 -172.9 2.0 75 SW 158.1 0.048 -175.1 -171 -172.1 -173.2 1.2 76

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106EXP 1 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 157 0.046 -175.4 -171.2 -172.3 -173.4 6.7 77 I 161.4 0.044 -175.6 -171.2 -172.5 -173.6 12.4 78 I 160.4 0.044 -175.9 -171.3 -172.8 -173.8 4.0 79 I 167.6 0.042 -176 -171.5 -173 -174 3.4 80 I 179.5 0.04 -176.2 -171.6 -173.3 -174.4 2.0 81 I 194.7 0.037 -176.5 -171.9 -173.6 -174.7 8.8 82 I 215.5 0.035 -177.6 -172.3 -174 -175.2 12.4 83 I 230.7 0.035 -178.8 -173 -174.7 -175.8 4.0 84 I 236.6 0.035 -179.5 -174.3 -175.5 -176.7 2.3 85 I 242.8 0.034 -179.7 -175.2 -176.2 -177.4 10.3 86 I 243.9 0.033 -180 -175.9 -176.8 -177.9 12.4 87 I 241.7 0.032 -180.2 -176.2 -177.1 -178.2 12.4 88 I 239.3 0.031 -180.4 -176.5 -177.3 -178.5 2.7 89 I 239.7 0.03 -180.6 -176.7 -177.5 -178.7 3.4 90 I 238.1 0.029 -180.6 -176.9 -177.5 -178.8 2.5 91 I 236.7 0.028 -180.5 -177.1 -177.6 -178.8 6.5 92 I 235.2 0.027 -180.4 -177.3 -177.7 -178.9 12.4 93 I 233.6 0.026 -180.8 -177.6 -177.8 -179.1 10.7 94 I 229.6 0.025 -181 -177.8 -178 -179.3 4.7 95 I 226.9 0.024 -181.6 -178.2 -178.2 -179.6 3.3 96 I 223.6 0.024 -182.1 -178.6 -178.5 -179.8 2.3 97 I 222.6 0.023 -182.2 -178.8 -178.7 -180 12.4 98 I 221.6 0.022 -182.4 -178.9 -178.8 -180.1 12.4 99 I 221.2 0.021 -182.5 -179 -178.9 -180.3 3.1 100 I 220.6 0.021 -182.7 -179.2 -179 -180.4 4.7 101 I 219.2 0.02 -182.8 -179.2 -179.1 -180.6 2.9 102 I 218 0.019 -182.9 -179.3 -179.2 -180.7 8.4 103 I 217.1 0.019 -182.9 -179.4 -179.2 -180.7 10.4 104 I 214.6 0.018 -183 -179.4 -179.2 -180.8 6.1 105 I 213 0.017 -183.3 -179.7 -179.5 -181.1 7.9 106 I 212.2 0.017 -183.8 -180.1 -180 -181.5 9.6 107 I 211.4 0.016 -184 -180.3 -180.2 -181.9 10.0 108 I 210.8 0.016 -184.1 -180.5 -180.3 -182.1 10.4 109 I 209.4 0.015 -184.7 -180.9 -180.8 -182.6 12.4 110 I 209.1 0.014 -185 -181.2 -181.1 -182.9 9.3 111 I 207.4 0.014 -185.1 -181.3 -181.2 -183.1 9.7 112 I 204.3 0.014 -185.1 -181.4 -181.3 -183.2 6.8 113

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107EXP 2 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 69 1 8.6 0.333 21 22.4 1009.7 0.333 20. 9 22.5 917.1 0.333 20 21.6 1330.2 0.0 1 N 45.5 1 4.5 0.333 20.8 21. 5 272.3 0.333 20.8 21.7 186.3 0.333 20.1 20.8 225.5 0.0 2 N 11.8 1 1.9 0.333 20.3 20.8 287.1 0.333 20.2 21 257.4 0.333 19.5 20.1 360.7 0.0 3 N 17.8 1 5.9 0.333 20.2 20.6 114 0.333 20. 2 20.8 45.2 0.333 19.5 19.9 141.8 0.0 4 N 38.1 1 8.5 0.333 20.1 20.4 95.1 0.333 20 20.6 25.3 0.333 19.3 19.7 128.1 0.0 5 N 48.1 1 6.3 0.333 19.5 20 206.5 0.333 19. 5 20.2 131.5 0.333 18.8 19.3 218.3 0.0 6 N 53 1 3.3 0.333 18.8 19.3 265.6 0.333 18. 9 19.6 183.2 0.333 18.2 18.7 265.4 0.0 7 N 55.5 1 0.5 0.333 18 18.5 278.6 0.333 18. 1 18.9 201.9 0.333 17.4 18 269.8 0.0 8 N 56.2 1 -2.5 0.333 17.1 17.6 297.4 0.333 17.3 18 206.1 0.333 16.6 17.2 287.7 0.0 9 N 54 1 -5.2 0.333 16.2 16.6 264.6 0.333 16. 3 17.1 196.6 0.333 15.6 16.2 259.4 0.0 10 N 49 1 -10.6 0.333 15.2 15.6 146.2 0.333 15. 4 16.2 108.7 0.333 14.7 15.2 144.5 0.0 11 N 56.4 1 -36.8 0.333 13.6 14. 1 161.6 0.333 13.8 14.8 120.2 0.333 12.4 13.2 237.2 0.0 12 N 57.6 1 -53.3 0.333 11.8 12. 3 177.2 0.333 11.8 12.9 134.4 0.333 9.2 10.2 306.1 0.0 13 N 57.7 1 -63.5 0.333 9.9 10.3 169 0.333 9. 7 10.9 130.4 0.333 6.3 7.1 278.7 0.0 14 N 60.7 1 -74.5 0.333 7.9 8.3 169.1 0.333 7.3 8.6 138.8 0.333 2. 8 3.4 329.3 0.0 15 N 60.4 1 -78.9 0.333 5.8 6. 1 163.7 0.333 4.8 6.1 136 0.333 -0.8 -0.3 331.3 0.0 16 N 58.6 1 -86.4 0.333 3.5 3. 9 171.8 0.333 2 3.3 149.1 0.333 -4.3 -4.2 337.6 0.0 17 N 57.2 1 -90.3 0.333 1.4 1.6 163.6 0.333 -0 .6 0.6 142 0.333 -7.6 -7.8 326.4 1.2 18 N 56.1 0.558 -93.1 0.333 -0.6 -0.5 143.4 0.333 -3.1 -2 125.8 0.333 -10.9 -11.3 313.2 1.8 19 N 59.7 0.335 -100.7 0.333 -2.7 -2.5 116.6 0.333 -5 .8 -4.7 108.9 0.333 -14.5 -15.1 281.7 1.5 20 N 60.7 0.242 -122.3 0.333 -4.7 -4.6 86.1 0.333 -8.6 -7.5 87 0.333 -18.2 -19 216.3 2.2 21 N 56.5 0.2 -164.7 0.333 -6.8 -6.7 84.2 0.333 11.3 -10.3 80.6 0.333 21.4 -22.5 199.5 1.6 22 N 55.5 0.167 -168.5 0.333 -8.8 -8.7 81.3 0.333 13.7 -12.9 74.4 0.333 24.3 -25.7 189.1 1.7 23 N 51.9 0.15 -168 0.333 -10.7 -10. 7 76.3 0.333 -16.1 -15.3 71.2 0.333 -27.2 -28.8 190.3 2.2 24 N 56.5 0.122 -169.4 0.333 -12.6 12.6 76.2 0.333 -18.3 -17.6 64.8 0.333 -29.6 -31.5 176.9 1.8 25 N 58.4 0.106 -169.4 0.333 -14.5 14.6 74.9 0.333 -20.7 -20 68.8 0.333 -32.7 -34.6 204.8 2.1 26 N 58.5 0.095 -168.9 0.333 -16.5 16.6 77.3 0.333 -23 -22.4 68.2 0.333 -35.4 -37.5 200.8 1.4 27 N 62.5 0.083 -168.5 0.333 -18.6 18.7 83.5 0.333 -25.5 -24.9 76.2 0.333 -38.2 -40.4 203.8 2.1 28 N 63.2 0.075 -168.8 0.333 -20.8 -20.9 85.6 0.333 -28 -27.5 77. 9 0.333 -41 -43.3 212.6 2.0 29 N 59.2 0.073 -168.9 0.333 -22.9 -23.1 86 0.333 -30.4 -30 74.9 0.333 -43.8 -46.3 216.1 2.1 30 N 52.3 0.074 -169.6 0.333 -25.1 25.3 86.5 0.333 -32.6 -32.3 72 0.333 -45.6 -48.4 171.5 2.2 31 N 50.4 0.07 -170 0.333 -27.2 -27. 5 85.8 0.333 -34.8 -34.6 70.6 0.333 -47.3 -50.2 161.4 2.5 32 N 53.4 0.063 -170.4 0.333 -31.2 -29.6 81.6 0.333 -39 -36.8 70 0.333 -51.4 -52.1 165.5 2.0 33 N 54.3 0.059 -170.7 0.333 -33.1 31.7 81.5 0.333 -41 -38.9 68.8 0.333 -53.8 -54.2 181.2 2.9 34 N 55.8 0.054 -170.9 0.333 -35 33.8 79.9 0.333 -43 -41 64.6 0.333 -56 -56.6 199.5 1.7 35 N 57.1 0.051 -170.9 0.333 -36.9 35.8 81 0.333 -45.1 -43.1 65.3 0.333 -58.3 -58.9 197.9 2.1 36 N 58.9 0.047 -170.8 0.333 -38.8 37.8 79.6 0.333 -47.1 -45.1 64. 3 0.333 -61 -61.3 207.4 2.5 37 SW 60.6 0.044 -171 0.333 -40.7 -39.8 79 0.333 -49.1 -47.2 60 0.333 -63.4 -64 229.9 2.5 38

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108EXP 2 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 59.9 0.043 -171.1 0.333 -42.6 -41.8 82.5 0.333 -51.2 -49.2 56. 7 0.333 -65.7 -66.6 229.7 2.5 39 SW 63.8 0.039 -171.2 0.333 -44.5 -43.7 79.3 0.333 -53.2 -51.3 63. 9 0.333 -68.4 -69.1 226.2 2.3 40 SW 72.4 0.035 -170.8 0.333 -46.3 -45.7 81.9 0.333 -55.4 -53.4 57. 9 0.333 -71.1 -71.8 257.9 2.3 41 SW 74.5 0.033 -170.6 0.333 -48.1 -47.6 78.5 0.333 -57.5 -55.6 60. 3 0.333 -73.6 -74.7 267.4 3.2 42 SW 75 0.032 -170.5 0.333 -50 -49.5 82.5 0.333 59.7 -57.8 63.3 0.333 76.1 -77.3 268.4 2.7 43 SW 74 0.031 -170.2 0.333 -52 -51.5 82.9 0.333 -61.9 -60 66.5 0.333 -78.7 -80 274.9 3.5 44 SW 82.6 0.028 -169.8 0.333 -53.9 -53.4 85.9 0.333 -64.2 -62.2 66. 8 0.333 -81 -82.7 292.9 5.6 45 SW 84.4 0.027 -169.5 0.333 -55.9 -55.4 87 0.333 -66.4 -64.6 75.4 0.333 -83.5 -85.2 281.8 4.6 46 SW 78.6 0.028 -169.5 0.333 -57.9 -57.5 89.5 0.333 -68.6 -66.9 74. 8 0.333 -85.7 -87.7 293.1 4.0 47 SW 83.3 0.026 -169.6 0.333 -59.8 -59.5 89.8 0.333 -70.7 -69.1 71. 9 0.333 -87.8 -90.1 291.2 4.0 48 SW 79.7 0.026 -169.5 0.333 -61.8 -61.6 90.4 0.333 -72.9 -71.3 72 0.333 -90 -92.3 285.7 3.5 49 SW 88.7 0.024 -169.6 0.333 -63.7 -63.6 90.9 0.333 -74.9 -73.5 76. 3 0.333 -91.9 -94.5 292.5 3.3 50 SW 86.4 0.024 -169.7 0.333 -65.6 -65.6 90.3 0.333 -76.8 -75.6 71. 7 0.333 -93.8 -96.5 282.5 2.8 51 SW 79.2 0.024 -169.9 0.333 -67.5 -67.6 88.1 0.333 -78.7 -77.6 67. 2 0.333 -95.6 -98.5 284.8 4.2 52 SW 83.3 0.023 -169.9 0.333 -69.3 -69.5 88.3 0.333 -80.6 -79.6 66. 9 0.333 -97.6 -100.4 286.2 3.7 53 SW 83.9 0.022 -169.8 0.333 -71.1 -71.5 87.5 0.333 -82.4 -81.5 63 0.333 -99.3 -102.3 299.4 3.3 54 SW 85.7 0.022 -170 0.333 -72.9 -73.4 88 0.333 -84.2 -83.4 64 0.333 -101 -104.1 290.7 4.7 55 SW 94.8 0.02 -169.8 0.333 -74.6 -75.2 87.2 0.333 -85.9 -85.3 65. 6 0.333 -102.7 -105.9 294 4.0 56 SW 78.9 0.022 -169.9 0.333 -76.3 -77 83.7 0.333 -87.7 -87 58.9 0.333 -104.2 -107.6 297.6 6.2 57 SW 76.8 0.022 -170.2 0.333 -78 78.9 88.8 0.333 -89.3 -88.8 63.4 0.333 -105.8 -109.2 285.9 4.2 58 SW 88.3 0.02 -170 0.333 -79.8 80.7 87.4 0.333 -91.1 -90.6 59. 1 0.333 -107.3 -110.8 300 3.9 59 SW 93.7 0.019 -169.8 0.333 -81.4 -82.5 91.9 0.333 -92.6 -92.3 67. 3 0.333 -108.7 -112.3 300 3.9 60 SW 81.8 0.02 -169.5 0.333 -83.1 -84.2 86.7 0.333 -94.3 -94 57.4 0.333 -110.1 -113.8 292.2 4.3 61 SW 80.7 0.02 -169.5 0.333 -84.7 -86 91.1 0.333 -95.9 -95.6 63.8 0.333 -111.5 -115.2 297.2 4.4 62 SW 80.7 0.02 -169.3 0.333 -86.5 -87.8 92.9 0.333 -97.6 -97.3 68. 3 0.333 -112.8 -116.6 305.1 4.2 63 SW 81.7 0.019 -169.1 0.333 -88.2 -89.6 98.9 0.333 -99.2 -99 75.2 0.333 -114.1 -117.9 294.3 4.3 64 SW 82 0.019 -169.1 0.333 -89.9 91.4 102.6 0.333 -100.8 -100.7 73 0.333 -115.4 -119.1 294.7 5.1 65 SW 82.8 0.018 -169.1 0.333 -91.4 -93.2 99.8 0.333 -102.3 -102.3 74. 4 0.333 -116.8 -120.4 305 5.2 66 SW 82.6 0.018 -169.2 0.333 -93 94.9 96.3 0.333 -103.8 -103.9 68.3 0.333 -117.9 -121.8 310.9 5.5 67 SW 81.2 0.018 -169.6 0.333 -94.5 -96.5 96.5 0.333 -105.2 -105.5 74. 1 0.333 -119.2 -123 294.7 5.3 68 SW 85.7 0.017 -169.8 0.333 -95.9 -98.1 91.4 0.333 -106.6 -106.9 64. 6 0.333 -120.5 -124.2 304.5 4.7 69 SW 83.8 0.017 -169.7 0.333 -97.3 -99.7 90.5 0.333 -107.8 -108.4 64. 7 0.333 -121.8 -125.5 313.5 6.3 70 SW 80.4 0.017 -170.1 0.333 -98.6 -101.1 86 0.333 -109.1 -109.7 52. 7 0.333 -123 -126.8 330.5 5.7 71 SW 81 0.017 -170.2 0.333 -99.9 -102.5 86.4 0.333 -110.3 -111 56. 4 0.333 -124.3 -128 318.5 8.6 72 SW 90.3 0.016 -170 0.333 -101.2 -104 87 0.333 -111. 6 -112.3 46.2 0.333 -125.4 -129.4 341.2 5.9 73 SW 84.4 0.016 -170.3 0.333 -102.4 -105.3 83.7 0.333 -112.9 -113.6 58. 4 0.333 -126.6 -130.5 328.1 5.6 74 SW 87.5 0.016 -170.3 0.333 -103.6 -106.6 82.2 0.333 -114.1 -114.9 58. 7 0.333 -127.7 -131.7 336.1 5.9 75 SW 89.9 0.016 -170.2 0.333 -104.8 -107.9 84.7 0.333 -115.2 -116.1 48. 1 0.333 -128.7 -132.9 344.3 6.0 76

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109EXP 2 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 79.3 0.017 -170.9 0.333 -105.9 -109.2 77.3 0.333 -116.3 -117.3 46. 8 0.333 -129.7 -133.9 324.5 6.2 77 SW 84.8 0.016 -171.2 0.333 -107 110.4 77.8 0.333 -117.3 -118.4 40.7 0.333 -130.7 -134.9 326.2 5.7 78 SW 83.8 0.016 -171.4 0.333 -108.1 -111.5 73.6 0.333 -118.4 -119.5 41. 6 0.333 -131.7 -135.9 332.6 7.2 79 SW 82.8 0.016 -171.5 0.333 -109.1 -112.7 77.6 0.333 -119.4 -120.6 41. 9 0.333 -132.7 -136.9 345.3 6.1 80 SW 83.1 0.016 -171.7 0.333 -110.1 -113.8 70.7 0.333 -120.5 -121.7 37. 7 0.333 -133.7 -138 351.6 5.1 81 SW 85.4 0.015 -171.9 0.333 -111.1 -114.9 72.8 0.333 -121.5 -122.7 40. 7 0.333 -134.6 -139 352.1 6.3 82 SW 83.2 0.016 -172 0.333 -112.1 115.9 64.7 0.333 -122.5 -123.8 38.1 0.333 -135.6 -139.9 356.4 6.0 83 SW 103.7 0.014 -171.9 0.333 -113.2 -117 75.8 0.333 -123.8 -124.8 45.9 0.333 -136.3 -140.9 366.1 6.4 84 SW 90.4 0.015 -171.5 0.333 -114.3 -118 69.7 0.333 -125.9 -126.1 84.5 0.333 -144.8 -141.6 328.7 5.1 85 SW 72.7 0.017 -172.1 0.333 -116 119.2 84.3 0.333 -133.2 -127.6 23.9 0.333 -162.5 -148.6 1487.5 6.5 86 SW 77.8 0.016 -172.3 0.333 -118.4 -120.4 76.4 0.333 -141.4 -133.3 435. 5 0.333 -162.8 -164.5 4170.2 6.5 87 SW 77.1 0.016 -172.3 0.333 -121 -121.7 50.2 0.333 -147 -142 1144.7 0.333 -162.1 -167.1 4361.8 6.7 88 SW 87.4 0.014 -172.1 -123.4 -148.7 -167.6 6.4 89 SW 85.6 0.015 -172.2 -125.6 -152.6 -167.7 6.6 90 SW 85.3 0.015 -172.1 -128.3 -154.9 -167.9 5.5 91 SW 86.3 0.015 -172.1 -131.1 -157.6 -168 6.8 92 SW 84.4 0.015 -172.5 -134 -159.6 -168.1 6.4 93 SW 82.2 0.015 -172.6 -136.9 -161.7 -168.4 5.8 94 SW 82.7 0.015 -172.6 -139.5 -162.3 -168.6 5.8 95 SW 87.7 0.014 -172.7 -142 -163.7 -168.8 4.7 96 SW 85.5 0.015 -172.7 -144.4 -164.4 -168.9 8.2 97 SW 82 0.015 -172.8 -146.5 -164.4 -168.9 8.4 98 SW 85 0.015 -172.7 -148.5 -165 -169 6.0 99 SW 87.3 0.014 -172.8 -150.3 -165.9 -169 6.9 100 SW 86.1 0.014 -172.9 -151.9 -166.3 -169.1 5.6 101 SW 90.5 0.014 -173 -153.4 -166.9 -169.2 6.6 102 SW 91.8 0.014 -173.1 -155 -167.4 -169.3 6.3 103 SW 88 0.014 -173.1 -157 -167.8 -169.4 8.5 104 SW 92.2 0.014 -173.3 -158.4 -168.2 -169.5 5.3 105 SW 75.8 0.016 -173.9 -159.3 -168.1 -169.7 5.7 106 SW 88.4 0.014 -174 -161.1 -169.1 -170.2 8.3 107 SW 87.6 0.014 -173.9 -163.3 -169.5 -170.4 5.9 108 SW 92.4 0.014 -173.9 -164.6 -169.8 -170.4 4.9 109 SW 85.9 0.014 -174.2 -166.6 -170 -170.5 10.1 110 SW 86.5 0.014 -174.4 -167.2 -170.2 -170.6 7.8 111 SW 84.1 0.014 -174.6 -167.1 -170.3 -170.7 6.3 112 SW 83.9 0.01 -174.5 -166.9 -170.3 -170.9 7.2 113 SW 93.9 0.01 -174.5 -166.7 -170.4 -171 8.6 114

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110EXP 2 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 80 0.01 -174.8 -166.5 -170.3 -171.1 5.6 115 SW 93.3 0.01 -174.7 -167.4 -170.7 -171.2 6.0 116 SW 94.3 0.01 -174.6 -167.4 -170.6 -171.3 7.4 117 SW 85 0.01 -174.7 -167.2 -170.5 -171.3 5.5 118 SW 79.5 0.01 -175 -166.9 -170.5 -171.3 6.8 119 SW 86.2 0.01 -174.9 -166.9 -170.7 -171.4 7.0 120 SW 90 0.01 -174.8 -167.9 -170.9 -171.5 6.3 121 SW 83.7 0.01 -174.9 -167.7 -170.7 -171.5 7.5 122 SW 78.8 0.01 -175.1 -167.4 -170.6 -171.6 9.2 123 SW 83.5 0.01 -175.2 -167.2 -170.9 -171.7 6.7 124 SW 86.1 0.01 -175.2 -167.1 -171 -171.8 6.5 125 SW 86.1 0.01 -175.2 -167.2 -171.1 -171.9 6.2 126 SW 92 0.01 -175.1 -167.6 -171.1 -172 6.6 127 SW 98.1 0.02 -175.2 -168.5 -171.4 -172 6.6 128 SW 87.6 0.02 -175.3 -169.8 -171.6 -172.1 6.8 129 SW 91.5 0.01 -175.3 -170 -171.6 -172.1 7.1 130 SW 78 0.02 -175.7 -169.7 -171.7 -172.2 6.9 131 SW 80.2 0.01 -175.8 -169.5 -171.7 -172.3 7.0 132 SW 88.5 0.01 -175.8 -170.5 -171.9 -172.5 6.3 133 SW 87.3 0.01 -175.7 -171.2 -172.1 -172.6 5.8 134 SW 85.2 0.02 -175.7 -171.1 -172.2 -172.6 10.7 135 SW 80.6 0.02 -175.9 -170.6 -172.1 -172.7 6.7 136 SW 80.2 0.01 -176.1 -170.1 -172.2 -172.7 6.5 137 SW 86.4 0.01 -175.9 -170.7 -172.2 -172.9 6.9 138 SW 90.7 0.02 -175.9 -170.7 -172.3 -172.9 7.5 139 SW 95.5 0.02 -175.8 -170.5 -172.3 -172.9 7.0 140 SW 87.4 0.02 -176 -170.2 -172.2 -173 7.5 141 SW 81.6 0.02 -176.2 -170 -172.2 -173 8.4 142 SW 87.8 0.02 -176.1 -169.8 -172.2 -173.1 9.2 143 SW 87.5 0.02 -176.2 -169.7 -172.3 -173.1 7.7 144 SW 83.8 0.02 -176.2 -169.5 -172.2 -173.1 9.4 145 SW 92 0.02 -176.2 -169.4 -172.3 -173.2 7.9 146 SW 89.6 0.02 -176.3 -169.9 -172.5 -173.2 8.2 147 SW 87.5 0.02 -176.4 -169.7 -172.5 -173.2 7.9 148

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111EXP 3 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 32.8 1 8.4 0.333 22.3 23. 3 745.4 0.333 22.4 23.6 556.6 0.333 21.5 22.8 1018.8 0.0 1 N 33.2 1 7.4 0.333 22.3 22.9 134.3 0.333 22.5 23.2 65.9 0.333 21.8 22.3 101 0.0 2 N 33.2 1 6.2 0.333 21.9 22.4 189.3 0.333 22 22.7 116.9 0.333 21.4 21.9 201.7 0.0 3 N 33.5 1 5 0.333 21.3 21.9 212.9 0.333 21. 5 22.3 124 0.333 20.9 21.4 202.1 0.0 4 N 33.5 1 3.8 0.333 20.8 21.4 199 0.333 21.1 21.8 117 0.333 20.4 21 197.2 0.0 5 N 33.6 1 2.1 0.333 20.3 20. 8 201.8 0.333 20.5 21.3 126.8 0.333 19.9 20.4 193.9 0.0 6 N 33.9 1 0.1 0.333 19.7 20.2 192.6 0.333 20 20.7 112.6 0.333 19.3 19.9 187.7 0.0 7 N 34.2 1 -3.5 0.333 18.9 19.4 196 0.333 19.2 20 129.2 0.333 18.6 19.2 185.2 0.0 8 N 34.1 1 -10.2 0.333 17.7 18.2 261.6 0.333 18.1 18.9 188. 2 0.333 17.4 18 258.8 0.0 9 N 34.3 1 -14.6 0.333 16.9 17.3 171 0.333 17. 3 18.1 113.7 0.333 16.5 17.1 187.5 0.0 10 N 34.7 1 -21.9 0.333 15.6 16 183.1 0.333 16 16.9 132.6 0.333 14.9 15.6 213.7 0.0 11 N 36.3 1 -34.8 0.333 14.7 15 118 0.333 14. 9 15.8 81 0.333 13.2 13.9 210.7 0.0 12 N 38.7 1 -48 0.333 13.6 13.9 116.6 0.333 13. 6 14.6 81.6 0.333 10.9 11.5 256.1 0.0 13 N 40.8 0.455 -57.6 0.333 12.5 12.7 109.1 0.333 12.2 13.1 78.3 0.333 8.3 8.8 277.7 0.0 14 S 40.2 0.407 -65.6 0.333 11.3 11.6 101.2 0.333 10.5 11.6 82.3 0.333 5.5 5.8 294.6 1.2 15 S 42.8 0.34 -71.1 0.333 10.1 10.4 93.4 0.333 8.7 9.8 82 0.333 2.5 2.6 301.4 1.0 16 S 42.4 0.311 -80.3 0.333 8.7 9 105.9 0.333 6.6 7.8 95.2 0. 333 -0.9 -1 340.3 1.3 17 S 41.5 0.287 -84.1 0.333 7.3 7. 7 98.4 0.333 4.6 5.7 95.1 0. 333 -3.8 -4.2 320.6 1.2 18 S 41.9 0.26 -84.4 0.333 6 6. 3 97.6 0.333 2.6 3.6 96.9 0. 333 -6.2 -6.9 292.5 1.1 19 S 42.6 0.235 -85.5 0.333 4.5 4. 9 103.5 0.333 0.6 1.6 98.8 0. 333 -8.6 -9.6 302.3 0.9 20 S 40.4 0.228 -86.2 0.333 2.8 3.3 110 0.333 -1.4 -0.4 95.7 0.333 -10.8 -12 281.6 1.2 21 S 45.9 0.188 -87.6 0.333 1.3 1. 7 104.7 0.333 -3.3 -2.5 96.7 0.333 -13.2 -14.4 297 1.3 22 S 42.1 0.192 -89.1 0.333 -0.3 0.1 109.1 0.333 -5 .2 -4.4 94.8 0.333 -15.2 -16.6 283 1.0 23 S 44.5 0.169 -88.8 0.333 -1.8 -1.5 98.5 0.333 -7 -6.3 85.2 0.333 -17.3 -18.8 271.5 1.3 24 S 42.8 0.166 -94.6 0.333 -3.5 -3.1 102.9 0.333 -8.9 -8.2 86.6 0.333 -19.4 -21 271.9 1.1 25 S 41.5 0.16 -98.4 0.333 -5.1 -4.8 108.5 0.333 10.8 -10.1 95.5 0.333 21.8 -23.5 335.3 1.1 26 S 46.8 0.135 -90.9 0.333 -6.8 -6.5 105.1 0.333 -12.5 -11.9 77.3 0.333 -23.2 -25.1 222 1.1 27 S 39 0.153 -101.3 0.333 -8.5 -8.3 117.2 0.333 14.6 -13.9 106.6 0.333 25.6 -27.4 324.9 1.1 28 S 46.2 0.122 -94 0.333 -10.2 -10. 1 119.3 0.333 -16.4 -15.9 96.3 0.333 -27.2 -29.2 279.7 1.2 29 S 46.3 0.117 -95.2 0.333 -12.1 12 86.8 0.333 -18.1 -17.6 60.6 0.333 -28.5 -30.7 149.9 2.4 30 S 39.4 0.129 -137.5 0.333 -13.9 13.8 67.5 0.333 -20.2 -19.7 60 0.333 -31.2 -33.1 170.2 3.3 31 S 50.6 0.097 -168.5 0.333 -15.6 15.7 65.6 0.333 -21.9 -21.6 51.3 0.333 -32.6 -34.8 126.8 3.3 32 S 51.9 0.093 -171 0.333 -17.4 -17. 5 66.9 0.333 -23.7 -23.4 50.3 0.333 -34.2 -36.5 128.2 3.4 33 S 41.7 0.109 -172.1 0.333 -19 19.3 62.2 0.333 -25.7 -25.4 55. 2 0.333 -37.5 -39.5 205 1.7 34 S 59.7 0.074 -172 0.333 -20.6 -20. 9 59.5 0.333 -27.5 -27.2 45.7 0.333 -39.6 -41.9 170.2 4.1 35 S 50.7 0.086 -172.4 0.333 -22.3 22.7 61.9 0.333 -29.1 -29 45.7 0.333 -40.8 -43.5 129.5 2.0 36 S 49.3 0.082 -172 0.333 -23.8 24.3 57.9 0.333 -31.1 -30.8 43 0.333 -44.3 -46.6 226.4 4.5 37 S 45.8 0.085 -172 0.333 -25.4 -26 61 0.333 -32. 9 -32.7 44.4 0.333 -46.5 -49.2 192.6 3.2 38

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112EXP 3 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t S 57.4 0.066 -172.5 0.333 -27.1 27.7 62.7 0.333 -34.5 -34.5 41.8 0.333 -47.1 -50.3 115.5 1.5 39 S 52.1 0.072 -172.3 0.333 -28.8 29.4 63.8 0.333 -36.5 -36.3 49 0.333 -49.9 -52.8 203.5 3.5 40 S 41.7 0.083 -172.2 0.333 -30.3 31.1 60.9 0.333 -38.3 -38.2 40.8 0.333 -52.9 -55.8 232.6 2.5 41 S 58.8 0.057 -172.4 0.333 -31.9 -32.7 59.7 0.333 -39.9 -40 43. 9 0.333 -53.6 -57.1 132 1.4 42 S 61 0.056 -172.7 0.333 -33.7 -34. 5 68.2 0.333 -41.8 -41.9 48.6 0.333 -55.3 -58.7 165.5 3.7 43 S 48.1 0.068 -172.2 0.333 -35.3 36.2 63.3 0.333 -43.7 -43.7 42.9 0.333 -58.6 -61.7 251.9 1.9 44 S 54.3 0.057 -172.5 0.333 -36.9 37.9 61.9 0.333 -45.5 -45.6 41. 2 0.333 -60.5 -64 203.2 3.3 45 S 66.4 0.047 -172.7 0.333 -38.6 39.7 68.8 0.333 -47 -47.3 43.6 0.333 -60.8 -64.8 114.3 3.4 46 S 55.2 0.056 -172.3 0.333 -40.3 41.4 66.2 0.333 -49 -49.2 45.3 0.333 -63.7 -67.1 228.1 2.2 47 S 42 0.067 -172.6 0.333 -41.8 43.1 61.6 0.333 -50.7 -51 42.2 0.333 -66 -69.6 231.5 4.5 48 S 63.4 0.043 -172.3 0.333 -43.5 44.7 64.6 0.333 -52.3 -52.7 41. 8 0.333 -66.6 -70.6 137 4.8 49 S 65 0.044 -172.8 0.333 -45.2 -46.5 72 0.333 -54 -54.4 49.4 0.333 -68 -71.9 163 3.5 50 S 51.1 0.053 -172 0.333 -46.7 48.2 62.5 0.333 -55.9 -56.2 42. 6 0.333 -71.1 -74.6 266 1.6 51 S 45.4 0.055 -172.3 0.333 -48.4 49.9 66.6 0.333 -57.6 -58 43.5 0.333 -72.8 -76.7 210.3 3.8 52 S 61.9 0.04 -173 0.333 -50 -51.6 68.9 0.333 59 -59.6 44.5 0.333 -72.7 -77 100.2 3.5 53 S 59.4 0.042 -172.6 0.333 -51.7 53.3 70.1 0.333 -60.8 -61.3 50. 1 0.333 -74.7 -78.6 197 3.9 54 S 49.5 0.048 -172.3 0.333 -53.2 54.9 63.5 0.333 -62.4 -63 41.4 0.333 -77.4 -81.1 259.1 5.4 55 S 44.4 0.05 -172.7 0.333 -54.8 56.6 68.9 0.333 -64.1 -64.8 47.3 0.333 -78.8 -82.8 198.8 4.4 56 S 67 0.033 -173.1 0.333 -56.4 -58. 3 70.8 0.333 -65.5 -66.3 47.2 0.333 -78.9 -83.2 111.8 2.9 57 S 59 0.039 -172.6 0.333 -58.1 -60 72.2 0.333 -67. 2 -67.9 46.8 0.333 -80.8 -84.8 204.6 6.1 58 S 51 0.042 -172.6 0.333 -59.5 -61. 6 63.1 0.333 -68.7 -69.5 38.8 0.333 -83.3 -87.1 256.4 5.1 59 S 50.1 0.041 -172.9 0.333 -61 63.2 69.4 0.333 -70.3 -71.1 41. 5 0.333 -84.8 -89 216.3 3.3 60 S 61.9 0.033 -173.3 0.333 -62.6 64.8 68.8 0.333 -71.7 -72.7 49 0.333 -85.2 -89.6 137.1 2.3 61 S 66.5 0.031 -172.7 0.333 -64 -66.4 68 0.333 -73. 3 -74.3 45.9 0.333 -87.2 -91.3 225.7 4.3 62 S 55.4 0.036 -172.4 0.333 -65.5 67.9 68.2 0.333 -74.9 -75.8 39.3 0.333 -89.6 -93.6 268.7 3.8 63 S 46.1 0.041 -173 0.333 -66.9 -69. 4 64.4 0.333 -76.4 -77.4 35.6 0.333 -91.3 -95.6 243.7 2.1 64 S 66.4 0.028 -173.5 0.333 -68.4 70.9 70 0.333 -77.8 -78.9 43.1 0.333 -91.7 -96.4 156.4 6.9 65 S 68.1 0.029 -173.1 0.333 -69.9 72.5 69.4 0.333 -79.3 -80.4 47. 2 0.333 -93 -97.5 192.9 4.6 66 S 61 0.031 -172.4 0.333 -71.2 -73. 9 65.7 0.333 -80.8 -81.9 33.6 0.333 -95.6 -99.8 295.9 3.1 67 S 50.3 0.035 -172.6 0.333 -72.6 75.4 65.4 0.333 -82.2 -83.4 35.5 0.333 -97.4 -101.8 266.6 3.7 68 S 50 0.033 -173.2 0.333 -74 -76.8 67.6 0.333 83.6 -84.8 36 0.333 -98.3 -103 203.8 3.9 69 S 61.8 0.027 -173.5 0.333 -75.4 -78.3 71 0.333 -84.8 -86.2 45 0.333 -98 -103 106.9 3.4 70 S 58.4 0.029 -172.6 0.333 -76.8 79.8 69.4 0.333 -86.4 -87.7 48.1 0.333 -99.8 -104.3 230.1 3.6 71 S 47.9 0.033 -172.5 0.333 -78.2 -81.2 70.6 0.333 -87.7 -89 36 0.333 -101.7 -106.1 266.3 3.5 72 S 41.5 0.036 -172.9 0.333 -79.6 -82.8 75.1 0.333 -89 -90.5 49. 2 0.333 -101.9 -107 147.2 3.8 73 S 59.7 0.025 -173.2 0.333 -81 -84. 3 74.9 0.333 -90.2 -91.7 45.7 0.333 -102.2 -106.6 136.8 2.9 74 S 63.3 0.024 -172.8 0.333 -82.5 85.8 78.2 0.333 -91.5 -93 53.9 0.333 -102.9 -107.4 150.3 2.5 75 S 56.3 0.027 -172.5 0.333 -83.7 87.1 69.7 0.333 -92.7 -94.2 31.9 0.333 -105.4 -109.5 296.5 4.6 76

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113EXP 3 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t S 48 0.03 -173.1 0.333 -85 -88.5 69.1 0.333 93.9 -95.5 38.9 0.333 -106.7 -111 237.6 5.4 77 S 63.2 0.022 -173.5 0.333 -86.2 89.8 72.7 0.333 -95.1 -96.8 42.6 0.333 -107.2 -111.8 170.7 3.6 78 S 67.7 0.021 -173.1 0.333 -87.5 -91.2 73.8 0.333 -96.3 -98 41. 9 0.333 -108 -112.6 186.7 4.4 79 S 60.6 0.023 -172.6 0.333 -88.7 92.5 68.4 0.333 -97.6 -99.3 41. 7 0.333 -110 -114.3 278.8 4.5 80 S 51.1 0.026 -173.1 0.333 -89.9 93.7 67.7 0.333 -98.8 -100.5 32.8 0.333 -111.4 -115.9 257.8 4.8 81 S 64.4 0.02 -173.7 0.333 -91 -94. 9 66.8 0.333 -99.9 -101.7 37.4 0.333 -112.2 -116.9 210.4 5.3 82 S 71.4 0.019 -173.5 0.333 -92.2 96.2 72.1 0.333 -101.1 -102.9 42.5 0.333 -112.9 -117.6 189.5 5.4 83 S 68.4 0.02 -172.6 0.333 -93.3 -97.4 68 0.333 -102.2 -104 31.6 0.333 -114.8 -119.3 295.8 5.3 84 S 56.6 0.023 -172.7 0.333 -94.3 98.5 63.1 0.333 -103.4 -105.2 33.2 0.333 -116.3 -120.9 287.5 4.8 85 S 51.1 0.024 -173.3 0.333 -95.4 99.6 63.9 0.333 -104.5 -106.4 32.4 0.333 -117.3 -122.1 243.8 5.3 86 S 63.5 0.019 -174 0.333 -96.6 -100. 8 72.8 0.333 -105.6 -107.6 38.6 0.333 -117.6 -122.6 178.9 5.8 87 S 74.7 0.017 -173.6 0.333 -97.7 -102 71.9 0.333 -106.8 -108.7 44. 2 0.333 -118.6 -123.4 227 4.7 88 S 68.7 0.018 -172.8 0.333 -98.7 103.1 65.3 0.333 -107.8 -109.8 26. 9 0.333 -120.4 -125 315.6 5.2 89 S 59.5 0.02 -172.9 0.333 -99.7 104.1 60.3 0.333 -108.9 -110.9 30.4 0.333 -121.8 -126.6 308.1 4.8 90 S 56.6 0.02 -173.5 0.333 -100.7 -105.2 62.9 0.333 -110 -112 29.5 0.333 -122.8 -127.8 272.8 5.4 91 S 72.1 0.016 -174 0.333 -101.8 -106. 3 71.3 0.333 -111.1 -113.1 31.1 0.333 -123.6 -128.7 246.7 9.7 92 S 75.7 0.016 -173.5 0.333 -102.8 107.4 66.5 0.333 -112.1 -114.2 24.9 0.333 -124.9 -129.9 304.8 6.3 93 S 72.9 0.016 -173.2 0.333 -103.7 108.4 60.5 0.333 -113.2 -115.3 26.6 0.333 -126.4 -131.3 332.8 6.5 94 S 72.8 0.016 -173.2 0.333 -104.6 109.3 56.8 0.333 -114.3 -116.4 27.6 0.333 -127.9 -132.9 366.4 7.0 95 S 69.6 0.016 -173.3 0.333 -105.6 110.3 63 0.333 -115.4 -117.5 26.1 0.333 -129.4 -134.5 368.2 4.4 96 S 73.5 0.015 -173.6 0.333 -106.6 111.3 60.9 0.333 -116.4 -118.6 24.6 0.333 -130.2 -135.5 312.5 4.5 97 S 83.9 0.013 -173.5 0.333 -107.6 112.3 67.7 0.333 -117.5 -119.7 25.5 0.333 -131.3 -136.6 334.7 5.7 98 S 83.1 0.014 -173.2 0.333 -108.5 -113.3 60.7 0.333 -118.5 -120.7 21 0.333 -132.4 -137.7 351 6.9 99 S 73.7 0.015 -173.2 0.333 -109.4 114.2 57.4 0.333 -119.5 -121.8 21.8 0.333 -133.5 -138.8 360.5 9.1 100 S 76.3 0.014 -173.5 0.333 -110.3 115.2 57.9 0.333 -120.5 -122.8 25.1 0.333 -134.4 -139.8 339.8 5.6 101 S 87.8 0.012 -173.6 0.333 -111.2 116.1 59.3 0.333 -121.5 -123.8 26.5 0.333 -135.2 -140.7 337.7 6.2 102 S 73.8 0.015 -173.4 0.333 -112.1 -117 60.7 0.333 -122.4 -124.8 19. 7 0.333 -136 -141.5 343.7 6.1 103 S 77.8 0.013 -173.5 0.333 -113.1 -118 65 0.333 -123. 5 -125.9 43.1 0.333 -136.8 -142.3 337.1 6.1 104 S 84.3 0.005 -173.3 0.333 -114.2 119.1 73.9 0.333 -124.9 -127.2 85 0.333 -137.7 -143.1 355.2 8.1 105 S 66.2 0.006 -173 0.333 -115.4 -120. 2 53.8 0.333 -130.4 -130.2 247.1 0.333 -156.2 -159.2 3024.4 9.0 106 I 66 0.005 -173.5 0.333 -117 -121.3 67.3 0.333 135.6 -136.8 332.6 0.333 -165.3 -168 5193.7 7.0 107 I 75.1 0.004 -173.6 0.333 -119.3 122.8 72.7 0.333 -141.2 -143.3 717.2 0.333 -164.4 -169.4 4979.8 12.3 108 I 77 0.004 -173.5 -124.6 -148.8 -169.7 6.2 109 I 81.3 0.004 -173.4 -126.9 -153.1 -169.8 7.3 110 I 78.1 0.004 -173.2 -129.4 -156.1 -169.9 6.2 111 I 78.5 0.003 -173.3 -132.2 -157.7 -169.8 7.3 112 I 78.4 0.003 -173.1 -134.9 -159.2 -169.9 11.1 113 I 79.4 0.003 -173.2 -137.5 -159.6 -169.8 11.2 114

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114EXP 3 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t I 76.7 0.003 -173.2 -139.9 -162 -169.9 8.8 115 I 77.2 0.002 -173.3 -142.2 -162.4 -170 6.9 116 I 83.1 0.002 -173.3 -144.3 -163.4 -170 7.2 117 I 82.1 0.002 -173.1 -146.3 -164.3 -170.1 8.5 118 I 82.3 0.002 -173 -148.2 -165.2 -170 11.8 119 I 75.7 0.002 -173.1 -150 -165.6 -170 8.7 120 I 78.4 0.001 -173.4 -151.7 -165.7 -170 12.3 121 I 80.2 0.001 -173.5 -153 -165.5 -170.2 8.2 122 I 88.7 0.001 -173.5 -154.2 -167.1 -170.4 8.7 123 I 87.3 0 -173.3 -155.9 -167.6 -170.4 12.2 124 I 83.9 0 -173.3 -157.3 -167.8 -170.4 12.2 125 I 86.6 0 -173.6 -158.8 -168.2 -170.3 12.4 126 I 90.5 0 -173.6 -159.7 -168.5 -170.5 9.0 127 I 89.6 0 -173.6 -160.5 -168.8 -170.6 12.4 128 I 96.2 0 -173.7 -161.2 -169 -170.6 12.1 129 I 97.1 0 -173.5 -161.7 -168.8 -170.7 12.2 130 I 98.6 0 -173.5 -162.1 -169 -170.6 12.2 131 I 91 0 -173.4 -162.4 -168.7 -170.6 11.9 132 I 96.4 0 -173.5 -162.8 -169 -170.5 12.2 133 I 91 0 -173.5 -163.1 -169.1 -170.6 12.3 134 I 95.4 0 -173.6 -163.4 -169.1 -170.6 12.4 135 I 98.1 0 -173.6 -163.6 -169.3 -170.7 12.4 136 I 94.7 0 -173.5 -164.1 -169.4 -170.7 12.0 137 I 92 0 -173.7 -164.4 -169.5 -170.8 12.4 138 I 95.3 0 -173.9 -164.7 -169.7 -170.9 11.6 139 I 96 0 -173.9 -165 -169.8 -171 12.3 140 I 94.5 0 -174 -166.3 -169.9 -171.1 12.4 141 I 100.3 0 -174.1 -167.3 -170.2 -171.2 12.4 142 I 99 0 -174.2 -167.6 -170.4 -171.3 12.4 143 I 102.1 0 -174.2 -168.1 -170.5 -171.4 12.3 144 I 104.8 0 -174.3 -168 -170.6 -171.5 11.8 145 I 104.7 0 -174.4 -168 -170.7 -171.5 12.0 146 I 106.2 0 -174.5 -167.8 -170.7 -171.6 11.9 147 I 104.8 0 -174.4 -167.5 -170.6 -171.6 11.6 148 I 106.2 0 -174.5 -167.3 -170.5 -171.6 12.0 149 I 106.5 0 -174.5 -167.8 -170.6 -171.7 12.4 150 I 110.8 0 -174.5 -169.2 -170.8 -171.8 12.2 151 I 110.9 0 -174.8 -170 -170.9 -171.8 12.4 152

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115EXP 3 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t I 109.5 0 -174.7 -170 -171 -171.9 12.1 153 I 107.1 0 -174.7 -170 -171 -172 12.4 154 I 102.3 0 -174.8 -170.2 -171 -172 12.4 155 I 112.1 0 -174.8 -170.2 -171.1 -172 11.5 156 I 129.8 0 -174.9 -170.2 -171.1 -172.1 12.1 157 I 121.4 0 -174.9 -170 -171.2 -172.2 11.9 158 I 124.1 0 -175.1 -169.7 -171.2 -172.3 12.3 159 I 122.7 0 -175.3 -169.6 -171.3 -172.5 12.4 160 I 123.7 0 -175.5 -169.5 -171.5 -172.7 12.4 161 EXP 4 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 0.3 1 17.4 0.333 23 24.1 245 0.333 22.9 24.1 216.9 0.333 22.1 23.3 432.4 0.0 1 N 8.3 1 17.4 0.333 22.1 24 74.1 0.333 22. 2 24 51.5 0.333 21.3 23.3 77.5 0.0 2 N 69.3 1 17 0.333 18.2 24 192 0.333 17.9 24 177.9 0.333 15.6 23.2 285.2 0.0 3 S 95.4 1 -8.5 0.333 13.8 23 188.2 0.333 12. 8 23.1 186.6 0.333 8.5 22.1 316.1 0.2 4 N 112.6 1 -73.7 0.333 9.5 19.7 166.7 0.333 7.6 19.8 170. 7 0.333 1 17.4 322.9 0.0 5 S 123.8 0.234 -109.1 0.333 4.8 15.4 183.4 0.333 1.6 15.1 200 0. 333 -7.4 10.6 380.3 0.4 6 S 137.4 0.168 -145.9 0.333 -0.4 11.1 200.1 0. 333 -5.4 10 249 0.333 -15.6 2.9 397.6 0.3 7 S 167.2 0.136 -170.5 0.333 -5.7 6.3 205.5 0.333 12.1 4.1 254.1 0.333 -23.5 -5.8 412.3 0.6 8 N 170.8 0.12 -170 0.333 -11.4 1. 2 224.5 0.333 -19 -2.7 271.6 0. 333 -30.8 -14.4 402.4 0.0 9 N 184.4 0.11 -169.9 0.333 -16.8 -4 221 0.333 25.3 -9.6 265 0.333 -37.7 -22.9 397.2 0.0 10 S 183.4 0.098 -170.2 0.333 -21.6 -9.6 201.1 0. 333 -31 -16.6 245 0.333 -44.2 -30.7 404 0.5 11 N 181.2 0.088 -170.5 0.333 -26.8 15.2 217.7 0.333 -36.9 -23.2 258. 5 0.333 -50.6 -38 410.1 0.0 12 N 187.6 0.082 -170.6 0.333 -31.5 -20.3 203.1 0.333 -42 -29.3 228. 4 0.333 -56.2 -45 391.9 0.0 13 S 226.1 0.079 -170 0.333 -35.7 -25.6 185 0.333 -46. 8 -35.3 223.3 0.333 -61.6 -51.7 399.7 3.7 14 N 235.2 0.076 -170.4 0.333 -40.2 30.6 193.8 0.333 -51.6 -40.7 223.7 0.333 -66.8 -57.8 397.9 0.0 15 S 203.4 0.066 -171.1 0.333 -44.5 35.1 190.4 0.333 -56.3 -45.8 224.8 0.333 -71.6 -63.6 392.9 4.0 16 N 218.9 0.063 -170.1 0.333 -48.4 39.7 177.3 0.333 -60.8 -50.8 229. 9 0.333 -76.3 -69 405.9 0.0 17 S 224.2 0.066 -170.7 0.333 -52.8 44.1 200.9 0.333 -65.2 -55.6 221.3 0.333 -80.6 -74.1 391.2 2.5 18 S 206.4 0.055 -170.9 0.333 -56.8 48.3 197.3 0.333 -69.4 -60.3 227. 4 0.333 -85 -79.1 414.8 1.4 19 S 226.9 0.062 -169.8 0.333 -61 52.8 201.5 0.333 -73.5 -64.8 221. 7 0.333 -89 -83.6 399.5 3.7 20 S 216.9 0.052 -171.3 0.333 -65.1 57.1 210.5 0.333 -77.7 -69.2 241.4 0.333 -92.6 -88.1 388.4 2.5 21 S 209.6 0.055 -169.6 0.333 -68.7 61.4 189.8 0.333 -81.4 -73.5 214. 4 0.333 -96.4 -92.3 411 4.6 22 S 221.6 0.05 -171.5 0.333 -72.6 65.7 208.4 0.333 -85.1 -77.8 226. 3 0.333 -99.8 -96.1 399 3.3 23 S 196.5 0.055 -169.7 0.333 -75.6 -69.7 170.3 0.333 -88.2 -81.7 187.4 0.333 -103.4 -100 433 5.0 24

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116EXP 4 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t S 258 0.051 -172 0.333 -79.2 -73.8 199.4 0.333 91.7 -85.5 226.6 0.333 -106.3 -103.5 401 4.3 25 S 208.2 0.053 -169.9 0.333 -82.6 77.2 192.6 0.333 -95.2 -88.9 224.7 0.333 -109.4 -107.2 412.6 3.4 26 S 259.9 0.051 -170.9 0.333 -86.1 80.9 210.2 0.333 -98.4 -92.5 228. 6 0.333 -112.1 -110.3 399 4.9 27 S 192.4 0.054 -170 0.333 -88.9 84.5 178.4 0.333 -101.5 -96 222.6 0.333 -115.2 -113.5 441.6 5.0 28 S 262.3 0.053 -171.7 0.333 -92 88.1 196.6 0.333 -104.3 -99.4 216. 8 0.333 -117.7 -116.2 418 3.8 29 S 213 0.054 -170.3 0.333 -94.9 91.3 186.6 0.333 -107 -102.6 200.9 0.333 -120.6 -119.3 453.3 2.9 30 S 257.1 0.052 -171.2 0.333 -97.8 94.5 200 0.333 -109.8 -105.6 221.3 0.333 -122.6 -121.9 406.5 5.9 31 S 200.2 0.057 -170 0.333 -100.6 -97. 6 201.3 0.333 -112.5 -108.4 219.6 0.333 -125.1 -124.8 442.7 4.0 32 S 247.8 0.05 -171.5 0.333 -103 100.7 175.5 0.333 -114.8 -111.2 211. 1 0.333 -127.1 -127 428.8 1.5 33 S 198.6 0.054 -169.9 0.333 -105.9 -103.8 213 0.333 -117.6 -114 246.9 0.333 -129.3 -129.4 457.6 6.7 34 S 220.2 0.051 -171.2 0.333 -108.4 106.4 195.1 0.333 -120.1 -116.5 237 0.333 -131.8 -131.6 484.2 4.3 35 S 222.7 0.051 -170.6 0.333 -110.6 109.3 180.7 0.333 -122.1 -119.3 205.9 0.333 -133.3 -133.7 428.1 1.1 36 S 221.7 0.052 -169.9 0.333 -112.8 112.1 183.1 0.333 -124.4 -121.9 240.8 0.333 -135.5 -136.1 503.7 7.6 37 S 204.3 0.046 -171.8 0.333 -114.7 114.5 147.3 0.333 -126.7 -124.1 252.4 0.333 -137.8 -137.9 543.1 7.4 38 S 238.2 0.046 -170.6 0.333 -117 -116. 9 192.4 0.333 -128.7 -126.4 242.3 0.333 -139.6 -139.9 537.9 4.7 39 S 218.3 0.047 -170 0.333 -121.2 118.9 158.2 0.333 -144.9 -128.8 1963 0.333 -160.1 -142.2 3521.3 9.5 40 S 209.2 0.042 -171.7 0.333 -126.9 121.2 167.6 0.333 -160.7 -130.9 4628.5 0.333 -163.4 -144.1 3866.8 5.2 41 S 234.1 0.034 -170.4 0.333 -132.6 -123.7 437.5 0.333 -161 -144 4509.1 0.333 -164 -160.1 3413.6 8.6 42 S 199.5 0.036 -169.7 0.333 -138 -126. 9 539.4 0.333 -162.2 -160.7 3671.7 0.333 -165.1 -165.1 3074.8 7.9 43 S 198.5 0.034 -173.1 -132.4 -163.8 -167.6 9.5 44 S 201.3 0.036 -171 -138.5 -165.7 -168.8 8.3 45 S 209 0.036 -170.5 -145 -165.9 -167.7 3.7 46 S 209.6 0.033 -171 -150.6 -166.3 -167.3 9.1 47 S 209.5 0.033 -171.2 -160.3 -166.6 -167.6 5.9 48 S 213.6 0.032 -171.4 -165.5 -166.9 -167.9 4.0 49 S 214.4 0.031 -171.7 -166.2 -167.3 -168.2 7.9 50 S 219 0.03 -172.2 -166.4 -167.6 -168.6 8.6 51 S 227.3 0.028 -172.6 -166.7 -168.1 -169.1 4.6 52 S 229.7 0.027 -172.9 -166.9 -168.5 -169.7 5.1 53 S 236.5 0.026 -173.2 -167.2 -169 -170.1 6.9 54 S 244.6 0.025 -173.5 -167.5 -169.4 -170.5 7.0 55 S 247.6 0.024 -173.7 -167.7 -169.8 -170.9 5.6 56 S 245.4 0.023 -174 -168 -170.1 -171.2 5.3 57 I 247.2 0.022 -174.2 -168.2 -170.3 -171.5 7.7 58 I 251.8 0.021 -174.3 -168.4 -170.5 -171.8 8.8 59 I 254.8 0.02 -174.9 -168.7 -170.8 -172.1 11.0 60 I 254.5 0.02 -175.5 -169.3 -171.4 -172.8 7.0 61 I 257.6 0.019 -176.1 -169.9 -172 -173.4 3.7 62

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117EXP 4 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t I 261.3 0.018 -176.8 -170.4 -172.5 -174 4.3 63 I 261.7 0.017 -177.2 -170.9 -172.9 -174.4 6.4 64 I 262.1 0.016 -177.8 -171.3 -173.3 -174.8 8.1 65 I 261.9 0.015 -178 -171.7 -173.7 -175.3 8.9 66 I 263 0.015 -178.1 -171.8 -173.9 -175.5 5.5 67 I 260.5 0.014 -178.1 -171.9 -173.9 -175.5 4.9 68 I 260.2 0.013 -178.2 -172.1 -174.1 -175.8 8.4 69 I 261.8 0.013 -178.5 -172.3 -174.2 -176 7.7 70 I 260.4 0.012 -178.7 -172.5 -174.5 -176.2 8.1 71 I 261.9 0.011 -178.8 -172.6 -174.7 -176.5 6.8 72 I 262.3 0.011 -179.3 -173 -174.8 -176.6 4.0 73 I 264 0.01 -179.7 -173.5 -175.1 -177 11.6 74 I 264.7 0.01 -179.8 -173.9 -175.4 -177.3 7.8 75 I 261.4 0.009 -180.4 -174.5 -175.9 -177.8 9.4 76 I 260.1 0.009 -180.7 -174.9 -176.3 -178.3 8.7 77 I 261.5 0.008 -180.9 -174.9 -176.4 -178.3 9.2 78 I 261.5 0.008 -181 -175.2 -176.6 -178.6 7.4 79 I 261.7 0.007 -181.3 -175.3 -176.9 -178.9 9.1 80 I 259.6 0.007 -181.6 -175.5 -177 -179.1 10.7 81 I 258.5 0.007 -181.7 -175.7 -177.2 -179.4 11.7 82 I 260.3 0.006 -181.9 -176 -177.4 -179.6 10.2 83 I 260 0.006 -182 -176.3 -177.5 -179.7 10.8 84 I 257.6 0.005 -182.4 -176.8 -178 -180.2 11.0 85 I 255.4 0.005 -183.3 -177.7 -178.8 -181 9.4 86 I 256.3 0.005 -184.3 -178.7 -179.8 -182.2 10.1 87 I 255.6 0.004 -185.3 -179.8 -180.9 -183.2 11.2 88 I 254.6 0.004 -185.8 -180.4 -181.4 -183.8 11.2 89 I 252.9 0.004 -185.8 -180.4 -181.5 -183.9 10.5 90 I 254 0.003 -185.7 -180.4 -181.4 -183.8 12.1 91 I 254.6 0.003 -185.5 -180.3 -181.3 -183.7 11.2 92 I 253.1 0.003 -185.3 -180.1 -181.1 -183.5 11.2 93 I 253.3 0.002 -185.4 -180.3 -181.3 -183.7 11.7 94 I 251.6 0.002 -185.5 -180.3 -181.4 -183.8 11.9 95 I 251.4 0.002 -185.4 -180.3 -181.4 -183.8 11.2 96 I 249.5 0.002 -185.4 -180.3 -181.3 -183.7 11.5 97 I 247.5 0.001 -185.2 -180.1 -181.2 -183.7 11.9 98 I 247.3 0.001 -185.2 -180.1 -181.2 -183.7 11.6 99 I 245.7 0.001 -185.2 -180.1 -181.2 -183.8 10.3 100

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118EXP 5 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 110.9 1 12.8 0.333 24.2 24.8 48 0.333 24 24.8 11.6 0.333 22.5 23.5 452.4 0.0 1 N 149.1 1 -3 0.333 22.9 23.8 186.5 0.333 22. 8 23.8 148.5 0.333 21.6 22.3 191.2 0.0 2 N 178 1 -19.4 0.333 20.5 21.6 257.3 0.333 20. 5 21.9 205.3 0.333 19.1 20.2 275.5 0.0 3 N 199.3 1 -39.9 0.333 17.1 18. 4 217.4 0.333 17.2 18.9 178.9 0.333 15.5 16.8 238.5 0.0 4 S 207.3 0.15 -88.7 0.333 12.4 13.9 204.1 0.333 12.5 14.6 179.9 0.333 10.1 11.8 234.3 1.2 5 N 209.9 0.128 -144.8 0.333 7 8. 6 207.9 0.333 6.7 9.1 190.2 0.333 3.4 5.3 263.3 0.0 6 N 224.6 0.113 -173.5 0.333 0.7 2. 3 249.6 0.333 -0.1 2.6 234.2 0.333 -4.8 -2.7 335.7 0.0 7 N 232.7 0.1 -173.7 0.333 -6.4 -4.8 287.5 0.333 -7 .8 -4.9 276.6 0.333 -13.1 -11.2 363.8 0.0 8 N 231.9 0.09 -173.9 0.333 -13.1 -11.8 288.5 0.333 -15 -12.4 278. 9 0.333 -21 -19.5 372.8 0.0 9 N 243.3 0.083 -174.2 0.333 -19.3 18.3 277.9 0.333 -21.9 -19.6 275.7 0.333 -28.4 -27.3 369.3 0.0 10 N 243 0.077 -174.4 0.333 -25.4 24.8 279.5 0.333 -28.7 -26.6 280 0.333 -35.6 -34.9 372 0.0 11 N 251.9 0.072 -174.6 0.333 -31.1 30.8 268.6 0.333 -35.1 -33.3 274.8 0.333 -42.2 -41.9 361.7 0.0 12 N 256.9 0.068 -174.8 0.333 -36.8 36.7 269.1 0.333 -41.3 -39.7 278.3 0.333 -48.7 -48.7 367.7 0.0 13 S 265.9 0.065 -174.9 0.333 -42 -42. 2 255.6 0.333 -47.2 -45.9 272.1 0.333 -54.6 -54.9 355.9 0.5 14 S 271.4 0.062 -175 0.333 -47.1 -47. 6 254.4 0.333 -52.7 -51.7 270.2 0.333 -60.2 -60.9 352.4 1.0 15 S 277.6 0.06 -175.1 0.333 -51.9 52.7 248.8 0.333 -58.1 -57.3 269.4 0.333 -65.4 -66.3 336.8 1.1 16 S 287 0.058 -175.2 0.333 -56.6 -57. 6 244.8 0.333 -63.1 -62.6 270.7 0.333 -69.7 -70.9 299.9 1.2 17 S 290.5 0.056 -175.4 0.333 -61.1 62.3 238.9 0.333 -67.8 -67.5 263.4 0.333 -74.4 -75.6 319.9 1.0 18 S 299.9 0.055 -175.5 0.333 -65.4 66.8 234 0.333 -72.3 -72.2 259.6 0.333 -78.8 -80.2 318.5 0.4 19 S 305.7 0.055 -175.8 0.333 -69.3 71 222.4 0.333 -76.4 -76.6 249.3 0.333 -82.8 -84.4 306.7 0.7 20 S 323.9 0.057 -175.6 0.333 -73 -75 217.5 0.333 -80. 3 -80.7 241.8 0.333 -86.7 -88.5 307.5 1.0 21 S 352.5 0.058 -175.3 0.333 -76.5 78.8 210.7 0.333 -83.9 -84.4 228.9 0.333 -90.4 -92.3 302.5 1.5 22 S 376.1 0.059 -175.1 0.333 -80 -82. 4 208.2 0.333 -87.4 -88.1 235.5 0.333 -93.8 -95.9 298.5 2.7 23 S 390.3 0.059 -175 0.333 -83.4 -86 212.6 0.333 91 -91.8 242.1 0.333 -97.2 -99.3 298 4.0 24 SW 374.9 0.059 -175.3 0.333 -86.8 -89.6 217.8 0.333 -94.5 -95.4 247. 7 0.333 -100.5 -102.7 305.9 4.4 25 SW 362.3 0.062 -175.3 0.333 -90 -93 213.9 0.333 -97.7 -98.8 241.9 0.333 -103.7 -106 302 4.4 26 SW 407.9 0.065 -175.6 0.333 -93.1 -96.3 211.2 0.333 -100.8 -102 237.9 0.333 -106.7 -109.1 300.9 4.6 27 SW 390.9 0.066 -175.7 0.333 -95. 9 -99.4 201 0.333 -103.7 -105 229. 5 0.333 -109.5 -112 293.7 5.4 28 SW 414.4 0.067 -175.9 0.333 -98.8 -102.4 201.9 0.333 -106.5 -108 230.8 0.333 -112.2 -114.8 294.6 4.6 29 SW 387.5 0.067 -176.2 0.333 -101.4 -105.2 194.6 0.333 -109.1 -110.7 220. 7 0.333 -114.7 -117.5 290.3 4.1 30 SW 394.5 0.068 -176.2 0.333 -103.8 -107.8 185.9 0.333 -111.5 -113.2 210. 5 0.333 -117.2 -120 289.1 6.1 31 SW 376 0.066 -176.6 0.333 -106.2 110.4 184.9 0.333 -114 -115.7 213.8 0.333 -119.6 -122.5 293.3 5.8 32 SW 368.6 0.065 -176.7 0.333 -108.5 -112.8 180.1 0.333 -116.3 -118.1 211. 8 0.333 -121.8 -124.9 287.6 5.7 33 SW 354.8 0.063 -176.9 0.333 -110.6 -115.1 177 0.333 -118.4 -120.4 207. 5 0.333 -123.9 -127 281.3 6.9 34 SW 342.5 0.061 -177.1 0.333 -112.6 -117.3 169.5 0.333 -120.4 -122.5 198. 6 0.333 -125.9 -129.1 280.6 3.7 35 SW 334.5 0.06 -177.2 0.333 -114.7 -119.4 172.4 0.333 -122.5 -124.6 202. 9 0.333 -127.8 -131.1 284.6 5.1 36 SW 329 0.06 -177.2 0.333 -116.7 121.5 176.8 0.333 -124.5 -126.7 210 0.333 -129.8 -133.1 293.2 4.7 37 SW 328.7 0.058 -177.2 0.333 -118.8 -123.7 191.8 0.333 -126.5 -128.8 220. 3 0.333 -131.7 -135 291.1 4.4 38

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119EXP 5 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 328.7 0.056 -177.3 0.333 -120.7 -125.8 183.9 0.333 -128.5 -130.8 216. 5 0.333 -133.6 -137 305.3 4.3 39 SW 326.2 0.055 -177.5 0.333 -122.5 -127.7 173.5 0.333 -130.2 -132.6 202 0.333 -135.2 -138.7 291.3 12.4 40 SW 323.3 0.053 -177.6 0.333 -124.2 -129.6 170.1 0.333 -131.9 -134.4 213. 2 0.333 -136.9 -140.4 293.2 11.7 41 SW 324 0.052 -177.7 0.333 -125.9 131.3 172.5 0.333 -133.6 -136.2 208. 3 0.333 -138.5 -142.1 302 3.4 42 SW 327.9 0.05 -177.9 0.333 -127.4 -133 165.4 0.333 -135.2 -137.8 211. 1 0.333 -140 -143.6 295.4 3.3 43 SW 331.3 0.049 -177.8 0.333 -129 134.7 171.1 0.333 -136.8 -139.4 212. 7 0.333 -141.3 -145 284.1 5.3 44 SW 324.2 0.026 -177.8 0.333 -130.6 -136.4 181.1 0.333 -138.5 -141.1 214. 3 0.333 -144.2 -147.6 499.4 6.4 45 SW 319.9 0.011 -177.7 0.333 -133.3 -138.1 152.3 0.333 -149.6 -149.8 1248 0.333 -164.4 -164.4 3141.8 8.3 46 SW 309.6 0.019 -177.8 0.333 -136.9 -139.6 30.1 0.333 -164.5 -164.8 3462. 8 0.333 -170 -171.5 3628.1 7.1 47 SW 302.3 0.014 -178 0.333 -139.6 141.6 47.1 0.333 -166.9 -169.8 3562. 7 0.333 -169 -172.8 1152.9 7.9 48 SW 294.5 0.044 -178.2 0.333 24.2 -145.3 0. 333 24 -171.4 0.333 22.5 -173.3 5.9 49 SW 285.1 0.043 -178.5 0.333 22.9 -152.5 0. 333 22.8 -172.2 0.333 21.6 -173.8 5.7 50 SW 281.6 0.043 -178.7 0.333 20.5 -166.3 0. 333 20.5 -172.7 0.333 19.1 -174.1 5.2 51 SW 275.5 0.042 -178.9 0.333 17.1 -171.7 0. 333 17.2 -173.2 0.333 15.5 -174.5 3.0 52 SW 275.3 0.041 -179.1 0.333 12.4 -172.7 0. 333 12.5 -173.5 0.333 10.1 -174.8 3.6 53 SW 266.4 0.041 -179.1 0.333 7 -172.9 0.333 6.7 -173.7 0.333 3.4 -174.9 4.8 54 SW 270.3 0.04 -179.4 0.333 0.7 -173.1 0.333 -0.1 -173.8 0.333 -4.8 -175 4.5 55 SW 267.6 0.039 -179.2 0.333 -6.4 -173.3 0.333 -7.8 -173.9 0.333 -13.1 -175.2 6.2 56 SW 263.7 0.038 -179.3 0.333 -13.1 -173.4 0.333 -15 -174 0.333 -21 -175.3 5.8 57 SW 267.1 0.037 -179.2 0.333 -19.3 -173.4 0. 333 -21.9 -174 0.333 -28.4 -175.3 6.4 58 SW 264.7 0.037 -179 0.333 -25.4 -173.4 0.333 -28.7 -174 0.333 -35.6 -175.4 8.3 59 SW 263.3 0.035 -179.1 0.333 -31.1 -173.4 0. 333 -35.1 -174 0.333 -42.2 -175.4 9.2 60 SW 262.4 0.034 -179.1 0.333 -36.8 -173.5 0. 333 -41.3 -174 0.333 -48.7 -175.4 5.5 61 SW 259.9 0.034 -179.1 0.333 -42 -173.5 0.333 -47.2 -174 0.333 -54.6 -175.4 12.4 62 I 255.6 0.033 -179.2 0.333 -47.1 -173.5 0.333 -52.7 -174.1 0.333 -60.2 -175.5 4.8 63 I 253.6 0.033 -179.3 0.333 -51.9 -173.6 0.333 -58.1 -174.2 0.333 -65.4 -175.6 3.7 64 I 252.2 0.032 -179.4 0.333 -56.6 -173.7 0.333 -63.1 -174.3 0.333 -69.7 -175.8 3.5 65 I 252.2 0.031 -179.6 0.333 -61.1 -173.9 0.333 -67.8 -174.5 0.333 -74.4 -175.9 4.5 66 I 249.9 0.031 -179.7 0.333 -65.4 -174.1 0.333 -72.3 -174.6 0.333 -78.8 -176.1 6.0 67 I 245.5 0.031 -179.8 0.333 -69.3 -174.2 0.333 -76.4 -174.7 0.333 -82.8 -176.3 7.9 68 I 248.6 0.03 -180 0.333 -73 -174.4 0.333 80.3 -174.9 0.333 -86.7 -176.5 4.6 69 I 247.8 0.03 -180.1 0.333 -76.5 -174.6 0.333 -83.9 -175 0.333 -90.4 -176.7 5.4 70 I 246.1 0.029 -180.3 0.333 -80 -174.7 0.333 87.4 -175.2 0.333 -93.8 -176.8 8.2 71 I 245.9 0.029 -180.4 0.333 -83.4 -174.8 0. 333 -91 -175.3 0.333 -97.2 -177 12.4 72 I 246.1 0.028 -180.5 0.333 -86.8 -174.9 0.333 -94.5 -175.4 0.333 -100.5 -177.1 12.4 73 I 242.4 0.028 -180.7 0.333 -90 -175.1 0.333 97.7 -175.5 0.333 -103.7 -177.2 8.4 74 I 240 0.027 -180.9 0.333 -93.1 -175.2 0.333 100.8 -175.7 0.333 -106.7 -177.5 12.4 75 I 239.5 0.027 -181 0.333 -95.9 -175.4 0.333 103.7 -175.9 0.333 -109.5 -177.7 6.2 76

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120EXP 5 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t I 240.5 0.026 -181.1 0.333 -98.8 -175.5 0.333 -106.5 -176 0.333 -112.2 -177.8 6.6 77 I 240.8 0.026 -181.1 0.333 -101.4 -175.5 0.333 -109.1 -176 0.333 -114.7 -177.8 4.2 78 I 235 0.026 -181.1 0.333 -103.8 -175.5 0.333 -111.5 -176 0.333 -117.2 -177.9 5.7 79 I 238.7 0.025 -181.1 0.333 -106.2 -175.5 0.333 -114 -176.1 0.333 -119.6 -177.9 6.7 80 I 241.3 0.024 -181.1 0.333 -108.5 -175.6 0.333 -116.3 -176 0.333 -121.8 -177.9 7.1 81 I 238.7 0.024 -181.1 0.333 -110.6 -175.6 0.333 -118.4 -176.1 0.333 -123.9 -177.9 5.8 82 I 237.2 0.024 -181.2 0.333 -112.6 -175.6 0.333 -120.4 -176.1 0.333 -125.9 -178 4.3 83 I 237.7 0.023 -181.3 0.333 -114.7 -175.6 0.333 -122.5 -176.1 0.333 -127.8 -178 4.5 84 I 238.2 0.023 -181.3 0.333 -116.7 -175.6 0.333 -124.5 -176.2 0.333 -129.8 -178.1 5.1 85 I 238.4 0.022 -181.3 0.333 -118.8 -175.6 0.333 -126.5 -176.2 0.333 -131.7 -178.1 4.1 86 I 237.9 0.022 -181.4 0.333 -120.7 -175.7 0.333 -128.5 -176.2 0.333 -133.6 -178.2 6.4 87 I 237.5 0.022 -181.4 0.333 -122.5 -175.8 0.333 -130.2 -176.3 0.333 -135.2 -178.3 5.4 88 I 235.3 0.021 -181.5 0.333 -124.2 -175.8 0.333 -131.9 -176.3 0.333 -136.9 -178.4 5.2 89 I 233.2 0.021 -181.6 0.333 -125.9 -175.9 0.333 -133.6 -176.4 0.333 -138.5 -178.5 7.6 90 I 233.7 0.021 -181.7 0.333 -127.4 -176 0.333 -135.2 -176.5 0.333 -140 -178.7 4.4 91 I 231.4 0.02 -182 0.333 -129 -176.2 0.333 136.8 -176.7 0.333 -141.3 -178.9 4.4 92 I 231.7 0.02 -182.1 -176.4 -176.9 -179.2 6.3 93 I 231.1 0.02 -182.4 -176.6 -177 -179.4 4.5 94 I 231.5 0.019 -182.9 -177.1 -177.5 -179.9 5.1 95 I 230.1 0.019 -183.5 -177.7 -178.2 -180.6 5.0 96 I 230.9 0.019 -184.1 -178.3 -178.7 -181.2 4.6 97 I 230.6 0.018 -184.4 -178.7 -179.1 -181.6 6.7 98 I 229.9 0.018 -184.6 -178.9 -179.3 -181.9 6.2 99 I 228.4 0.018 -184.9 -179 -179.5 -182.1 6.5 100 I 231.1 0.017 -184.9 -179.2 -179.7 -182.1 12.4 101 I 227.8 0.017 -184.9 -179.1 -179.7 -182.2 5.6 102 I 228.1 0.017 -184.9 -179.1 -179.6 -182.2 3.9 103 I 228.1 0.017 -184.9 -179.2 -179.7 -182.2 3.7 104 I 226.2 0.016 -184.9 -179.2 -179.7 -182.3 6.4 105 I 224.4 0.016 -185.1 -179.4 -179.9 -182.5 7.3 106 I 225.4 0.016 -185.2 -179.5 -180.1 -182.7 5.7 107 I 225.5 0.016 -185.3 -179.6 -180.2 -182.8 10.0 108 I 222.3 0.015 -185.3 -179.7 -180.3 -182.9 9.6 109 I 223.5 0.015 -185.5 -179.8 -180.3 -183 10.5 110 I 223.9 0.015 -185.5 -179.8 -180.3 -183.1 12.4 111 I 222.1 0.015 -185.6 -179.8 -180.4 -183.2 8.2 112 I 220.6 0.015 -185.7 -180 -180.5 -183.4 10.2 113

PAGE 140

121 EXP 6 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 123.3 1 -11.1 0.333 21.5 22.8 206.5 0. 333 21.4 22.9 175 0.333 20 21.6 314.2 0.0 1 N 140.4 1 -61.5 0.333 18.6 19.9 166 0.333 18. 6 20.2 143.7 0.333 17.2 18.5 176.2 0.0 2 N 157.6 1 -104.8 0.333 14.4 16 165.3 0.333 14. 1 16.1 157.7 0.333 11.8 13.6 217.2 0.0 3 N 171.1 0.595 -154.4 0.333 10.3 11.7 161.7 0.333 9.4 11.5 160.9 0.333 5.9 7.7 237.6 0.0 4 N 180.7 0.354 -172.8 0.333 5.9 7.3 171.2 0.333 4.3 6.5 172.3 0.333 -0.8 0.9 280.7 0.0 5 N 197.5 0.265 -173 0.333 1.1 2.5 187 0.333 -1.6 0.8 206.3 0.333 -7.8 -6.4 312.9 0.0 6 N 191.9 0.217 -173 0.333 -3.9 -2.5 197.4 0.333 -7 .5 -5.3 222.6 0.333 -14.3 -13.2 306.9 0.0 7 SW 195.6 0.185 -173 0.333 -8.3 -7.2 182.3 0.333 12.9 -10.9 209.7 0.333 20.5 -19.9 309.5 1.3 8 SW 229.7 0.162 -172.9 0.333 -13.1 -12 194.2 0.333 -18.5 -16.6 221.6 0.333 -26.8 -26.4 320.9 2.7 9 SW 224.3 0.143 -173.1 0.333 -17.3 -16.5 177.6 0.333 -23.5 -21.9 209. 9 0.333 -32.1 -32.3 299.7 2.9 10 SW 221.8 0.128 -173.2 0.333 -21.7 -21 183 0.333 28.5 -27.1 209.9 0.333 37.5 -37.9 300.8 2.3 11 SW 220.5 0.113 -173.3 0.333 -26.1 -25.5 184.6 0.333 -33.4 -32.2 216. 3 0.333 -42.6 -43.2 297.6 2.4 12 SW 230.7 0.106 -173.5 0.333 -30.6 -30.1 190.9 0.333 -38.2 -37.2 215. 5 0.333 -47.6 -48.5 306.4 2.5 13 SW 236.7 0.101 -173.5 0.333 -34.3 -34.1 166.2 0.333 -42.4 -41.7 196. 1 0.333 -52.3 -53.4 299.6 0.0 14 SW 257.4 0.094 -173.5 0.333 -38.5 -38.4 180.6 0.333 -47 -46.3 212. 3 0.333 -57 -58.3 307.9 0.0 15 SW 227.9 0.087 -173.8 0.333 -42.5 -42.6 180.3 0.333 -51.5 -50.9 219. 8 0.333 -61.5 -63 309.7 4.5 16 SW 252.6 0.083 -173.4 0.333 -46.3 -46.5 174.3 0.333 -55.6 -55.2 208. 9 0.333 -65.9 -67.6 313.6 4.1 17 SW 296.6 0.087 -173 0.333 -49.8 50.3 165.6 0.333 -59.2 -59.1 186 0.333 -69.9 -71.9 303.8 2.8 18 SW 244 0.077 -174.1 0.333 -52.9 53.7 144.8 0.333 -62.8 -62.8 187.5 0.333 -73.6 -75.8 298.1 6.3 19 SW 278.5 0.078 -173.1 0.333 -56.8 -57.6 183.4 0.333 -67 -66.8 202.8 0.333 -79.4 -81.3 421.7 2.0 20 SW 318 0.082 -173.2 0.333 -60.4 61.4 178.2 0.333 -70.6 -70.7 198. 3 0.333 -82.6 -85.2 314 3.5 21 SW 277.7 0.07 -174.2 0.333 -63.7 -64.9 167.6 0.333 -74.1 -74.4 195. 9 0.333 -86.1 -88.9 322.4 0.0 22 SW 283.4 0.069 -172.9 0.333 -67.3 -68.6 181.2 0.333 -77.7 -78.1 198. 4 0.333 -89.5 -92.5 328.6 2.7 23 SW 309.5 0.067 -173.5 0.333 -70.4 -72 170.1 0.333 -80.9 -81.4 188.1 0.333 -92.7 -95.8 324.4 0.0 24 SW 253.4 0.062 -173.2 0.333 -73.2 -75.1 150.8 0.333 -83.9 -84.6 181. 6 0.333 -95.9 -99.1 333 3.2 25 SW 311.1 0.065 -173.4 0.333 -76.2 -78.2 161.5 0.333 -86.9 -87.8 185. 7 0.333 -98.5 -101.9 303.4 0.0 26 SW 274 0.065 -172.7 0.333 -79.3 -81.4 168 0.333 89.9 -90.8 187.6 0.333 101.3 -104.8 314.8 3.9 27 SW 314.4 0.063 -173.7 0.333 -82.4 -84.7 181.5 0.333 -92.9 -93.9 196. 7 0.333 -104.1 -107.6 321.2 3.3 28 SW 267.2 0.062 -173.2 0.333 -85.5 -87.9 182.5 0.333 -96.2 -97.2 217. 7 0.333 -107.2 -110.6 353 2.7 29 SW 317.8 0.066 -173.5 0.333 -88.2 -90.9 170.1 0.333 -98.7 -99.9 178. 4 0.333 -109.6 -113.2 326.7 5.0 30 SW 292.3 0.058 -173.6 0.333 -90.7 -93.6 157.2 0.333 -101.3 -102.6 187. 2 0.333 -112.1 -115.8 341 4.3 31 SW 281 0.062 -172.6 0.333 -93.1 -96.2 155 0.333 103.7 -105.1 176.6 0.333 114.5 -118.3 335.4 5.1 32 SW 308.9 0.061 -173.1 0.333 -95.8 -99 173.6 0.333 -106.4 -107.8 199 0.333 -117.1 -120.8 360.6 4.0 33 SW 290 0.057 -173.3 0.333 -98.3 -101.6 169.4 0.333 -108.7 -110.3 186.3 0.333 -119 -123 323.5 2.9 34 SW 267.5 0.06 -172.7 0.333 -100.4 -104 146.2 0.333 -110.9 -112.6 180.6 0.333 -121.3 -125.2 352.4 5.1 35 SW 300.4 0.057 -173.3 0.333 -102.6 -106.3 158.1 0.333 -113.1 -114.9 188. 4 0.333 -123.2 -127.2 342.4 3.5 36 SW 283.5 0.06 -172.1 0.333 -104.9 -108.7 165.4 0.333 -115.3 -117.1 183. 9 0.333 -125.3 -129.3 356.6 4.3 37 SW 259.4 0.054 -173.9 0.333 -107.2 -111.1 170.1 0.333 -117.4 -119.3 197. 6 0.333 -127 -131.1 331.7 4.1 38

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122EXP 6 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 289.9 0.055 -172.6 0.333 -109.2 -113.3 162.7 0.333 -119.4 -121.4 184. 2 0.333 -128.9 -133 365.7 2.8 39 SW 276 0.054 -172.8 0.333 -111.1 115.4 146.8 0.333 -121.2 -123.3 171.6 0.333 -130.8 -134.9 370.9 5.5 40 SW 277.6 0.048 -173.6 0.333 -113 117.4 156.7 0.333 -123 -125.2 180.4 0.333 -132.4 -136.6 354.4 2.7 41 SW 299.1 0.048 -172.7 0.333 -114.8 -119.3 149.6 0.333 -124.8 -127 173.5 0.333 -134.1 -138.4 389.3 3.3 42 SW 283.7 0.047 -172.6 0.333 -116.5 -121.1 144.7 0.333 -126.5 -128.8 180.8 0.333 -135.7 -140 376 5.9 43 SW 286.1 0.043 -173.1 0.333 -118.1 -122.9 147 0.333 -128.1 -130.5 181. 2 0.333 -137.1 -141.4 368 3.4 44 SW 291.8 0.042 -172.7 0.333 -119.8 -124.7 152.8 0.333 -129.7 -132.1 173. 5 0.333 -138.4 -142.8 375.1 6.3 45 SW 282 0.042 -172.4 0.333 -121.3 126.3 140.9 0.333 -131.2 -133.7 174.2 0.333 -139.9 -144.3 404.4 4.9 46 SW 265.6 0.013 -172.6 0.333 -123.1 -128.1 168.6 0.333 -133.6 -135.7 197. 2 0.333 -146 -149.6 1170.9 8.1 47 SW 262.7 0.014 -173 0.333 -126.6 129.8 101.2 0.333 -149.3 -148.7 2042.5 0.333 -164.1 -164.4 3757.5 7.8 48 SW 261.8 0.009 -172.5 0.333 -130.2 -131.6 16.2 0.333 -160.8 -161.7 3928. 6 0.333 -164.7 -167.5 3199.4 8.8 49 SW 252.9 0.035 -172.6 -135 -165.6 -167.9 4.1 50 SW 255.8 0.033 -173 -141.1 -166.9 -168.4 4.4 51 SW 257.3 0.032 -172.8 -154.4 -167.4 -168.8 5.2 52 SW 250.4 0.032 -172.7 -164.8 -167.5 -168.9 4.6 53 SW 249.3 0.03 -172.9 -166.5 -167.6 -168.9 5.1 54 SW 251.5 0.029 -172.9 -166.8 -167.8 -169.1 5.0 55 SW 253.7 0.028 -173 -166.8 -167.9 -169.3 5.0 56 SW 252.5 0.027 -173.1 -167.1 -167.9 -169.4 5.8 57 SW 258.5 0.026 -173.2 -167.2 -168 -169.6 4.9 58 SW 265.1 0.024 -173.6 -167.4 -168.2 -169.8 4.7 59 SW 267.3 0.023 -173.7 -167.5 -168.4 -170.1 4.9 60 SW 271.2 0.022 -174 -167.6 -168.7 -170.4 5.3 61 SW 274.6 0.021 -174.3 -167.8 -168.9 -170.9 6.3 62 SW 277.8 0.02 -174.8 -168.2 -169.4 -171.4 6.1 63 I 283.2 0.019 -175.2 -168.6 -169.9 -171.9 12.4 64 I 292.6 0.019 -175.7 -169 -170.5 -172.4 12.4 65 I 300.9 0.018 -176.3 -169.4 -171 -173 7.3 66 I 304.8 0.017 -176.9 -169.9 -171.7 -173.6 6.6 67 I 308.1 0.016 -177.5 -170.6 -172.3 -174.3 7.7 68 I 308.4 0.016 -178 -171.1 -172.8 -174.7 7.7 69 I 310.1 0.015 -178.3 -171.4 -173.1 -175.1 6.7 70 I 313.1 0.014 -178.6 -171.7 -173.4 -175.5 7.1 71 I 317.1 0.013 -178.8 -171.9 -173.6 -175.7 7.8 72 I 320.9 0.013 -178.9 -172.1 -173.8 -175.9 8.8 73 I 323.6 0.012 -179 -172.2 -174 -176 12.4 74 I 326.8 0.011 -179.2 -172.4 -174.2 -176.2 8.1 75 I 330.5 0.01 -179.5 -172.6 -174.4 -176.5 6.2 76

PAGE 142

123EXP 6 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t I 332.7 0.01 -179.6 -172.8 -174.5 -176.6 9.6 77 I 335.4 0.009 -179.7 -173 -174.7 -176.8 10.0 78 I 338.1 0.009 -179.7 -173.2 -174.8 -176.9 12.4 79 I 339 0.008 -179.7 -173.2 -174.8 -177 12.4 80 I 339.4 0.008 -179.8 -173.4 -174.9 -177.2 12.4 81 I 340.9 0.007 -180.1 -173.7 -175.2 -177.5 10.1 82 I 340.8 0.006 -180.2 -174 -175.5 -177.7 9.0 83 I 343.4 0.006 -180.3 -174.1 -175.5 -177.9 10.8 84 I 345.8 0.005 -180.1 -174.1 -175.5 -177.9 10.8 85 I 346.7 0.005 -180.4 -174.3 -175.6 -178 9.0 86 I 345.9 0.005 -180.6 -174.4 -175.6 -178.1 9.6 87 I 345.9 0.004 -180.7 -174.7 -175.8 -178.2 9.9 88 I 347.9 0.004 -180.9 -175 -176 -178.5 10.2 89 I 344.6 0.003 -181 -175.2 -176.1 -178.7 12.4 90 I 344.6 0.003 -181.1 -175.3 -176.2 -178.8 12.4 91 I 343.9 0.002 -181.2 -175.6 -176.4 -179.1 9.6 92 I 342 0.002 -181.4 -175.7 -176.6 -179.2 12.4 93 I 343.6 0.002 -181.4 -175.8 -176.7 -179.3 9.5 94 I 342.4 0.001 -181.5 -175.8 -176.7 -179.4 9.8 95 I 342.3 0.001 -181.6 -175.8 -176.7 -179.4 10.3 96 I 341.3 0.001 -181.6 -176 -176.7 -179.5 11.0 97 I 342.2 0 -181.7 -176.2 -176.9 -179.7 12.4 98 I 339.5 0 -182 -176.6 -177.3 -180 9.8 99 I 339.7 0 -182.4 -176.8 -177.5 -180.2 9.8 100 I 337.5 0 -182.4 -177 -177.7 -180.4 12.4 101 I 336.5 0 -182.5 -177.1 -177.7 -180.5 12.4 102 I 337.7 0 -182.7 -177.2 -177.9 -180.7 9.4 103 I 335.8 0 -182.8 -177.4 -178 -180.9 10.6 104 EXP 7 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 135.6 1 -12.3 0.333 19.2 21 655.1 0.333 19 21.1 617.9 0.333 18.1 20.3 773.4 0.0 1 N 137.8 1 -23.3 0.333 17.9 18.8 224 0.333 17.9 19.2 174.6 0.333 17 18.1 224 0.0 2 N 145.6 1 -43.4 0.333 15.1 16. 1 218.5 0.333 15.1 16.6 185.5 0.333 13.9 15.2 242.1 0.0 3 N 159.4 0.07 -73.5 0.333 11.9 12.9 204.9 0.333 11.9 13.5 181.3 0.333 10.4 11.7 227.6 0.0 4 S 174.4 0.067 -97.1 0.333 8. 2 9.3 208.5 0.333 8 9.8 190. 7 0.333 6 7.5 254.3 1.3 5

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124EXP 7 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 184.1 0.063 -114.4 0.333 3.9 5 225.6 0.333 3.5 5.5 204.2 0.333 0.9 2.4 278.2 0.0 6 N 187.1 0.064 -128.4 0.333 -1.1 0.1 197.9 0.333 -1 .7 0.5 182.1 0.333 -4.8 -3.3 239.3 0.0 7 N 182.7 0.06 -173.7 0.333 -6.1 -5 204 0.333 -7.1 -4.9 193.6 0.333 -10.6 -9.3 254.6 0.0 8 N 193.7 0.057 -175.8 0.333 -10.7 -9.8 199.6 0.333 -12.1 -10 186.9 0.333 -16.1 -15 252.9 0.0 9 N 210 0.058 -175.5 0.333 -15.6 -14. 8 207.1 0.333 -17.6 -15.4 202.7 0.333 -22.1 -21.2 282.2 0.0 10 N 206.4 0.057 -175.9 0.333 -20.5 19.8 212.9 0.333 -23.1 -20.9 211.9 0.333 -28.2 -27.5 297.6 0.0 11 N 211 0.057 -176 0.333 -25.2 -24.6 208.7 0.333 -28. 5 -26.3 212.6 0.333 -33.9 -33.5 293.5 0.0 12 N 214.6 0.056 -176.2 0.333 -29.9 29.4 209.1 0.333 -33.9 -31.7 220.5 0.333 -39.5 -39.4 300.7 0.0 13 N 217.6 0.055 -176.5 0.333 -34.3 33.9 200.4 0.333 -38.9 -36.9 215. 2 0.333 -44.8 -45 294.7 0.0 14 S 211.1 0.056 -176.7 0.333 -38.6 38.4 199.9 0.333 -43.7 -41.9 210.4 0.333 -49.7 -50.2 287.1 2.3 15 N 219.7 0.055 -176.9 0.333 -42.8 -42.7 197 0.333 -48.2 -46.5 205. 2 0.333 -54.3 -55 279.4 0.0 16 N 219.2 0.055 -176.9 0.333 -46.7 46.7 188.1 0.333 -52.3 -50.8 191. 7 0.333 -58.5 -59.5 269 0.0 17 N 233.9 0.055 -176.7 0.333 -50.6 50.8 189.3 0.333 -56.5 -55.2 200. 8 0.333 -62.9 -64 278.6 0.0 18 N 229.5 0.054 -177.2 0.333 -54.4 54.7 186.4 0.333 -60.9 -59.5 211.6 0.333 -67.2 -68.5 285.1 0.0 19 N 216 0.053 -177.6 0.333 -58.1 -58. 4 181.7 0.333 -64.8 -63.7 203.2 0.333 -71.2 -72.6 274.7 0.0 20 S 220.2 0.054 -177.9 0.333 -61.5 62 174.1 0.333 -68.4 -67.5 189.4 0.333 -74.8 -76.5 268.1 2.3 21 N 230.4 0.054 -177.8 0.333 -64.9 -65.5 177 0.333 -71.9 -71.1 186. 9 0.333 -78.4 -80.3 269 0.0 22 S 232.6 0.054 -177.8 0.333 -68.1 68.8 166.1 0.333 -75.3 -74.6 185.4 0.333 -81.7 -83.8 260.2 1.9 23 SW 224.1 0.054 -178 0.333 -71.3 72.1 169.1 0.333 -78.7 -78.1 191.1 0.333 -85.1 -87.2 263.5 5.8 24 SW 214.8 0.054 -178.6 0.333 -74.2 -75.2 158.5 0.333 -81.7 -81.3 179. 1 0.333 -88.1 -90.4 253.9 5.2 25 SW 211.4 0.054 -179 0.333 -77 -78.2 151.8 0.333 84.5 -84.3 166.6 0.333 90.9 -93.4 245.3 4.8 26 SW 209.2 0.054 -179.3 0.333 -79.8 -81.1 156.3 0.333 -87.4 -87.2 168. 3 0.333 -93.9 -96.4 254.4 5.7 27 SW 206.5 0.054 -179.6 0.333 -82.3 -83.8 143.4 0.333 -89.9 -89.9 158. 2 0.333 -96.5 -99.2 247.2 3.6 28 SW 220.3 0.055 -179.6 0.333 -84.7 -86.3 136.5 0.333 -92.4 -92.5 150. 9 0.333 -99 -101.8 241.7 5.2 29 SW 221.6 0.058 -179.6 0.333 -87 88.7 131.1 0.333 -94.7 -94.9 144.9 0.333 -101.4 -104.4 243.2 6.1 30 SW 212.4 0.058 -179.8 0.333 -89.1 -91 126.3 0.333 -96.9 -97.2 141 0.333 -103.7 -106.8 237.5 4.4 31 SW 205.4 0.058 -180.2 0.333 -91.3 -93.2 127.8 0.333 -99.1 -99.4 137. 4 0.333 -105.9 -109.1 239.3 6.9 32 SW 222.2 0.062 -180 0.333 -93.3 95.3 121.5 0.333 -101.1 -101.5 130. 2 0.333 -108 -111.3 238.2 3.3 33 SW 225.1 0.061 -180.3 0.333 -95.2 -97.4 116.3 0.333 -103.1 -103.6 132. 2 0.333 -110 -113.4 231.8 5.0 34 SW 212 0.062 -180.5 0.333 -97 -99.3 111.6 0.333 -105 -105.6 121.8 0.333 -112 -115.5 238.1 3.9 35 SW 216.8 0.064 -180.7 0.333 -98.8 -101.2 111.8 0.333 -106.8 -107.5 128. 1 0.333 -113.8 -117.4 228.2 4.3 36 SW 215.7 0.063 -180.9 0.333 -100.6 -103 112.3 0.333 -108.6 -109.4 122.4 0.333 -115.5 -119.2 225.3 3.5 37 SW 202.2 0.063 -181 0.333 -102.2 104.8 101.1 0.333 -110.3 -111.1 117.2 0.333 -117.1 -120.9 223.3 7.3 38 SW 203.1 0.067 -180.9 0.333 -103.9 -106.5 108.1 0.333 -111.9 -112.8 119. 2 0.333 -118.8 -122.6 230.6 3.5 39 SW 208.7 0.073 -180.6 0.333 -105.4 -108.1 101.3 0.333 -113.5 -114.4 113. 5 0.333 -120.4 -124.2 226.4 5.2 40 SW 216.2 0.075 -180.8 0.333 -107 -109.8 102.6 0.333 -115 -116.1 115. 8 0.333 -121.9 -125.8 226 3.3 41 SW 218 0.082 -180.6 0.333 -108.5 111.4 104.2 0.333 -116.6 -117.7 120.7 0.333 -123.4 -127.3 231.7 2.8 42 SW 257 0.086 -180.3 0.333 -110.1 -113 106 0.333 -118. 2 -119.3 125.5 0.333 -124.9 -128.9 241.7 2.5 43

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125EXP 7 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 259.1 0.084 -180.5 0.333 -111.5 -114.5 101.8 0.333 -119.6 -120.8 111. 3 0.333 -126.3 -130.4 238.3 4.6 44 SW 251.4 0.088 -180.1 0.333 -113 -116 101.4 0.333 121.1 -122.3 119.4 0.333 -127.8 -131.9 243 4.1 45 SW 249.7 0.086 -180.3 0.333 -114.4 -117.5 101.7 0.333 -122.5 -123.8 123. 3 0.333 -129.1 -133.3 240.7 3.4 46 SW 242.8 0.086 -180.3 0.333 -115.8 -118.9 102.1 0.333 -124 -125.3 133.2 0.333 -130.4 -134.6 238.5 3.4 47 SW 244.4 0.088 -180 0.333 -117.2 120.4 105.5 0.333 -125.4 -126.8 129. 8 0.333 -131.8 -136 246.2 4.1 48 SW 242 0.087 -180.3 0.333 -118.6 121.9 107.9 0.333 -126.8 -128.3 130.2 0.333 -133.1 -137.3 247.5 4.0 49 SW 232.5 0.09 -180.1 0.333 -119.9 -123.3 102 0.333 -128 -129.5 112.6 0.333 -134.3 -138.5 241.7 2.8 50 SW 227.4 0.087 -180.4 0.333 -121.3 -124.7 108.1 0.333 -129.3 -130.9 125. 9 0.333 -135.5 -139.8 249.9 3.0 51 SW 228 0.09 -180.1 0.333 -122.6 126.1 107.2 0.333 -130.5 -132.2 127. 6 0.333 -136.6 -141 247.7 3.2 52 SW 222.5 0.088 -180.3 0.333 -123.8 -127.4 101.2 0.333 -131.8 -133.5 129. 3 0.333 -137.7 -142.1 239.8 5.9 53 SW 216.4 0.088 -180.5 0.333 -125.1 -128.7 104.7 0.333 -132.9 -134.7 120. 8 0.333 -138.7 -143.1 240 3.7 54 SW 212.1 0.088 -180.5 0.333 -126.2 -130 99.2 0.333 -134 -135.9 118.8 0.333 -139.8 -144.2 244.7 3.8 55 SW 209.6 0.086 -180.8 0.333 -127.4 -131.2 103.1 0.333 -135 -137 115.1 0.333 -140.8 -145.3 248.1 6.3 56 SW 205.3 0.088 -180.6 0.333 -128.5 -132.4 100.6 0.333 -136.1 -138.1 116. 7 0.333 -141.8 -146.3 251.1 5.5 57 SW 196.7 0.086 -181.1 0.333 -129.9 -133.8 128.8 0.333 -137.1 -139.1 109. 8 0.333 -142.7 -147.3 246.3 2.9 58 SW 205.1 0.084 -180.9 0.333 -130.7 -134.8 78.4 0.333 -138 -140.1 104 0.333 -143.8 -148.3 269.6 3.3 59 SW 205.2 0.086 -180.7 0.333 -131.6 -135.7 86.2 0.333 -139.1 -141.2 108. 5 0.333 -145.5 -149.9 361 3.0 60 SW 205.7 0.027 -181.1 0.417 -133.1 -136.8 86.1 0.292 -146 -145.2 337. 9 0.292 -164.5 -166.1 2941 6.2 61 SW 206.9 0.008 -180.6 0.417 -136.7 -137.8 5.8 0.292 -164.3 -161.1 2648. 8 0.292 -172.2 -174.1 3480.1 8.9 62 SW 204.6 0.078 -180.8 -139 -169.9 -175.4 4.3 63 SW 199.2 0.081 -180.7 -140.9 -173.2 -175.8 4.1 64 SW 200.6 0.076 -180.8 -143.6 -174.7 -176.1 3.5 65 SW 208 0.076 -180.9 -147 -175.3 -176.2 2.6 66 SW 204.5 0.077 -180.7 -151.2 -175.8 -176.4 6.9 67 SW 205.9 0.075 -180.8 -156.3 -176.1 -176.5 5.0 68 SW 204.2 0.076 -180.9 -163 -176.3 -176.5 2.6 69 SW 193.7 0.078 -180.8 -171.3 -176.6 -176.7 4.0 70 SW 200.4 0.073 -181.4 -174.9 -176.9 -176.9 3.8 71 SW 192.1 0.078 -181 -175.8 -177.1 -177.1 3.5 72 SW 185.8 0.075 -181.3 -176.4 -177.4 -177.3 3.7 73 SW 189.7 0.074 -181.5 -176.5 -177.3 -177.3 5.6 74 SW 173.9 0.078 -181.1 -176.7 -177.5 -177.4 5.0 75 SW 178.6 0.072 -181.9 -176.8 -177.6 -177.6 3.4 76 SW 172 0.077 -181.6 -177 -177.7 -177.8 4.9 77 SW 162.6 0.076 -182 -177.4 -178.1 -178.1 4.0 78 SW 170.4 0.073 -182.6 -177.6 -178.3 -178.3 4.3 79 SW 154.2 0.08 -182.4 -178.1 -178.8 -178.8 2.8 80 SW 164.4 0.073 -183.4 -178.5 -179.1 -179.2 4.4 81

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126EXP 7 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 157.3 0.077 -183.3 -178.8 -179.4 -179.5 4.3 82 SW 147.9 0.078 -183.7 -179.3 -179.9 -179.9 4.9 83 SW 156.8 0.074 -184.3 -179.6 -180.2 -180.2 2.7 84 SW 145.8 0.079 -183.9 -179.8 -180.4 -180.6 5.4 85 SW 154.3 0.072 -184.6 -180 -180.6 -180.7 6.4 86 SW 148.9 0.076 -184.5 -180.1 -180.8 -180.9 6.1 87 SW 146.4 0.074 -184.7 -180.3 -181 -181.2 4.8 88 SW 141.9 0.076 -185 -180.4 -181.1 -181.3 3.8 89 SW 139.9 0.075 -184.9 -180.6 -181.3 -181.5 2.2 90 SW 148.8 0.071 -185.2 -180.7 -181.3 -181.6 5.3 91 SW 134.5 0.077 -185.1 -180.8 -181.4 -181.7 2.4 92 SW 146.2 0.068 -185.3 -181 -181.6 -181.9 5.3 93 SW 137.3 0.074 -185.3 -181 -181.6 -181.9 5.0 94 SW 137.3 0.071 -185.5 -181.2 -181.8 -182.1 4.7 95 SW 138.6 0.071 -185.6 -181.4 -182 -182.3 4.3 96 SW 133.8 0.072 -185.9 -181.7 -182.3 -182.7 3.3 97 SW 143.4 0.068 -186.5 -182.2 -182.8 -183.1 4.2 98 SW 131.7 0.073 -186.8 -182.5 -183.2 -183.5 3.0 99 SW 133.5 0.07 -187.3 -183 -183.7 -184.1 2.3 100 SW 137.2 0.069 -187.8 -183.5 -184.2 -184.6 2.8 101 SW 131.2 0.071 -187.9 -183.9 -184.7 -185 6.2 102 SW 140.1 0.066 -188.6 -184.3 -184.9 -185.3 2.9 103 SW 125.7 0.072 -188.5 -184.6 -185.3 -185.7 3.7 104 SW 130.7 0.068 -189.1 -184.8 -185.6 -186 2.5 105 SW 128.2 0.07 -189.2 -185.1 -185.9 -186.3 2.4 106 SW 124.3 0.07 -189.5 -185.4 -186.1 -186.6 2.7 107 SW 134.4 0.065 -189.6 -185.6 -186.4 -186.9 2.4 108 SW 125.8 0.07 -189.8 -185.7 -186.6 -187.1 3.1 109 SW 123.7 0.068 -190 -185.9 -186.7 -187.2 2.7 110 SW 126 0.067 -189.9 -185.9 -186.7 -187.3 4.6 111 SW 124.6 0.067 -189.9 -185.8 -186.7 -187.2 3.2 112 SW 131 0.064 -190.1 -186.1 -187 -187.6 2.9 113 SW 134.8 0.063 -190.4 -186.3 -187.2 -187.9 3.6 114 SW 121.2 0.068 -190.5 -186.5 -187.4 -188.1 4.5 115 SW 122.2 0.066 -190.8 -186.8 -187.7 -188.3 5.1 116 SW 117.2 0.068 -190.9 -187 -187.9 -188.6 5.2 117 SW 123.8 0.064 -190.9 -187 -188 -188.7 7.4 118 SW 123.7 0.064 -191 -187.2 -188.2 -188.9 4.8 119

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127EXP 7 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 121.4 0.064 -191.4 -187.5 -188.5 -189.2 3.2 120 SW 125.1 0.063 -191.6 -187.8 -188.8 -189.6 4.8 121 SW 121.6 0.064 -191.7 -187.8 -188.8 -189.7 6.1 122 SW 115.3 0.065 -191.8 -188 -189 -189.9 3.6 123 SW 124.5 0.061 -192 -188.2 -189.1 -190 3.4 124 SW 114.4 0.066 -192.1 -188.3 -189.3 -190.3 3.9 125 SW 120 0.061 -192.3 -188.5 -189.6 -190.4 4.2 126 SW 124.4 0.06 -192.2 -188.5 -189.5 -190.5 4.7 127 SW 117.3 0.063 -192.3 -188.5 -189.6 -190.6 4.0 128 SW 119.7 0.06 -192.7 -189 -190.1 -191.1 3.7 129 SW 115.5 0.062 -192.8 -189.2 -190.2 -191.3 4.3 130 SW 118.5 0.06 -192.8 -189 -190.1 -191.2 3.1 131 SW 116.1 0.061 -192.4 -188.8 -189.9 -191 3.2 132 SW 121 0.059 -192.2 -188.5 -189.6 -190.8 4.2 133 SW 117.9 0.06 -192.1 -188.3 -189.5 -190.7 3.8 134 SW 113.6 0.06 -192.1 -188.3 -189.5 -190.7 4.6 135 SW 118.1 0.059 -192.1 -188.3 -189.5 -190.6 8.9 136 SW 114 0.06 -192 -188.2 -189.4 -190.6 2.7 137 SW 118.6 0.058 -191.8 -188.1 -189.3 -190.5 5.5 138 SW 118.3 0.058 -191.8 -188 -189.2 -190.5 6.6 139 SW 112.8 0.06 -191.8 -188 -189.2 -190.5 5.0 140 SW 114 0.059 -191.9 -188 -189.3 -190.6 3.5 141 SW 113.1 0.059 -192.1 -188.3 -189.6 -190.9 5.8 142 SW 120.5 0.055 -192.7 -188.8 -190.1 -191.3 5.3 143 SW 106.8 0.061 -193 -189.4 -190.6 -192 6.2 144 SW 116.2 0.056 -193.8 -190.1 -191.3 -192.7 5.4 145 EXP 8 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 71.9 1 3.5 0.333 21.4 22.7 780.7 0.333 21.2 22.9 663.1 0.333 20.1 21.8 1060 0.0 1 N 73.6 1 0.9 0.333 21.4 21. 9 169.2 0.333 21.3 22.2 89.3 0.333 20.5 21.2 139.7 0.0 2 N 75.3 1 -1.3 0.333 20.6 21.1 237.8 0.333 20.5 21.5 157.6 0.333 19. 7 20.4 233.8 0.0 3 N 76 1 -3.9 0.333 19.7 20.2 238.7 0.333 19. 8 20.7 162.9 0.333 18.9 19.6 244.4 0.0 4 N 76.4 1 -6.4 0.333 18.8 19.3 250.9 0.333 18.9 19.9 166.8 0.333 18 18.7 251.6 0.0 5 N 76.8 1 -8.9 0.333 17.9 18.3 237.5 0. 333 18 19 154.6 0.333 17.1 17.8 244.7 0.0 6 N 77.8 1 -12.4 0.333 16.8 17.2 237.1 0. 333 17 17.9 162.3 0.333 16 16.7 244.6 0.0 7

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128EXP 8 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t N 78.3 1 -16.9 0.333 15.7 16 224 0.333 15. 9 16.9 152.6 0.333 14.8 15.5 240.1 0.0 8 N 79.3 1 -22.8 0.333 14.4 14.7 196.1 0.333 14.7 15.6 136 0.333 13.5 14.2 206.3 0.0 9 N 80.4 1 -34.3 0.333 12.9 13. 3 162.5 0.333 13.2 14.3 117.7 0.333 11.9 12.6 178.5 0.0 10 N 82.1 1 -53.3 0.333 11.3 11.6 145.6 0.333 11.5 12.6 110. 2 0.333 9.8 10.6 186 0.0 11 N 84.5 1 -72.2 0.333 9.5 9.8 136.1 0.333 9.5 10.8 103.9 0.333 7. 3 8.1 192.4 0.0 12 N 87.3 1 -89.7 0.333 7.6 7.9 130.1 0.333 7.2 8.7 105.2 0.333 4. 2 5.1 215.1 0.0 13 N 90.3 1 -101.4 0.333 5.4 5.8 132.8 0.333 4.6 6.3 110.4 0.333 0.7 1.5 241 0.0 14 N 94.7 1 -110.6 0.333 3.2 3. 5 132.1 0.333 1.7 3.6 114.9 0. 333 -3.1 -2.3 248.9 0.0 15 N 99 0.346 -118.4 0.333 0.7 1.1 137.6 0.333 -1.5 0.6 129.2 0.333 -6.9 -6.3 256.6 0.1 16 N 97.6 0.193 -123.8 0.333 -1.6 -1.2 128.7 0.333 -4 .5 -2.3 122.2 0.333 -10.6 -10.3 256.3 0.0 17 N 97.8 0.131 -127.8 0.333 -3.9 -3.5 96.8 0.333 -7 .5 -5.2 92.9 0.333 -14.2 -14.1 199.3 0.0 18 SW 101.1 0.098 -165.5 0.333 -6.2 -5.8 92.6 0.333 -10.5 -8.2 93.1 0.333 -17.8 -17.9 196.6 3.2 19 SW 103.6 0.078 -169.8 0.333 -8.5 -8.1 93 0.333 -13.4 -11 90.7 0.333 -21.2 -21.6 198 3.7 20 SW 107.1 0.064 -170.1 0.333 -10.9 -10.4 92.2 0.333 -16.4 -14 94. 1 0.333 -24.7 -25.2 204 2.9 21 N 112.2 0.054 -170.2 0.333 -13.2 12.6 90.4 0.333 -19.4 -16.9 94. 9 0.333 -28.3 -29 218.1 0.0 22 SW 120.1 0.046 -170.2 0.333 -15.5 -14.9 90.3 0.333 -22.4 -19.8 97. 2 0.333 -31.9 -32.8 221.7 3.3 23 N 121.8 0.042 -170 0.333 -17.8 -17. 2 89.8 0.333 -25.4 -22.8 97.9 0.333 -35.4 -36.4 226.5 0.0 24 SW 127.6 0.036 -170.2 0.333 -20.1 -19.4 87.6 0.333 -28.3 -25.6 95. 1 0.333 -38.6 -39.9 223.6 2.1 25 SW 124.4 0.036 -169.9 0.333 -22.4 -21.7 88.4 0.333 -31.1 -28.5 96. 2 0.333 -41.9 -43.4 230.2 2.8 26 SW 126.3 0.031 -170.3 0.333 -24.7 -24 87.2 0.333 -33.9 -31.3 96.1 0.333 -44.9 -46.6 223.8 2.6 27 SW 145.8 0.027 -170.1 0.333 -27.1 -26.3 88.3 0.333 -36.7 -34.1 99. 2 0.333 -47.9 -49.7 225.9 1.9 28 SW 128.9 0.03 -169.9 0.333 -29.4 -28.6 86.7 0.333 -39.5 -36.8 96. 9 0.333 -51.2 -53.1 245.7 3.3 29 SW 143 0.022 -170.7 0.333 -31.5 -30.7 81.1 0.333 -42 -39.4 90. 9 0.333 -53.8 -56 227.1 8.1 30 SW 171.6 0.024 -170.1 0.333 -33.9 -33.1 91.5 0.333 -44.5 -42 92.3 0.333 -56.4 -58.8 223.2 6.4 31 SW 126 0.026 -169.8 0.333 -35.9 35.2 76.8 0.333 -47.1 -44.5 91.9 0.333 -59.3 -61.7 241.4 5.6 32 SW 146.4 0.019 -171.1 0.333 -38 37.3 74.6 0.333 -49.4 -47 92.5 0.333 -61.5 -64.2 216.3 8.0 33 SW 180.6 0.021 -170.2 0.333 -40.4 -39.7 94.3 0.333 -51.8 -49.4 92. 3 0.333 -64 -66.7 231.9 3.7 34 SW 137 0.022 -169.6 0.333 -42.5 41.8 77.9 0.333 -54.3 -51.8 90. 2 0.333 -67 -69.7 259.9 6.4 35 SW 149.3 0.017 -171 0.333 -44.6 43.9 79.5 0.333 -56.8 -54.4 102.1 0.333 -69.4 -72.3 239.3 6.8 36 SW 186.8 0.017 -170.8 0.333 -46.9 -46.2 89.4 0.333 -59 -56.7 90.1 0.333 -71.5 -74.6 232.9 6.7 37 SW 166.1 0.019 -169.6 0.333 -49.1 -48.5 86.9 0.333 -61.3 -59 91.2 0.333 -74.4 -77.3 268.1 3.3 38 SW 155 0.017 -170.7 0.333 -50.9 50.5 72.7 0.333 -63.5 -61.3 88.6 0.333 -76.7 -79.9 256.2 1.6 39 SW 181.6 0.015 -171.4 0.333 -53 52.6 81.7 0.333 -65.6 -63.5 90. 4 0.333 -78.6 -82 232.6 5.9 40 SW 184.7 0.017 -169.8 0.333 -55 54.6 76.7 0.333 -67.8 -65.6 85. 5 0.333 -81.1 -84.5 272 4.2 41 SW 146 0.018 -170.1 0.333 -56.9 -56.6 72 0.333 -70.1 -68 97.7 0.333 -83.6 -87 270.6 6.6 42 SW 165.3 0.013 -171.8 0.333 -58.8 -58.5 72.4 0.333 -72.1 -70.1 89. 1 0.333 -85.3 -88.9 240.9 8.3 43 SW 201.3 0.015 -170.4 0.333 -60.9 -60.6 82.5 0.333 -74.2 -72.2 90. 6 0.333 -87.4 -91.1 266 4.6 44 SW 157.5 0.017 -169.7 0.333 -63 62.7 84.2 0.333 -76.4 -74.3 92. 9 0.333 -90 -93.6 297.2 5.4 45

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129EXP 8 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t SW 172.4 0.013 -171.6 0.333 -64.7 -64.7 71.9 0.333 -78.2 -76.3 83. 7 0.333 -91.8 -95.6 259.8 7.8 46 SW 196.9 0.013 -171.2 0.333 -66.8 -66.7 86.1 0.333 -80.1 -78.4 95. 8 0.333 -93.2 -97.2 238.7 5.4 47 SW 178.1 0.014 -169.5 0.333 -68.9 -68.9 87.1 0.333 -82.4 -80.6 111. 6 0.333 -95.5 -99.3 287.1 3.1 48 SW 159.2 0.014 -170.4 0.333 -70.7 -70.8 75.8 0.333 -84.3 -82.6 91. 2 0.333 -97.4 -101.3 273.3 3.1 49 SW 174.6 0.011 -172.4 0.333 -72.5 -72.7 76 0.333 -85.8 -84.4 80.9 0.333 -98.6 -102.7 233.5 10.4 50 SW 194.3 0.012 -170.2 0.333 -74.5 -74.7 88 0.333 -87.8 -86.3 98.6 0.333 -100.6 -104.6 288.8 3.7 51 SW 152.7 0.015 -169.6 0.333 -76.3 -76.7 80 0.333 -89.8 -88.3 104.4 0.333 -102.6 -106.7 294.6 4.8 52 SW 173.1 0.011 -171.9 0.333 -78.1 -78.5 75.6 0.333 -91.4 -90.1 88. 7 0.333 -104.1 -108.3 266.7 5.6 53 SW 196.1 0.011 -171.3 0.333 -79.9 -80.4 86.5 0.333 -93 -91.8 81 0.333 -105.5 -109.8 265.4 6.7 54 SW 173.8 0.013 -169.6 0.333 -81.9 -82.5 94.9 0.333 -95 -93.8 107.6 0.333 -107.7 -111.8 320.2 2.3 55 SW 158.3 0.013 -170.5 0.333 -83.6 -84.3 81 0.333 -96.7 -95.6 93. 5 0.333 -109.3 -113.6 294 3.7 56 SW 173.4 0.01 -172.4 0.333 -85.2 -86.1 77.1 0.333 -98.1 -97.2 82. 6 0.333 -110.3 -114.8 245.8 8.9 57 SW 189.8 0.011 -170.6 0.333 -86.9 -87.8 81.6 0.333 -99.7 -98.8 84. 6 0.333 -111.9 -116.3 300.7 4.9 58 SW 179.6 0.012 -169.7 0.333 -88.5 -89.5 77 0.333 -101.6 -100.6 109. 2 0.333 -114 -118.3 339.7 5.7 59 SW 178.9 0.012 -170.7 0.333 -89.9 -91.1 65.3 0.333 -103 -102.2 84.1 0.333 -115.3 -119.8 291.4 3.2 60 SW 176.2 0.009 -172.5 0.333 -91.4 -92.6 70.8 0.333 -104.3 -103.7 82. 9 0.333 -116.1 -120.8 245.2 7.1 61 SW 190.4 0.01 -170.8 0.333 -93 94.2 76.6 0.333 -105.7 -105.1 76.3 0.333 -117.7 -122.2 317.7 5.0 62 SW 177.2 0.012 -169.8 0.333 -94.6 -95.9 80.7 0.333 -107.4 -106.8 108. 5 0.333 -119.5 -123.9 351.7 7.0 63 SW 192.9 0.013 -170.1 0.333 -96 97.4 70.5 0.333 -108.8 -108.3 83.8 0.333 -120.8 -125.4 309.6 3.6 64 SW 176.1 0.01 -172.4 0.333 -97.4 -98.9 74 0.333 -110 -109.6 77.6 0.333 -121.6 -126.4 261.3 7.3 65 SW 174.8 0.009 -171.8 0.333 -98.8 -100.4 76.9 0.333 -111.1 -110.9 71. 5 0.333 -122.6 -127.4 287.6 11.1 66 SW 150.1 0.012 -170.4 0.333 -100 101.8 60.7 0.333 -112.5 -112.2 74.3 0.333 -124.3 -128.9 370.4 7.2 67 SW 223.2 0.014 -169.7 0.333 -101.2 -103 59.9 0.333 -113.9 -113.6 90.1 0.333 -125.9 -130.5 367.5 7.3 68 SW 209.3 0.013 -170.8 0.333 -102.5 -104.3 58.7 0.333 -115.1 -114.9 77. 1 0.333 -126.9 -131.7 313.7 5.4 69 SW 191.3 0.009 -172.5 0.333 -103.8 -105.6 67.5 0.333 -116.2 -116.1 76. 3 0.333 -127.5 -132.5 275 8.3 70 SW 164.4 0.009 -171.4 0.333 -105 106.9 66.9 0.333 -117.3 -117.3 68.9 0.333 -128.6 -133.5 325.6 10.7 71 SW 196.4 0.012 -170.2 0.333 -106.1 -108.1 56.6 0.333 -118.7 -118.6 98.6 0.333 -130.3 -135 409 8.4 72 SW 253.2 0.012 -169.7 0.333 -107.2 -109.3 54 0.333 -120.1 -120 100.1 0.333 -131.6 -136.4 406.5 8.8 73 SW 183.6 0.014 -169.8 0.333 -108.5 -110.6 66.4 0.333 -121.2 -121.3 83. 2 0.333 -132.6 -137.6 345.5 4.7 74 SW 181.3 0.01 -172.6 0.333 -109.8 -111.9 73.1 0.333 -122.2 -122.4 79.1 0.333 -133 -138.1 259 3.5 75 SW 177.7 0.007 -172.8 0.333 -111.1 -113.3 79.6 0.333 -123 -123.4 73.9 0.333 -133.2 -138.4 244.5 4.2 76 SW 153.1 0.008 -170.9 0.333 -112.3 -114.6 75.2 0.333 -124.1 -124.5 84. 7 0.333 -134.6 -139.4 383.3 9.0 77 SW 198 0.01 -169.9 0.333 -113.2 115.6 45.2 0.333 -125.3 -125.6 94. 7 0.333 -136 -140.8 433.3 6.2 78 SW 214.2 0.011 -169.8 0.333 -114.3 -116.7 60.7 0.333 -126.3 -126.7 76. 8 0.333 -136.9 -141.9 382.8 6.9 79 SW 165.1 0.011 -171.2 0.333 -115.4 -117.9 70.2 0.333 -127.2 -127.7 76. 7 0.333 -137.6 -142.6 313.4 6.1 80 SW 184.3 0.007 -173.6 0.333 -116.6 -119.1 70.8 0.333 -128.1 -128.8 88. 5 0.333 -137.8 -143 261.9 4.8 81 SW 164 0.007 -172.1 0.333 -117.8 120.5 88.6 0.333 -129.7 -130 94.4 0.333 -140.7 -145.3 672.1 9.8 82 I 156.4 0.008 -170.5 0.417 -120.1 121.8 63.6 0.292 -140.6 -137.4 963.7 0.292 -157.1 -158.4 3147.7 9.6 83

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130EXP 8 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t I 202.8 0.009 -170 0.417 -123.6 -123.1 30.3 0.292 -154.1 -151 3313.8 0.292 -160.9 -163.6 3123 10.8 84 I 187.1 0.009 -170.2 0.417 -126.5 124.8 33.7 0.292 -158.4 -157.6 3669. 5 0.292 -160.6 -164.9 930 6.1 85 I 152 0.009 -171.9 0.417 -129.3 -127 67.9 0.292 -159. 1 -159.4 2415.9 0.292 -161.6 -165.9 811.8 5.7 86 I 182.2 0.007 -173.5 0.417 -132.1 129.8 119.3 0.292 -159.9 -160.6 2192.2 0.292 -163.8 -167.9 1717.4 4.5 87 I 138.2 0.007 -172.7 0.417 -135 -132.7 112.7 0.292 162.1 -163.3 3950.2 0.292 164.2 -168.5 1242.4 12.4 88 I 199 0.008 -171.6 -135.9 -165.4 -168.5 12.0 89 I 201.4 0.008 -171.2 -140.4 -166 -168.2 12.1 90 I 193.7 0.007 -171.1 -145.4 -166.3 -167.9 10.1 91 I 187 0.007 -171.2 -150.7 -166.5 -167.5 9.3 92 I 188.2 0.007 -171.5 -155.6 -166.8 -167.4 10.2 93 I 197.9 0.006 -171.9 -161.1 -166.9 -167.5 9.2 94 I 205.9 0.006 -172.2 -164.9 -167.1 -167.8 12.4 95 I 212.9 0.006 -172.2 -165.8 -167.4 -168.1 8.7 96 I 217.8 0.006 -172.6 -166.2 -167.6 -168.4 12.3 97 I 223.4 0.005 -172.8 -166.4 -168 -168.7 11.8 98 I 232.2 0.005 -173 -166.6 -168.3 -169 12.3 99 I 243.4 0.005 -173.3 -166.7 -168.6 -169.3 11.6 100 I 248.9 0.005 -173.5 -166.9 -169 -169.7 10.9 101 I 252.7 0.005 -173.9 -167.1 -169.3 -170 12.2 102 I 257 0.004 -174.1 -167.4 -169.7 -170.4 12.1 103 I 258.5 0.004 -174.4 -167.7 -170 -170.7 12.4 104 I 261.8 0.004 -174.7 -168 -170.2 -171 12.3 105 I 266.4 0.004 -175 -168.3 -170.5 -171.2 12.4 106 I 264.9 0.004 -175.2 -168.5 -170.8 -171.5 12.4 107 I 267 0.003 -175.3 -168.7 -171 -171.6 12.4 108 I 263.7 0.003 -175.4 -168.9 -171.2 -171.8 12.1 109 I 261.4 0.003 -175.6 -169.1 -171.3 -172 10.7 110 I 261.1 0.003 -175.8 -169.3 -171.5 -172.1 12.4 111 I 259.7 0.003 -176.1 -169.6 -171.7 -172.3 12.4 112 I 259.7 0.003 -176.3 -169.8 -171.8 -172.4 12.4 113 I 262.7 0.002 -176.4 -170 -172 -172.6 12.4 114 I 263.2 0.002 -176.6 -170.2 -172.2 -172.8 12.4 115 I 264.7 0.002 -176.7 -170.3 -172.4 -173 12.4 116 I 260.8 0.002 -176.7 -170.5 -172.5 -173.2 12.3 117 I 257.5 0.002 -176.8 -170.7 -172.6 -173.3 11.9 118 I 257.5 0.002 -176.8 -170.8 -172.6 -173.4 12.3 119 I 260.5 0.001 -176.9 -170.8 -172.7 -173.4 11.5 120 I 262.6 0.001 -177 -170.9 -172.8 -173.5 11.8 121

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131EXP 8 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t I 263.8 0.001 -177.1 -171 -172.8 -173.6 11.3 122 I 264.8 0.001 -177.3 -171.1 -173 -173.7 10.2 123 1 263.2 0.001 -177.5 -171.3 -173.1 -173.9 12.4 124 1 261.5 0 -177.7 -171.4 -173.2 -174.1 12.4 125 1 261.1 0 -177.7 -171.6 -173.4 -174.3 12.3 126 1 260.7 0 -177.8 -171.8 -173.6 -174.4 12.3 127 1 262.8 0 -177.9 -172 -173.7 -174.6 12.4 128 1 261.3 0 -178 -172.3 -174 -174.8 12.4 129 1 262.7 0 -178.1 -172.6 -174.2 -175.1 12.1 130 1 260.1 0 -178.3 -172.8 -174.4 -175.3 11.0 131 1 259.9 0 -178.5 -173.1 -174.5 -175.5 12.4 132 1 259.8 0 -178.7 -173.3 -174.7 -175.7 12.4 133 1 257.7 0 -179.2 -173.5 -174.9 -175.9 12.4 134 1 257 0 -179.6 -173.9 -175.1 -176.1 12.4 135 1 255.2 0 -179.6 -174.2 -175.2 -176.2 12.4 136 1 254.2 0 -179.8 -174.6 -175.4 -176.4 11.7 137 1 253 0 -179.9 -174.7 -175.6 -176.5 12.4 138 1 251.8 0 -180.1 -174.9 -175.7 -176.6 12.4 139 1 251.2 0 -180.2 -175.1 -175.8 -176.8 12.4 140 1 249.3 0 -180.3 -175.2 -176 -177 12.0 141 1 249.6 0 -180.5 -175.4 -176.1 -177.1 12.4 142 1 248.6 0 -180.6 -175.4 -176.2 -177.2 12.4 143 1 248.5 0 -180.6 -175.5 -176.3 -177.3 11.9 144 1 247.2 0 -180.6 -175.5 -176.4 -177.4 12.4 145 1 248 0 -180.9 -175.6 -176.4 -177.4 12.4 146 1 248.4 0 -180.8 -175.6 -176.5 -177.5 12.4 147 1 245.4 0 -180.9 -175.7 -176.5 -177.6 12.4 148 1 245.8 0 -181.1 -175.8 -176.6 -177.7 12.4 149 1 246.3 0 -181.1 -176 -176.7 -177.8 12.4 150 1 245.8 0 -181.2 -176.2 -176.9 -177.9 12.4 151 1 244.8 0 -181.6 -176.3 -176.9 -178 12.4 152 1 243.3 0 -181.6 -176.4 -177.1 -178.2 12.4 153 1 241.4 0 -181.5 -176.5 -177.2 -178.2 12.4 154 1 243 0 -181.7 -176.6 -177.2 -178.4 12.4 155 1 242.5 0 -181.7 -176.6 -177.2 -178.5 12.4 156 1 242.7 0 -181.8 -176.7 -177.3 -178.5 12.4 157

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132EXP 8 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t 1 241 0 -182 -176.7 -177.4 -178.6 12.4 158 1 239.6 0 -182 -176.8 -177.5 -178.7 12.4 159 1 237.8 0 -182 -176.9 -177.6 -178.8 12.4 160 1 237.8 0 -182 -177 -177.7 -178.9 12.4 161 1 236 0 -182.2 -177.1 -177.8 -178.9 12.4 162 EXP 9 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 24.9 1 19.6 0.33 23.6 24. 3 766.5 0.33 23.7 24.4 626.7 0.33 23 24.4 666 0.0 1 0.107 N 44.9 1 17.6 0.33 23.6 24.1 96.5 0.33 23.8 24.3 66.9 0.33 23.1 24.3 0.9 0.0 2 0.294 N 53.5 1 15.1 0.33 23.3 23.8 198.4 0.33 23.5 24 132 0.33 22.8 24 203.1 0.0 3 0.324 N 55 1 13.1 0.33 23 23.5 214.9 0.33 23.1 23. 7 145.7 0.33 22.3 23.6 257.7 0.0 4 0.337 N 55.5 1 11.7 0.33 22.4 23 299.9 0.33 22.6 23.2 319.5 0. 33 22 23.2 211.7 0.0 5 0.337 N 55 1 10.4 0.33 22.1 22.6 222. 5 0.33 22.2 22.8 155.9 0.33 21.5 22.7 253.3 0.0 6 0.344 N 56 1 8.8 0.33 21.6 22 296.4 0.33 21.9 22.5 111 0.33 21.3 22.4 130.5 0.0 7 0.348 N 56.3 1 7.6 0.33 21 21.5 247. 4 0.33 21.2 21.9 244.3 0.33 20.4 21.7 327.6 0.0 8 0.339 N 56.3 1 5.8 0.33 20.5 20.9 262.9 0.33 20.8 21.4 168.3 0.33 20.1 21.3 179.8 0.0 9 0.351 N 57 1 4.4 0.33 19.7 20.1 308.8 0.33 20 20. 7 260.7 0.33 19.4 20.6 270.9 0.0 10 0.344 N 57.3 0.643 2.5 0.33 19.2 19. 5 271.5 0.33 19.6 20.2 106.7 0. 33 18.8 20 222.8 0.0 11 0.34 N 57.8 0.379 0.9 0.33 18.4 18. 7 298.8 0.33 18.7 19.4 258.4 0. 33 18 19.2 293.7 0.0 12 0.336 N 57.6 0.269 -0.9 0.33 17.6 17.9 295 0.33 17. 9 18.7 205 0.33 17.2 18.3 290.5 0.0 13 0.344 N 58.1 0.204 -2.9 0.33 17.1 17.2 210.3 0.33 17. 5 18.1 135.8 0.33 16.8 17.8 169.1 0.0 14 0.346 N 58.8 0.162 -4.8 0.33 16.1 16.4 290 0.33 16. 5 17.2 206.1 0.33 15.7 16.8 305.2 0.0 15 0.353 N 59.1 0.132 -7 0.33 15.3 15.5 257.8 0.33 15.6 16.3 235.2 0.33 15 16 219 0.0 16 0.344 N 58.8 0.109 -9.1 0.33 14.2 14.4 334.4 0.33 14. 9 15.6 138.4 0.33 14.2 15.2 233.9 0.0 17 0.339 N 60 0.086 -11.5 0.33 13.5 13. 6 223.4 0.33 13.9 14.7 183.3 0. 33 13.1 14.2 272.8 0.0 18 0.371 N 59.3 0.06 -13.6 0.33 12.4 12. 5 289.4 0.33 12.8 13.6 224.9 0. 33 12.2 13.2 241.1 0.0 19 0.344 N 60.5 0.018 -16.4 0.33 11.4 11.4 244.5 0.33 11.8 12.6 175.4 0.33 11.2 12.1 239 0.0 20 0.358 N 61.4 0.016 -20.2 0.33 10.1 10. 1 300.9 0.33 10.6 11.4 184.9 0. 33 9.8 10.8 285.2 0.0 21 0.396 N 61.1 0.124 -23.4 0.33 8.9 8. 8 277.7 0.33 9.4 10.2 187.9 0. 33 8.7 9.6 243.7 0.0 22 0.361 N 61.6 0.1 -26.1 0.33 7.5 7.3 328 0.33 8. 2 9 189.8 0.33 7.5 8.3 259.2 0.0 23 0.397 N 61.1 0.091 -26.8 0.33 6.4 6.1 241.4 0.33 6.8 7.7 207.4 0.33 6 6.9 286 0.0 24 0.396 N 61.6 0.083 -29.9 0.33 4.9 4.7 312 0.33 5.5 6.3 220.6 0. 33 4.8 5.6 267.8 0.0 25 0.41 N 60.5 0.077 -30.1 0.33 3.5 3.2 265.3 0.33 4.2 5 156.3 0. 33 3.5 4.2 219.5 0.0 26 0.409 N 62.5 0.071 -40 0.33 2.2 1. 8 239.8 0.33 2.9 3.6 163.7 0. 33 2.2 2.9 219.3 0.0 27 0.406 N 62 0.064 -42.8 0.33 0.6 0. 2 296.5 0.33 1.3 2.2 192.4 0. 33 0.6 1.2 288 0.0 28 0.368

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133EXP 9 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 60.3 0.059 -40.1 0.33 -0.9 -1.4 193.3 0.33 -0 .2 0.6 142.4 0.33 -0.8 -0.3 168.4 0.0 29 0.353 N 65.6 0.053 -63.6 0.33 -2.8 -3.3 202.7 0.33 -2 .3 -1.2 141.2 0.33 -3.2 -2.5 231 0.0 30 0.357 SW 64.2 0.051 -73.4 0.33 -4.9 -5.4 199.2 0.33 -4 .4 -3.5 177.6 0.33 -4.8 -4.3 165.6 1.3 31 0.382 SW 64.3 0.049 -82.4 0.33 -7.1 -7.6 174.8 0.33 -6 .8 -5.7 136.4 0.33 -7.5 -6.9 199.7 2.4 32 0.363 SW 70.8 0.044 -101.4 0.33 -9.5 -9.9 174.9 0.33 -9 .5 -8.3 162.3 0.33 -10.2 -9.7 199.1 2.2 33 0.361 N 67.7 0.044 -107.4 0.33 -11.9 -12. 4 177.6 0.33 -11.9 -10.8 140.6 0. 33 -12.6 -12.3 181.5 0.0 34 0.399 SW 66.3 0.043 -112.6 0.33 -14.1 14.8 152.3 0.33 -14.5 -13.3 130.3 0.33 -15.4 -15.1 185 1.9 35 0.341 SW 77.8 0.037 -125.8 0.33 -16.8 17.4 173.7 0.33 -17.6 -16.2 164.7 0. 33 -18.4 -18.2 205.4 2.9 36 0.328 SW 71.2 0.038 -123.9 0.33 -19.6 20.2 183.3 0.33 -20.5 -19.1 158.3 0. 33 -21.4 -21.3 203.8 2.3 37 0.388 SW 73.4 0.036 -127.8 0.33 -22.1 22.9 169.1 0.33 -23.1 -21.8 145.8 0.33 -23.9 -24 178.3 1.7 38 0.352 SW 78.3 0.034 -132 0.33 -24.3 -25. 2 157.3 0.33 -25.6 -24.4 146.9 0. 33 -26.4 -26.8 190.1 3.0 39 0.381 SW 72.8 0.034 -128 0.33 -27 -27.8 170.4 0.33 -28. 5 -27.2 151.5 0.33 -29.4 -29.8 208 3.1 40 0.328 SW 76.5 0.032 -133.1 0.33 -29.5 30.4 164.6 0.33 -31.2 -29.9 144.6 0. 33 -32.2 -32.7 191.2 1.7 41 0.367 SW 77.5 0.031 -139.9 0.33 -32.2 -33.2 121.5 0.33 -34 -32.7 104.8 0.33 -35 -35.7 139.9 3.5 42 0.384 SW 79.6 0.03 -185 0.33 -34.8 -35. 8 121.2 0.33 -36.9 -35.6 115.5 0. 33 -37.7 -38.5 138.4 3.5 43 0.34 SW 81.6 0.029 -185.8 0.33 -37.6 38.7 129.4 0.33 -39.7 -38.4 112.3 0. 33 -40.6 -41.5 144.5 3.0 44 0.383 SW 83.3 0.028 -185.5 0.33 -40 -41. 3 117.1 0.33 -42.4 -41.1 105.1 0. 33 -43.3 -44.4 142.4 4.7 45 0.363 SW 90.2 0.026 -186.6 0.33 -42.7 43.9 125.9 0.33 -45.4 -44 119.1 0. 33 -46.2 -47.4 155.7 3.6 46 0.376 SW 85.6 0.026 -185.1 0.33 -45 -46. 4 115.3 0.33 -47.9 -46.6 102.5 0. 33 -48.9 -50.3 146.2 3.9 47 0.303 SW 82.3 0.026 -186.1 0.33 -47.7 49.1 130.2 0.33 -50.9 -49.5 120.3 0. 33 -51.9 -53.4 166.3 3.1 48 0.385 SW 87.5 0.148 -185.2 0.33 -50.1 -51.6 121 0.33 -53.3 -52.1 110 0. 33 -54.2 -55.9 137.1 4.2 49 0.353 SW 91.7 0.125 -185.9 0.33 -52.8 -54.4 133.5 0.33 -56.1 -54.9 121. 6 0.33 -57 -58.8 158 3.8 50 0.362 SW 88.3 0.113 -185.3 0.33 -54.9 56.7 112.5 0.33 -58.4 -57.2 96.7 0. 33 -59.3 -61.4 145.3 4.2 51 0.337 SW 88.7 0.101 -186.3 0.33 -57.3 -59.1 120.5 0.33 -61 -59.8 113.9 0.33 -62 -64.1 156.1 4.1 52 0.356 SW 91.7 0.09 -185.4 0.33 -59.8 61.6 127.6 0.33 -63.7 -62.5 121.6 0. 33 -64.5 -66.7 156.1 3.7 53 0.329 SW 97.7 0.08 -185.8 0.33 -62.1 -64 123.9 0.33 -66 -64.9 109.7 0. 33 -66.8 -69.2 152.8 3.9 54 0.356 SW 92.5 0.077 -185.5 0.33 -64.1 66.2 114 0.33 -68.1 -67.1 93.8 0. 33 -68.9 -71.5 141.3 4.3 55 0.346 SW 101.7 0.069 -186 0.33 -66.2 68.3 111.8 0.33 -70.6 -69.6 119.9 0.33 -71.4 -74 156.3 3.9 56 0.344 SW 94.5 0.068 -185.6 0.33 -68.6 70.7 127.5 0.33 -73.2 -72.2 126 0. 33 -73.8 -76.6 163.4 2.2 57 0.329 SW 99 0.062 -185.9 0.33 -70.8 -73 121.2 0.33 -75. 3 -74.5 111.7 0.33 -75.8 -78.8 141.1 4.1 58 0.352 SW 97.4 0.06 -185.8 0.33 -73 -75.2 120 0.33 -77. 7 -76.9 122 0.33 -78.2 -81.2 163.3 3.1 59 0.325 SW 99.1 0.056 -185.8 0.33 -75.2 77.5 125.4 0.33 -80 -79.2 119.5 0. 33 -80.5 -83.6 160.5 3.3 60 0.37 SW 99 0.054 -185.8 0.33 -77.1 79.5 112.3 0.33 -82.2 -81.4 115 0. 33 -82.5 -85.8 152.3 4.3 61 0.343 SW 101.4 0.052 -185.8 0.33 -80.1 82.4 163 0.33 -85.1 -84.3 161.7 0. 33 -85.1 -88.4 179.2 3.6 62 0.331 SW 101.6 0.05 -186 0.33 -82 -84.5 121.4 0.33 -87 -86.4 111.6 0.33 -87.2 -90.7 163.7 4.4 63 0.353 SW 100.8 0.049 -185.7 0.33 -83.8 -86.4 107 0.33 -89 -88.6 126 0.33 -88.9 -92.6 138.7 3.7 64 0.354 SW 106.2 0.047 -186.1 0.33 -85.8 88.4 115.5 0.33 -91.2 -90.7 120.7 0. 33 -91.2 -94.9 169.9 3.8 65 0.335 SW 104.1 0.046 -185.8 0.33 -87.9 90.6 130.9 0.33 -93.2 -92.9 129.5 0. 33 -92.8 -96.7 139.7 3.0 66 0.354

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134EXP 9 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 104.2 0.045 -186.1 0.33 -89.7 92.6 118.3 0.33 -95.1 -94.7 102.6 0.33 -95.1 -99 174.6 2.2 67 0.368 SW 109.3 0.043 -185.6 0.33 -91.4 94.3 99.2 0.33 -97.1 -96.8 136 0. 33 -96.8 -100.9 149.5 3.3 68 0.339 SW 105 0.043 -186.3 0.33 -93.2 -96. 2 120.3 0.33 -98.8 -98.6 107.7 0. 33 -98.4 -102.6 144.5 3.1 69 0.352 SW 109.4 0.042 -185.7 0.33 -95.1 98.1 123.9 0.33 -100.5 -100.3 104 0. 33 -100.2 -104.5 152.7 3.2 70 0.352 SW 106.9 0.042 -186.3 0.33 -96.9 -100 115.4 0.33 -102.5 -102.3 135.9 0.33 -102 -106.4 161.9 6.5 71 0.347 SW 112.6 0.041 -185.6 0.33 -98.6 101.8 120.8 0.33 -104 -104.1 111.3 0. 33 -103.4 -107.9 136.1 5.3 72 0.341 SW 106.4 0.041 -186.3 0.33 -100.2 103.5 111.6 0.33 -105.9 -105.8 112.1 0. 33 -105.4 -109.9 174.2 5.9 73 0.361 SW 111.3 0.04 -185.8 0.33 -102 105.3 121.3 0.33 -107.5 -107.6 125.2 0.33 -106.8 -111.5 144 5.7 74 0.338 SW 107.3 0.04 -185.8 0.33 -103.6 107 114.4 0.33 -109.5 -109.5 129.5 0. 33 -108.8 -113.5 178.1 3.4 75 0.345 SW 109.3 0.039 -186 0.33 -105 -108.5 101.8 0.33 -110. 7 -111 104.7 0.33 -109.9 -114.9 135.2 4.6 76 0.319 SW 103.5 0.04 -185.7 0.33 -106.9 110.4 134.7 0.33 -112.6 -112.8 134 0. 33 -111.7 -116.6 168.2 3.3 77 0.351 SW 111.7 0.038 -185.9 0.33 -108 111.6 86.2 0.33 -113.9 -114.2 109.2 0.33 -112.8 -118 132.8 2.9 78 0.307 SW 104 0.04 -186.4 0.33 -109.9 -113. 4 133.7 0.33 -115.6 -115.9 131.7 0. 33 -114.5 -119.6 161.4 4.1 79 0.345 SW 113.2 0.039 -186 0.33 -111.2 -114. 9 100.2 0.33 -117.3 -117.6 131.5 0. 33 -116.1 -121.2 166.7 5.7 80 0.337 SW 111.7 0.039 -186.2 0.33 -112.4 116.2 97.9 0.33 -118.4 -118.9 100.7 0. 33 -117.2 -122.5 140.5 6.4 81 0.348 SW 113.9 0.04 -185.9 0.33 -114 -117.8 124 0.33 120 -120.4 131 0.33 -118.8 -124.1 164.2 7.2 82 0.251 SW 119.1 0.04 -185.9 0.33 -115.3 119.2 101.9 0.33 -121.5 -121.9 119.6 0. 33 -120.3 -125.7 172.2 6.0 83 0.373 SW 113.3 0.04 -186.4 0.33 -116.5 120.4 94.5 0.33 -122.5 -123.2 115.8 0. 33 -120.9 -126.6 103.1 4.3 84 0.314 SW 112.7 0.04 -186.1 0.33 -118 -122 129.2 0.33 -123. 9 -124.5 116.3 0.33 -122.5 -128 167.2 5.2 85 0.373 SW 109.6 0.04 -186.5 0.33 -119 -123. 2 89.1 0.33 -125.2 -125.8 103.8 0. 33 -123.9 -129.5 167.4 4.4 86 0.321 SW 118.6 0.039 -186.3 0.33 -120.4 124.6 121.1 0.33 -126.3 -127 107.1 0. 33 -124.9 -130.7 146.7 4.2 87 0.358 SW 108.7 0.042 -186.4 0.33 -121.3 -125.6 75.8 0.33 -127.5 -128.3 120 0.33 -126 -131.8 142 3.4 88 0.262 SW 120 0.041 -185.8 0.33 -122.7 126.9 115.7 0.33 -129 -129.7 136.2 0. 33 -127.5 -133.2 178.6 4.5 89 0.351 SW 113.3 0.043 -186.2 0.33 -123.6 127.9 79.6 0.33 -130 -130.8 112.4 0. 33 -128.4 -134.3 144.4 4.3 90 0.256 SW 124.4 0.042 -186 0.33 -125 -129.2 120.1 0.33 -131. 3 -132 119.2 0.33 -129.7 -135.7 173.6 4.4 91 0.315 SW 123.1 0.049 -186.3 0.33 -125.9 130.3 88.6 0.33 -132.1 -133.2 128.9 0. 33 -130.1 -136.3 93.4 4.0 92 0.266 SW 133.6 0.049 -186 0.33 -127.2 -131. 6 115.3 0.33 -133.7 -134.3 107.2 0. 33 -132.4 -138.2 254.4 4.0 93 0.308 SW 123.3 0.052 -186.3 0.33 -127.9 132.4 72.8 0.33 -134.6 -135.3 100.1 0. 33 -133.1 -139.3 149.5 4.3 94 0.314 SW 128.6 0.049 -186.5 0.33 -128.9 133.4 93.2 0.33 -135.6 -136.4 119.5 0. 33 -133.9 -140.2 144.7 8.1 95 0.332 SW 105.4 0.049 -185.9 0.33 -130.3 134.8 129.2 0.33 -136.8 -137.5 119.8 0. 33 -135.2 -141.4 179.2 7.6 96 0.313 SW 112.2 0.046 -186.3 0.33 -131.1 135.7 84.1 0.33 -137.8 -138.7 133.5 0.33 -136 -142.4 152.4 7.6 97 0.303 SW 114.2 0.049 -186.4 0.33 -132.1 136.7 96.9 0.33 -138.8 -139.7 110.7 0.33 -137 -143.4 168.6 6.5 98 0.269 SW 126.8 0.054 -186.2 0.33 -133 -137. 7 100.5 0.33 -139.6 -140.6 104.8 0. 33 -137.8 -144.3 149.4 6.7 99 0.311 SW 120.3 0.056 -186.2 0.33 -134 -138. 7 102.9 0.33 -140.5 -141.6 117.7 0. 33 -138.5 -145.1 139.7 5.6 100 0.269 SW 120.5 0.056 -186.4 0.33 -135.1 139.8 101.5 0.33 -141.8 -142.8 156.6 0. 33 -139.8 -146.3 200.4 5.4 101 0.291 SW 116 0.056 -186.4 0.33 -135.8 -140. 6 90.6 0.33 -142.5 -143.6 101.8 0. 33 -140.4 -147.1 146.9 5.4 102 0.33 SW 115.3 0.056 -186.1 0.33 -136.9 141.7 117.5 0.33 -143.4 -144.6 127.8 0. 33 -141.2 -147.9 152.6 4.3 103 0.267 SW 113.1 0.056 -185.8 0.33 -138 -142.8 122 0.33 -144. 4 -145.6 139.1 0.33 -142.2 -148.9 176.2 3.8 104 0.357

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135EXP 9 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 108.5 0.057 -186.5 0.33 -138.7 143.6 72 0.33 -145.4 -146.6 143.9 0. 33 -143.1 -149.8 181.9 3.9 105 0.306 SW 100.2 0.058 -186.1 0.33 -139.6 144.5 104.1 0.33 -146.2 -147.5 129.2 0. 33 -143.9 -150.7 159.1 4.0 106 0.346 SW 101.8 0.059 -186.8 0.33 -140.4 145.3 94.9 0.33 -147.1 -148.4 124.3 0. 33 -144.7 -151.5 172.9 5.8 107 0.288 SW 99.7 0.059 -186.6 0.33 -141.2 146.2 100.1 0.33 -147.8 -149.2 113.7 0. 33 -145.4 -152.3 162.1 7.4 108 0.303 SW 103.8 0.058 -186.7 0.33 -141.9 147 93.9 0.33 -148.4 -149.8 91.9 0. 33 -146.2 -153.1 165.8 4.9 109 0.248 SW 101.3 0.058 -186.2 0.33 -142.7 147.8 94.4 0.33 -149.3 -150.6 136.5 0. 33 -146.9 -153.9 173.8 5.8 110 0.269 SW 102.4 0.057 -186.6 0.33 -143.6 148.7 104.9 0.33 -150.5 -151.8 181.3 0.33 -148 -154.9 215.1 6.4 111 0.251 SW 102.7 0.057 -186.4 0.33 -144.5 149.6 109.3 0.33 -151.5 -152.7 153.5 0. 33 -149.2 -156.1 239.2 5.8 112 0.242 SW 103.3 0.056 -186.5 0.33 -145.1 -150.2 78.8 0.33 -152 -153.6 149 0. 33 -149.4 -156.6 123.6 7.7 113 0.273 SW 102.4 0.055 -186.5 0.33 -145.6 150.8 64.5 0.33 -152.6 -154.1 103 0. 33 -150.2 -157.3 183.7 5.6 114 0.283 SW 100 0.056 -186.9 0.33 -146.1 -151. 3 60.3 0.33 -153.2 -154.8 133.1 0. 33 -150.6 -157.8 143.7 6.1 115 0.225 SW 98.9 0.055 -186.7 0.33 -147.2 152.3 132.4 0.33 -154.1 -155.6 150.7 0. 33 -151.4 -158.6 195.6 5.7 116 0.354 SW 97.2 0.054 -187 0.33 -147.8 -153 83.1 0.33 -154. 7 -156.3 135.4 0.33 -152.2 -159.4 199.6 2.9 117 0.237 SW 97.3 0.054 -186.3 0.33 -148.5 153.7 93.2 0.33 -155.7 -157.1 155.7 0. 33 -153.2 -160.4 249.1 4.6 118 0.198 SW 102.3 0.051 -187.1 0.33 -149.1 154.3 82.7 0.33 -156.5 -157.9 158.8 0. 33 -154.1 -161.3 231.9 3.0 119 0.224 SW 96.1 0.052 -186.5 0.33 -150.2 -155.4 146 0.33 -157.5 -158.9 198.8 0.33 -155 -162.3 260.7 4.2 120 0.182 SW 96.8 0.066 -186.7 0.42 -151.2 156.1 78.7 0.17 -165 -162.5 746.7 0. 17 -179.1 -183.7 5418.5 4.1 121 0.222 EXP 10 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 52.3 1 15.3 0.33 23.2 24 658.5 0.33 23.3 24.1 578.3 0.33 22.7 24.2 514.3 0.0 1 0.508 N 56.4 1 12.4 0.33 23 23.5 192.7 0.33 23.2 23.8 103.5 0.33 22.5 23.7 202.9 0.0 2 0.469 N 56.9 1 10.1 0.33 22.7 23.2 174.1 0.33 22.7 23.3 198.4 0.33 22 23.3 203 0.0 3 0.498 N 56.9 1 8.5 0.33 21.8 22.3 395.9 0.33 22.1 22.8 237.8 0.33 21.4 22.7 289.6 0.0 4 0.514 N 57.4 1 6.7 0.33 21.3 21.7 258.4 0.33 21.6 22.2 214.1 0.33 20.9 22.2 193.2 0.0 5 0.573 N 58.3 1 4.9 0.33 20.7 21.1 254.8 0.33 21.1 21.7 144.2 0.33 20.3 21.6 235.3 0.0 6 0.409 N 59.5 1 2.8 0.33 20 20.4 243.5 0.33 20.3 21 226.2 0.33 19.6 20.8 263.2 0.0 7 0.622 N 59.2 1 0.3 0.33 19.2 19.6 296.4 0.33 19.6 20.3 189.3 0.33 18.9 20.1 226.1 0.0 8 0.703 N 59.8 1 -2.4 0.33 18.1 18.5 327.1 0.33 18.4 19.2 273.4 0.33 17.7 19 324.8 0.0 9 0.639 N 58.4 1 -5.1 0.33 17.2 17.4 305.2 0.33 17.7 18.4 160.4 0.33 16.9 18.1 238 0.0 10 0.62 N 60.3 1 -8.3 0.33 16.2 16.4 271.7 0.33 16.5 17.4 236.3 0.33 15.7 16.9 310.5 0.0 11 0.682 N 59.5 1 -11 0.33 15 15.2 312.3 0.33 15.4 16.2 240.8 0.33 14.7 15.8 266.2 0.0 12 0.67 N 60.8 1 -13.1 0.33 13.9 14.1 271.4 0.33 14.4 15.1 194.5 0.33 13.7 14.8 224 0.0 13 0.431 N 60.1 1.034 -18.1 0.33 12.6 12.8 252.5 0.33 13.2 14 180.6 0.33 12.5 13.6 236.1 0.0 14 0.58 N 62.1 0.376 -25 0.33 11.1 11.3 246.4 0.33 11.7 12.6 177.7 0.33 11 12.1 231.9 0.0 15 0.594 N 63 0.248 -34.1 0.33 9.7 9.8 208.4 0.33 10.1 11.1 161.7 0.33 9.3 10.4 219.4 0.0 16 0.772 N 64.5 0.197 -44.2 0.33 8.1 8.1 203.6 0.33 8.6 9.5 155.2 0.33 7.8 8.8 195.5 0.0 17 0.57 N 63.3 0.163 -50.6 0.33 5.7 5.9 228.1 0.33 6 7.3 185.8 0.33 5.1 6.3 246.1 0.0 18 0.578

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136EXP 10 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 66.7 0.132 -68.8 0.33 3.8 3.8 234.9 0.33 4 5.2 194.9 0. 33 3.1 4.1 245.8 0.0 19 0.664 N 63.6 0.121 -59.3 0.33 1.6 1.5 239.8 0.33 2 3.1 171.9 0. 33 1.1 2 215.7 0.0 20 0.509 N 64 0.108 -67.5 0.33 -0.5 -0.7 241.4 0.33 -0.4 0.8 208.5 0.33 -1.3 -0.5 268.8 0.0 21 0.625 N 65.3 0.096 -65.9 0.33 -2.5 -2.8 199.1 0.33 -2 .1 -1.1 130.2 0.33 -3 -2.4 174.8 0.0 22 0.597 N 64.9 0.088 -81.3 0.33 -4.6 -4.9 155.4 0.33 -4.6 -3.3 135.8 0.33 -5.5 -4.9 181.6 0.0 23 0.528 N 71.6 0.076 -103.9 0.33 -7.5 -7.7 200.7 0.33 -7.6 -6.2 167.8 0.33 -8.6 -7.9 212.7 0.0 24 0.678 N 65.7 0.075 -109.3 0.33 -9.9 -10.3 152.3 0.33 10.3 -8.8 127.4 0.33 -11.5 -11 184.5 0.0 25 0.672 N 79.4 0.062 -130.5 0.33 -12.9 13.2 171 0.33 -13.8 -12.1 171.4 0. 33 -14.9 -14.4 203.5 0.0 26 0.513 SW 77.2 0.022 -133 0.33 -16 -16.3 181.4 0.33 -17. 1 -15.4 160.7 0.33 -18.3 -17.9 209.1 1.8 27 0.43 SW 77.4 0.022 -136.8 0.33 -18.9 19.3 173.3 0.33 -20.2 -18.6 159.2 0. 33 -21.3 -21.1 192.8 1.9 28 0.593 SW 76.6 0.022 -139.7 0.33 -22.1 22.5 133.7 0.33 -23.6 -22 125.3 0. 33 -24.7 -24.6 154.1 2.1 29 0.65 SW 85.8 0.021 -185.4 0.33 -25.1 25.5 128.3 0.33 -27.1 -25.4 130.2 0. 33 -28.1 -28.2 158.8 3.7 30 0.561 SW 82.5 0.022 -185.9 0.33 -27.9 28.5 127.9 0.33 -30.2 -28.5 116.9 0.33 -31.5 -31.7 161 2.6 31 0.6 SW 86 0.021 -186 0.33 -30.9 -31.6 133.2 0.33 -33. 3 -31.7 121.2 0.33 -34.6 -35.1 157 4.1 32 0.594 SW 88.5 0.021 -185.1 0.33 -33.8 34.6 130.2 0.33 -36.7 -35 129.6 0. 33 -38.1 -38.7 170.9 4.1 33 0.575 SW 85 0.021 -185.8 0.33 -36.5 -37. 4 126.2 0.33 -39.5 -37.9 116.8 0. 33 -40.8 -41.7 148.8 3.0 34 0.726 SW 89.5 0.021 -185.3 0.33 -39.4 40.3 129.3 0.33 -42.9 -41.1 126.1 0.33 -44.4 -45.3 182 2.9 35 0.532 SW 89.9 0.021 -185.6 0.33 -42 43.1 126.6 0.33 -45.6 -43.9 115 0. 33 -47.1 -48.3 153.4 5.5 36 0.502 SW 94.3 0.021 -185.2 0.33 -44.8 45.9 128.8 0.33 -48.7 -47 125.3 0. 33 -50.1 -51.5 167.5 4.8 37 0.397 SW 94.5 0.021 -185.4 0.33 -47.3 48.5 122 0.33 -51.5 -49.8 122.5 0. 33 -52.9 -54.4 158.7 3.3 38 0.389 SW 94 0.021 -185.1 0.33 -50 -51.2 126.5 0.33 -54. 2 -52.6 117.3 0.33 -55.5 -57.2 156 3.7 39 0.374 SW 99.4 0.02 -185.6 0.33 -52.5 -53.8 123.5 0.33 -57 -55.4 119 0. 33 -58.5 -60.3 172.7 6.1 40 0.398 SW 97 0.021 -185.5 0.33 -55 -56.4 126.4 0.33 -59. 5 -58.1 119 0.33 -60.6 -62.8 141.2 5.0 41 0.387 SW 99.7 0.021 -185.6 0.33 -57.7 59.1 131.7 0.33 -62.3 -60.9 129.1 0. 33 -63.3 -65.5 162.6 5.7 42 0.412 SW 98.6 0.021 -185.6 0.33 -59.8 61.4 109.9 0.33 -64.6 -63.3 107 0. 33 -65.7 -68.1 154.4 4.3 43 0.424 SW 99.6 0.021 -185.6 0.33 -62.4 64 132.7 0.33 -67.3 -65.9 122.1 0. 33 -68.4 -70.8 166.2 4.1 44 0.404 SW 100.1 0.021 -185.7 0.33 -64.5 66.3 110.1 0.33 -69.7 -68.4 116.5 0. 33 -70.8 -73.4 161.6 5.0 45 0.437 SW 99.4 0.021 -185.7 0.33 -67.1 68.9 135.6 0.33 -72 -70.8 119.7 0. 33 -72.9 -75.7 148.9 4.7 46 0.426 SW 101.6 0.021 -185.6 0.33 -69.4 71.3 122.9 0.33 -74.7 -73.5 131.6 0. 33 -75.5 -78.3 171.5 3.8 47 0.348 SW 99.6 0.021 -185.9 0.33 -71.5 73.5 116.9 0.33 -76.9 -75.8 119 0. 33 -77.5 -80.6 149.5 5.1 48 0.432 SW 103.2 0.021 -185.8 0.33 -73.8 -75.9 126.9 0.33 -79.3 -78.2 120. 9 0.33 -80 -83 168.1 3.2 49 0.403 SW 102.6 0.021 -185.7 0.33 -76.2 78.3 128.7 0.33 -81.8 -80.8 143 0. 33 -82.3 -85.5 166.6 4.4 50 0.419 SW 109.2 0.021 -185.7 0.33 -78.9 80.9 147.3 0.33 -84.5 -83.5 143.8 0. 33 -85.1 -88.3 192.7 4.2 51 0.451 SW 107.7 0.022 -186.2 0.33 -80.9 83.2 123.6 0.33 -86.6 -85.7 116.7 0. 33 -87.2 -90.7 169.8 4.3 52 0.498 SW 112.3 0.021 -185.8 0.33 -83.1 85.5 126.7 0.33 -88.9 -88.1 132.5 0. 33 -89.2 -92.9 161.7 6.2 53 0.456 SW 109.1 0.022 -185.9 0.33 -85 87.4 109.9 0.33 -91.1 -90.3 133.6 0.33 -91.3 -95 164.7 5.6 54 0.404 SW 112.4 0.022 -185.7 0.33 -86.9 -89.5 118 0.33 -92.9 -92.3 109.4 0.33 -93 -97 149.8 6.2 55 0.386 SW 117.7 0.022 -186 0.33 -88.8 -91. 3 106.1 0.33 -95.1 -94.4 132.3 0. 33 -95.3 -99.2 176.6 6.9 56 0.396

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137EXP 10 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 113.2 0.023 -186.2 0.33 -90.4 93.1 103.6 0.33 -96.7 -96.2 103.1 0.33 -96.9 -101 147.2 5.4 57 0.449 SW 118.5 0.023 -185.9 0.33 -92 94.8 98.2 0.33 -98.5 -98 113.5 0. 33 -98.6 -102.9 154.5 4.4 58 0.522 SW 122.1 0.023 -186 0.33 -93.9 96.7 113.5 0.33 -100.5 -99.9 116 0.33 -100.8 -105 182 6.3 59 0.553 SW 119.5 0.024 -185.9 0.33 -95.2 98.2 87.2 0.33 -101.9 -101.4 93.5 0. 33 -102.2 -106.7 145.6 2.5 60 0.378 SW 122.2 0.024 -185.6 0.33 -96.9 -99.7 95.5 0.33 -104 -103.4 130 0. 33 -104.4 -108.8 186.2 3.4 61 0.303 SW 130.3 0.025 -186 0.33 -98.3 101.3 94.2 0.33 -105.5 -105 105.3 0. 33 -105.8 -110.4 152 3.2 62 0.426 SW 132.2 0.025 -186.1 0.33 -99.6 -102.7 84.8 0.33 -106.9 -106.4 92 0.33 -107.3 -112.1 157 4.2 63 0.343 SW 128.6 0.026 -186.4 0.33 -101.2 -104.3 98.6 0.33 -108.5 -108 106.7 0.33 -108.8 -113.6 156 8.1 64 0.242 SW 135.1 0.026 -186.4 0.33 -102.7 105.8 98.9 0.33 -110.2 -109.7 116.6 0. 33 -110.5 -115.3 171.1 4.4 65 0.398 SW 127.5 0.027 -186 0.33 -104 -107.2 82.3 0.33 -111. 6 -111.2 103.8 0.33 -111.9 -116.9 158.5 4.9 66 0.334 SW 135 0.027 -185.9 0.33 -105.5 -108. 7 97.3 0.33 -113.3 -112.8 118.1 0. 33 -113.5 -118.5 175.3 5.7 67 0.261 SW 132.5 0.028 -185.9 0.33 -106.7 110 79.6 0.33 -114.4 -114.1 91.1 0. 33 -114.7 -119.9 148.5 3.1 68 0.272 SW 135.3 0.028 -186.1 0.33 -108.3 111.5 107.2 0.33 -115.9 -115.5 105.3 0. 33 -116.1 -121.4 167.3 5.0 69 0.307 SW 137.7 0.029 -185.8 0.33 -109.5 -112.8 80.9 0.33 -117.4 -117 116.8 0.33 -117.6 -122.9 171 8.1 70 0.269 SW 134.2 0.03 -186.2 0.33 -110.7 114.1 85 0.33 -118.8 -118.4 106.6 0. 33 -118.9 -124.3 166.8 4.3 71 0.298 SW 136.2 0.031 -186.2 0.33 -111.9 115.3 80.5 0.33 -119.9 -119.7 96.3 0.33 -120 -125.5 149.1 8.4 72 0.341 SW 134.5 0.032 -185.8 0.33 -113.4 116.8 103.1 0.33 -121.3 -121.1 113.3 0. 33 -121.3 -126.9 171.3 4.4 73 0.266 SW 128.4 0.033 -186 0.33 -114.4 -118 76.4 0.33 -122. 5 -122.4 108.8 0.33 -122.2 -127.9 141.8 3.7 74 0.409 SW 134.4 0.034 -186 0.33 -116 -119.5 111.1 0.33 -123. 9 -123.8 121.9 0.33 -123.5 -129.2 164.7 4.0 75 0.4 SW 131.1 0.035 -186.4 0.33 -117 -120. 7 84.8 0.33 -124.9 -124.9 89.4 0. 33 -124.6 -130.4 154.3 6.3 76 0.557 SW 133.3 0.037 -185.8 0.33 -118.5 122.1 103.7 0.33 -126.4 -126.4 138.8 0. 33 -125.8 -131.6 169.8 3.9 77 0.263 SW 130 0.037 -185.9 0.33 -119.7 -123.4 95 0.33 -127. 4 -127.7 117.8 0.33 -126.6 -132.6 137.2 4.5 78 0.321 SW 138.1 0.038 -185.9 0.33 -120.9 124.7 95.6 0.33 -128.7 -128.8 110.6 0.33 -128 -133.9 175.9 4.5 79 0.333 SW 125 0.039 -186.2 0.33 -122 -125.9 87.3 0.33 -129. 6 -130 113.2 0.33 -128.7 -134.8 137.8 5.6 80 0.421 SW 121 0.038 -186.1 0.33 -123.2 -127. 2 104.1 0.33 -130.8 -131.1 112.6 0. 33 -129.8 -135.9 158.7 5.1 81 0.445 SW 120.5 0.037 -185.9 0.33 -124.5 128.5 102.2 0.33 -132.1 -132.5 145.1 0. 33 -130.8 -136.9 157.7 4.1 82 0.365 SW 121.1 0.037 -186 0.33 -125.7 -129. 7 94.8 0.33 -133.1 -133.8 133.3 0. 33 -131.6 -137.8 133.1 7.1 83 0.56 SW 127.6 0.038 -186.2 0.33 -126.8 130.9 99.2 0.33 -134 -134.7 104.2 0. 33 -132.6 -138.8 161.2 4.3 84 0.351 SW 122.6 0.038 -185.7 0.33 -128.3 -132.4 134 0.33 -135.3 -136 147.2 0. 33 -133.7 -139.9 165 4.6 85 0.559 SW 123.6 0.038 -186.1 0.33 -129.1 133.3 73.5 0.33 -136.4 -137.1 126.2 0.33 -134.7 -141 161.5 8.4 86 0.417 SW 117.5 0.039 -186.3 0.33 -130.4 134.7 124 0.33 -137.1 -138.1 107.2 0. 33 -135.2 -141.7 118.8 4.2 87 0.403 SW 115.1 0.039 -186.7 0.33 -131.5 135.8 101.4 0.33 -138.3 -139.3 153.3 0. 33 -136.3 -142.7 159.1 3.8 88 0.455 SW 109.4 0.039 -185.9 0.33 -132.7 137 114.1 0.33 -139.5 -140.6 157.4 0. 33 -137.2 -143.7 160.9 3.7 89 0.432 SW 121.5 0.039 -186.1 0.33 -133.6 138.1 100.2 0.33 -140.3 -141.4 108.4 0. 33 -138.2 -144.7 166.6 7.6 90 0.46 SW 127.2 0.042 -185.4 0.33 -134.7 139.2 111.3 0.33 -141.2 -142.5 143.8 0. 33 -138.8 -145.4 125.8 3.1 91 0.49 SW 125.1 0.045 -185.9 0.33 -135.4 140.1 75.7 0.33 -142.2 -143.5 133.2 0. 33 -139.9 -146.5 180.2 6.7 92 0.57 SW 143.1 0.048 -186.1 0.33 -136.5 141.1 110.2 0.33 -143.2 -144.5 143.7 0. 33 -140.8 -147.4 167.1 4.1 93 0.657 SW 119.1 0.052 -186.1 0.33 -137.6 142.3 124.2 0.33 -144.2 -145.5 133.7 0. 33 -141.9 -148.5 184.8 5.1 94 0.526

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138EXP 10 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 133.7 0.051 -186.4 0.33 -138.2 143 69.1 0.33 -145.4 -146.3 101.8 0. 33 -143.8 -150.2 281.2 4.8 95 0.434 SW 124.6 0.053 -186.2 0.33 -139.3 144.1 115.7 0.33 -146.4 -147.4 158.7 0. 33 -144.4 -151.2 172.1 4.0 96 0.463 SW 124.2 0.053 -186.1 0.33 -140.1 -145 97.6 0.33 -147.1 -148.3 122.8 0.33 -145.1 -152 169.9 5.8 97 0.409 SW 123.7 0.053 -186.3 0.33 -141.4 -146.3 153.6 0.33 -148 -149.1 121.3 0.33 -146 -152.9 192.4 7.3 98 0.492 SW 122.7 0.053 -186.3 0.33 -141.9 -147 71 0.33 -148. 9 -150.2 151.4 0.33 -146.6 -153.6 164.4 8.6 99 0.443 SW 123.9 0.052 -186.4 0.33 -142.7 147.7 89.8 0.33 -149.6 -150.9 111 0. 33 -147.4 -154.4 179.3 4.9 100 0.475 SW 124.1 0.052 -186.5 0.33 -143.4 -148.5 99.4 0.33 -150 -151.4 74.1 0.33 -148 -155.1 161.7 3.5 101 0.3 SW 126.1 0.052 -186.4 0.33 -144.1 -149.2 79.9 0.33 -151.2 -152.4 168 0.33 -149.1 -156.1 231 4.5 102 0.336 SW 120.4 0.052 -186.2 0.33 -145.2 150.3 140.8 0.33 -152 -153.3 142.2 0. 33 -149.8 -156.9 199.4 9.4 103 0.355 SW 122.2 0.052 -186.1 0.33 -145.9 151.1 94.2 0.33 -152.9 -154.2 150 0. 33 -150.6 -157.8 204.3 4.2 104 0.282 SW 123.8 0.052 -186.3 0.33 -146.7 152 127.9 0.33 -153.4 -154.8 105.7 0. 33 -151.2 -158.4 176.3 5.4 105 0.367 SW 121.2 0.052 -186.1 0.33 -147.4 152.7 90.1 0.33 -154.4 -155.7 156.6 0. 33 -152.2 -159.4 244.8 7.1 106 0.325 SW 121.3 0.052 -186.1 0.33 -148 153.3 90.4 0.33 -155 -156.4 121.1 0. 33 -152.7 -160 182.5 3.3 107 0.294 SW 124.8 0.051 -186.3 0.33 -148.9 154.2 120.1 0.33 -155.9 -157.2 137.1 0.33 -153.7 -161 249.8 4.7 108 0.226 SW 126.5 0.05 -186.5 0.42 -149.5 154.9 103.8 0.42 -159.7 -158.2 115.4 0.17 -174.8 -180 4801.7 5.0 109 0.327 SW 127.8 0.023 -186.3 0.42 -152.7 155.6 43.8 0.42 -179.2 -173.6 3656.4 0.17 -182 -185.9 21329.9 3.0 110 0.223 SW 120.2 0.051 -186.2 -156.9 -183.2 -186.8 4.4 111 0.127 EXP 11 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 53.8 1 11.5 0.33 22.6 23. 5 759 0.33 22.7 23.7 668.1 0. 33 22 23.7 689.5 0.0 1 0.354 N 55.1 1 9.5 0.33 22.1 22.7 331.6 0.33 22.3 23 254.5 0.33 21.6 22.9 311.3 0.0 2 0.302 N 56.9 1 7.4 0.33 21.6 22.1 269.5 0.33 21.7 22.4 191.6 0. 33 21 22.3 255.3 0.0 3 0.358 N 55.8 1 5.2 0.33 20.9 21.3 300.2 0.33 21.1 21.8 215.4 0.33 20.4 21.6 245.7 0.0 4 0.371 M 56.1 1 3.1 0.33 20.1 20.6 266.2 0.33 20.1 20.9 297.1 0.33 19.3 20.7 351.3 0.0 5 0.375 M 56.7 1 0.6 0.33 19 19.5 355. 6 0.33 19.4 20.1 205.3 0.33 18.6 19.9 244.2 0.0 6 0.307 M 57.7 1 -2.6 0.33 18 18.4 321.1 0.33 18.4 19.2 204.6 0.33 17.5 18. 8 307.3 0.0 7 0.372 M 57.8 1 -6.9 0.33 16.7 17.2 323 0.33 16.9 17.9 306.8 0.33 16.2 17. 5 325.2 0.0 8 0.375 M 57.5 1 -10.9 0.33 15.3 15. 7 343.8 0.33 15.8 16.6 244.7 0. 33 15.2 16.4 252.2 0.0 9 0.394 M 60.3 1 -15 0.33 13.9 14.2 260.8 0.33 14. 3 15.2 205 0.33 13.4 14.7 288.6 0.0 10 0.309 M 59.2 1 -26.7 0.33 12.1 12. 5 295.8 0.33 12.3 13.4 261 0.33 11.4 12.7 323.8 0.0 11 0.395 M 60 1 -31.2 0.33 10.3 10.5 254.4 0.33 10. 8 11.8 162.3 0.33 9.9 11 220.1 0.0 12 0.369 M 61.6 1 -45 0.33 8.1 8.4 297.3 0.33 8.5 9.7 249.7 0.33 7.7 8.9 287.8 0.0 13 0.33 M 59.7 1 -44.2 0.33 6 6.1 225.4 0.33 6.2 7.5 176.6 0.33 5.1 6.3 258.4 0.0 14 0.338 M 63.9 1 -65.8 0.33 3.2 3. 4 276.9 0.33 3.4 5 209.8 0.33 2.2 3.4 289.7 0.0 15 0.414

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139EXP 11 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P M 62.7 0.652 -67.9 0.33 0.7 0.7 277.5 0.33 1 2.4 219.4 0. 33 0.1 1 245.8 0.0 16 0.322 SW 63.7 0.05 -68.7 0.33 -2.2 -2.2 313.4 0.33 -2 -0.5 259.1 0.33 -3.1 -2.1 337.2 3.3 17 0.417 SW 64.5 0.049 -67.9 0.33 -4.6 -4.8 180.9 0.33 -4 .7 -3.2 153.9 0.33 -5.8 -5 203.5 3.1 18 0.346 SW 68.5 0.046 -106.4 0.33 -7.8 -7.9 196.5 0.33 -8 .1 -6.3 165.3 0.33 -9.4 -8.5 220.6 1.9 19 0.368 SW 73.5 0.044 -122.1 0.33 -11.5 11.5 211.1 0.33 -12.3 -10.3 201.4 0. 33 -13.5 -12.6 243.6 2.7 20 0.309 SW 74.9 0.043 -132.8 0.33 -15.2 15.3 175.4 0.33 -16.4 -14.3 163.3 0.33 -17.8 -17 208.5 2.4 21 0.388 SW 76.8 0.042 -164.7 0.33 -18.6 18.8 144.2 0.33 -20.2 -18.1 133.8 0. 33 -21.8 -21.3 182.5 3.5 22 0.36 SW 84.8 0.039 -185.5 0.33 -22.8 22.9 174.6 0.33 -24.6 -22.3 159 0. 33 -26.2 -25.9 200.7 3.4 23 0.371 SW 83.5 0.039 -185 0.33 -26.1 -26. 5 151.3 0.33 -28.5 -26.3 145.4 0. 33 -30.3 -30.2 196.7 3.1 24 0.315 SW 84.3 0.039 -184.9 0.33 -29.8 30.2 162.2 0.33 -32.4 -30.2 149.2 0. 33 -34.2 -34.3 190.4 3.2 25 0.319 SW 87.9 0.037 -185.3 0.33 -33.6 34.1 170.4 0.33 -36.6 -34.3 160.3 0. 33 -38.4 -38.7 210.7 3.3 26 0.334 SW 87.9 0.037 -185 0.33 -37 -37.6 155.5 0.33 -40. 4 -38.2 151.2 0.33 -42.2 -42.8 197.1 2.7 27 0.269 SW 91.4 0.036 -185.5 0.33 -40.4 41.1 156.1 0.33 -44.1 -41.9 151.1 0. 33 -45.9 -46.7 196.6 3.5 28 0.309 SW 93.8 0.036 -185.3 0.33 -43.8 44.6 160.1 0.33 -48 -45.7 160.1 0. 33 -49.8 -50.8 209.9 4.7 29 0.308 SW 96.5 0.035 -185.1 0.33 -47 -48 154.4 0.33 -51. 3 -49.2 142 0.33 -53.2 -54.5 196.8 3.9 30 0.297 SW 96.9 0.035 -185.3 0.33 -50.2 51.3 154.7 0.33 -54.8 -52.7 150.2 0. 33 -56.6 -58.1 197.4 3.6 31 0.354 SW 102.3 0.034 -185.4 0.33 -53.8 54.8 171.5 0.33 -58.5 -56.4 164 0. 33 -60.2 -61.8 211.4 4.4 32 0.328 SW 99.4 0.035 -185.1 0.33 -56.7 58 149.3 0.33 -61.8 -59.8 146.9 0. 33 -63.5 -65.4 204.9 4.6 33 0.346 SW 100 0.035 -185.3 0.33 -59.7 61.1 153.2 0.33 -64.8 -63 144.1 0. 33 -66.4 -68.6 186.2 2.9 34 0.31 SW 104.5 0.034 -185.2 0.33 -62.9 64.3 161.8 0.33 -68.1 -66.3 155.6 0. 33 -69.5 -71.8 197.5 4.6 35 0.337 SW 100 0.035 -185.3 0.33 -65.5 -67.1 143 0.33 -71. 1 -69.4 146.4 0.33 -72.6 -75 202.1 3.4 36 0.324 SW 104.2 0.034 -185.4 0.33 -68.8 70.4 171.1 0.33 -74.1 -72.5 149.8 0. 33 -75.5 -78.1 197.9 4.4 37 0.355 SW 103.8 0.035 -185.1 0.33 -71.4 73.2 142.2 0.33 -77.3 -75.7 169.1 0. 33 -78.5 -81.3 205.8 4.7 38 0.381 SW 105 0.035 -184.9 0.33 -74.3 -76.2 162 0.33 -80 -78.6 142.2 0.33 -81.1 -84.1 194.2 4.4 39 0.327 SW 106.2 0.035 -185.3 0.33 -77.1 78.9 150.9 0.33 -83.2 -81.8 172.3 0. 33 -84.1 -87.2 211.4 5.7 40 0.318 SW 110.7 0.034 -185 0.33 -79.5 -81. 6 147.5 0.33 -85.7 -84.3 130.9 0. 33 -86.9 -90.1 206.9 4.6 41 0.339 SW 106.2 0.035 -185.5 0.33 -82.5 84.6 171.5 0.33 -88.5 -87.2 161.7 0. 33 -89.3 -92.7 190.1 5.8 42 0.326 SW 111 0.035 -185.3 0.33 -84.6 86.9 126.8 0.33 -91.3 -90 156.3 0. 33 -92.2 -95.7 219.8 5.2 43 0.328 SW 111.4 0.036 -185.3 0.33 -87 -89. 4 140.2 0.33 -93.6 -92.5 138.6 0. 33 -94.5 -98.3 196.9 5.8 44 0.317 SW 113.8 0.036 -185.4 0.33 -89.5 91.9 149.5 0.33 -96.4 -95.1 156.1 0. 33 -97.2 -101.1 220.9 4.8 45 0.341 SW 116.3 0.036 -185.5 0.33 -91.7 94.3 142.1 0.33 -98.5 -97.5 141.9 0. 33 -99.1 -103.3 181.7 5.2 46 0.289 SW 117 0.037 -185.8 0.33 -93.9 96.5 129.5 0.33 -101 -100 157.2 0.33 -101.7 -105.8 213.9 6.1 47 0.256 SW 115.9 0.038 -185.3 0.33 -95.7 98.4 118.6 0.33 -103 -102.1 127.7 0.33 -103.6 -108 188.9 5.6 48 0.27 SW 115.3 0.039 -185.4 0.33 -98 -100. 7 145.7 0.33 -105.2 -104.3 144.7 0.33 -105.7 -110.2 195.2 5.0 49 0.221 SW 118.8 0.04 -185.6 0.33 -100.1 -102. 9 139.3 0.33 -107.3 -106.5 144.2 0.33 -107.8 -112.4 202 6.0 50 0.298 SW 117.7 0.042 -185.6 0.33 -101.9 104.8 119 0.33 -109.7 -108.7 148.6 0.33 -110.3 -114.9 235.4 5.1 51 0.292 SW 118.3 0.044 -185.5 0.33 -103.7 -106. 7 123.7 0.33 -111.3 -110.5 115.9 0.33 -111.9 -116.8 188.7 3.4 52 0.284 SW 120.2 0.046 -185.6 0.33 -105.5 -108. 6 122.4 0.33 -113.2 -112.5 141.4 0.33 -113.7 -118.7 194.7 3.7 53 0.248

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140EXP 11 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 128.9 0.052 -185.6 0.33 -107.4 -110. 5 126.3 0.33 -115.5 -114.6 153.6 0.33 -116 -120.9 229.6 3.0 54 0.265 SW 134.2 0.058 -185.7 0.33 -109.1 112.3 125 0.33 -117 -116.4 127.3 0.33 -117.3 -122.6 179.8 3.6 55 0.29 SW 131.1 0.058 -185.5 0.33 -110.9 -114. 1 119.8 0.33 -119.3 -118.5 156.1 0.33 -119.8 -124.9 256.8 3.1 56 0.255 SW 131.3 0.059 -185.7 0.33 -112.5 -115. 9 125.6 0.33 -120.4 -119.9 106.2 0.33 -120.7 -126.3 157.2 4.7 57 0.261 SW 124 0.059 -185.5 0.33 -114.1 -117. 5 115.7 0.33 -122.5 -121.9 158.3 0.33 -122.8 -128.2 228.3 3.9 58 0.29 SW 124.1 0.062 -185.6 0.33 -115.8 -119. 2 120.7 0.33 -124.1 -123.6 134.7 0.33 -124.3 -129.9 207 2.9 59 0.305 SW 120.1 0.064 -186 0.33 -117.7 -121. 2 148.7 0.33 -125.9 -125.5 162.3 0.33 -125.8 -131.5 201.3 3.2 60 0.268 SW 113.9 0.066 -185.6 0.33 -119.5 123 139.5 0.33 -127.6 -127.3 159.5 0.33 -127.5 -133.2 223.3 3.9 61 0.246 SW 111.8 0.067 -185.6 0.33 -121.6 -125. 2 172.9 0.33 -129.7 -129.4 180.1 0.33 -129.5 -135.2 258.5 4.7 62 0.33 SW 108.4 0.067 -185.8 0.33 -123.2 127 139.7 0.33 -131.2 -131.1 163.8 0.33 -130.7 -136.7 197.4 6.4 63 0.326 SW 103.9 0.069 -185.8 0.33 -124.7 -128. 5 126.2 0.33 -132.7 -132.8 159.7 0.33 -132 -138 196 4.4 64 0.272 SW 104.9 0.068 -185.7 0.33 -126.5 -130. 3 147.6 0.33 -134.4 -134.5 177.5 0.33 -133.6 -139.6 226 5.2 65 0.285 SW 100.7 0.069 -185.8 0.33 -127.9 131.9 134.1 0.33 -135.8 -136 156 0.33 -134.8 -141 204.6 2.9 66 0.317 SW 101.4 0.069 -185.6 0.33 -129.2 -133. 3 123.8 0.33 -136.9 -137.3 136.3 0.33 -135.9 -142.2 195.5 4.1 67 0.397 SW 100 0.069 -185.6 0.33 -130.7 -134. 8 134.6 0.33 -138.6 -139 183.1 0.33 -137.5 -143.7 231.4 6.4 68 0.313 SW 99.7 0.068 -185.9 0.33 -131.3 -135. 5 47.1 0.33 -139.8 -140.3 162.6 0.33 -138.6 -145 202.7 3.5 69 0.335 SW 99.1 0.068 -185.8 0.33 -134 138 249 0.33 -141.2 -141.8 181.9 0.33 -139.6 -146.1 195.6 4.4 70 0.391 SW 99.5 0.068 -185.6 0.33 -135.2 -139. 5 145.2 0.33 -142.6 -143.3 182.1 0.33 -140.9 -147.4 221.3 2.6 71 0.382 SW 96.8 0.069 -185.7 0.33 -136.7 -141 147.4 0.33 -144.3 -145 214 0.33 -142.4 -148.9 250.8 4.7 72 0.413 SW 98.7 0.067 -185.9 0.33 -137.7 -142. 3 121.3 0.33 -145.3 -146.1 147.9 0.33 -143.5 -150.2 220.9 2.9 73 0.505 SW 99.6 0.067 -185.8 0.33 -139 -143. 6 145 0.33 -146.2 -147.2 146.7 0.33 -144.4 -151.2 193.9 4.2 74 0.476 SW 96.3 0.068 -185.9 0.33 -140.2 -144. 9 130.2 0.33 -147.6 -148.6 197.1 0.33 -145.6 -152.3 224.3 4.2 75 0.467 SW 98.9 0.066 -185.9 0.33 -141.5 -146. 2 146.4 0.33 -148.9 -149.9 199.4 0.33 -146.7 -153.5 226.2 3.9 76 0.639 SW 93.7 0.067 -186.1 0.33 -142.6 147.4 141.8 0.33 -149.8 -151 156.6 0.33 -147.6 -154.6 218 3.5 77 0.498 SW 93 0.067 -186 0.33 -144.1 -148.8 161.9 0.33 -151.3 -152.4 236.6 0.33 -148.9 -155.8 250.9 3.3 78 0.473 SW 92.4 0.067 -185.8 0.33 -145.2 150 146.2 0.33 -152.5 -153.7 217.5 0.33 -149.9 -156.9 236.1 6.1 79 0.428 SW 89.1 0.069 -185.9 0.33 -146.2 151 119.1 0.33 -153.7 -154.9 210.3 0.33 -151.2 -158.2 272.8 5.9 80 0.372 SW 91.5 0.068 -185.9 0.33 -147.3 152.2 155.2 0.33 -154.6 -156 200.9 0.33 -152 -159.1 225.2 4.0 81 0.428 SW 89.2 0.069 -185.6 0.33 -148.4 153.3 139.3 0.33 -155.7 -157.1 209 0.33 -153 -160.2 261.9 3.8 82 0.41 SW 91.5 0.068 -185.8 0.33 -149.5 -154. 5 165.2 0.33 -156.8 -158.2 214.8 0.33 -154.1 -161.3 276 6.5 83 0.402 SW 88.4 0.069 -185.8 0.33 -150.4 -155. 5 128.8 0.33 -157.6 -159.2 221.6 0.33 -154.7 -162.1 207 5.1 84 0.46 SW 89.1 0.068 -186.3 0.33 -151.2 156.4 122.7 0.33 -158.3 -160 180.7 0.33 -155.3 -162.7 196.6 5.2 85 0.494 SW 90.1 0.068 -185.8 0.33 -152.1 -157. 3 138.1 0.33 -159.4 -160.9 218.7 0.33 -156.5 -163.8 297 4.1 86 0.515 SW 87.7 0.068 -185.8 0.33 -152.7 158 103 0.33 -161.2 -161.7 119.1 0.33 -160.2 -167 815.9 3.9 87 0.428 SW 90.5 0.095 -185.5 0.42 -154.3 -158. 8 92.7 0.42 -171.2 -167.7 1546.8 0.17 -183 -187.8 6990.7 4.0 88 0.309 SW 92.7 0.065 -185.4 -159.9 -183.8 -189.6 5.1 89 0.298

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141EXP 12 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 59.9 1 13.1 0.33 22.2 23.2 1083.8 0.33 22.5 23.5 859.9 0.33 21.8 23.5 876.7 0.0 1 0.404 N 60 1 11.4 0.33 22.5 22.9 33.5 0.33 22.5 23.1 92.8 0. 33 21.8 23 208.5 0.0 2 0.407 N 59.8 1 10.3 0.33 22 22.5 256.2 0.33 22.2 22.8 148 0.33 21.5 22.7 171.1 0.0 3 0.426 N 59.2 1 8.9 0.33 21.4 21.8 325.7 0.33 21.6 22.2 245.5 0.33 20.8 22.1 298.9 0.0 4 0.413 N 58.2 1 7.5 0.33 21.3 21.6 95.3 0.33 21.4 21.9 98.1 0.33 20.7 21.8 120.1 0.0 5 0.432 N 60.8 1 5.9 0.33 20.8 21.2 210.6 0.33 21 21.7 74.4 0.33 20.2 21.4 185.7 0.0 6 0.51 N 60.2 1 4.5 0.33 20.2 20. 6 234.4 0.33 20.4 21 237 0.33 19.8 20.9 182.8 0.0 7 0.428 N 60.8 1 2.9 0.33 19.6 20 258.4 0.33 19.8 20.5 162.7 0. 33 19 20.2 285.3 0.0 8 0.422 N 60.8 1 1.5 0.33 18.9 19.2 312.4 0.33 19.3 19.9 160.8 0.33 18.5 19.6 220.8 0.0 9 0.411 N 60.2 1 0.2 0.33 18.3 18.6 225.1 0.33 18.7 19.3 159.4 0. 33 18 19.1 187.7 0.0 10 0.452 N 59.7 1 -1.4 0.33 17.7 17.9 243.4 0.33 18 18.7 175 0.33 17.3 18.4 238.2 0.0 11 0.428 N 61.4 1 -3.5 0.33 17 17.2 233.8 0.33 17.3 17.9 191.2 0.33 16.6 17. 7 222.2 0.0 12 0.515 N 62.9 1 -5.6 0.33 16.3 16.4 238.7 0.33 16. 6 17.3 134.6 0.33 15.8 16.9 228.4 0.0 13 0.431 N 62.3 1 -8.2 0.33 15.6 15.7 196.4 0.33 15. 8 16.5 178.4 0.33 15.1 16.1 208.6 0.0 14 0.408 N 62.6 1 -10.4 0.33 14.8 14. 9 234.4 0.33 15.2 15.9 125.1 0. 33 14.4 15.4 204.4 0.0 15 0.417 N 61.1 1 -12 0.33 13.8 13.9 259.4 0.33 14. 3 15 150.2 0.33 13.5 14.5 205.8 0.0 16 0.485 N 61.2 1 -15.8 0.33 12.9 12. 9 211.3 0.33 13.2 14 176.2 0.33 12.4 13.4 231.1 0.0 17 0.516 N 64.2 1 -22 0.33 11.8 11.8 240.8 0.33 12. 2 13 163.1 0.33 11.5 12.4 203.6 0.0 18 0.465 N 63.1 1 -23.1 0.33 10.9 10.9 207 0.33 11. 2 12 144.4 0.33 10.4 11.3 238.8 0.0 19 0.403 N 63.8 1 -24 0.33 9.8 9.7 228.3 0.33 10.4 11.1 103.4 0.33 9.4 10. 3 185.6 0.0 20 0.424 N 64 1 -30.2 0.33 8.7 8.6 198.9 0.33 9.1 9.9 166.6 0.33 8.3 9. 2 193.2 0.0 21 0.49 N 63.2 1 -34.1 0.33 7.5 7.4 226.5 0.33 7. 9 8.8 152.9 0.33 6.9 7.8 250 0.0 22 0.507 N 62.5 1 -32.7 0.33 6.2 5.9 242.3 0.33 6. 7 7.6 136.9 0.33 5.7 6.5 213.6 0.0 23 0.513 N 63.9 1 -39.1 0.33 4.9 4.6 235.3 0.33 5. 3 6.1 184.4 0.33 4.5 5.2 219.9 0.0 24 0.482 N 64.6 1 -38.1 0.33 3.6 3.3 171.3 0.33 4 4.9 110.3 0.33 3.1 3. 7 180.7 0.0 25 0.409 N 66.7 1 -55.8 0.33 1.8 1.5 271 0.33 2. 2 3.2 193 0.33 1.2 2 267.1 0.0 26 0.491 N 62.8 1 -47 0.33 0.5 0.1 205.6 0.33 1 1.8 130.5 0.33 0.2 0. 7 172.2 0.0 27 0.498 N 62.9 1 -53.7 0.33 -0.9 -1.4 171.9 0.33 -0.5 0.4 120.9 0.33 -1.3 -0.8 172.2 0.0 28 0.392 N 72.1 1 -65.9 0.33 -2.4 -2.9 130.4 0.33 -2.1 -1.2 96.6 0.33 -2.9 -2.4 136 0.0 29 0.446 N 71 1 -91.2 0.33 -4.5 -4.9 147.5 0.33 -4.5 -3.2 120.9 0.33 -5.6 -5 186.2 0.0 30 0.421 N 71.8 1 -105.8 0.33 -6.8 -7.2 170.4 0.33 -7 -5.7 142.5 0.33 -8.1 -7.5 185.4 0.0 31 0.467 N 68.2 1 -106.8 0.33 -8.9 -9.4 147.1 0.33 -9.2 -7.9 114.2 0.33 -10.3 -9.9 163.9 0.0 32 0.378 N 80.2 1 -116.3 0.33 -11 -11.5 138 0.33 -11.6 -10.2 117.3 0.33 -12.9 -12.6 170.5 0.0 33 0.428 N 77 1 -124.7 0.33 -13.4 -13.9 152.1 0.33 -14.3 -12.8 132.2 0.33 -15.6 -15.4 183.2 0.0 34 0.397 N 76.7 1 -127.1 0.33 -15.7 -16. 3 150.1 0.33 -16.8 -15.3 126.9 0. 33 -18.2 -18.1 179.2 0.0 35 0.418 N 81.2 1 -128.1 0.33 -17.7 -18. 5 132.7 0.33 -18.9 -17.5 103.9 0. 33 -20.2 -20.4 149.7 0.0 36 0.396 N 78.3 1 -132.5 0.33 -20.3 -21 152.7 0.33 -21.9 -20.2 136.4 0.33 -23.5 -23.5 199.2 0.0 37 0.4 N 81.9 1 -137.5 0.33 -22.6 -23. 4 119.1 0.33 -24.2 -22.7 99.7 0.33 -25.6 -26 127 0.0 38 0.401

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142EXP 12 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 86.6 1 -165.1 0.33 -24.7 -25. 6 96.1 0.33 -26.7 -25.2 85.9 0. 33 -28.3 -28.7 128.6 0.0 39 0.388 N 88.4 1 -185.7 0.33 -27.4 -28. 2 115.1 0.33 -29.7 -28 101.5 0.33 -31.4 -31.8 146.4 0.0 40 0.39 N 85.2 1 -186 0.33 -29.8 -30.7 107.7 0.33 -32.1 -30.6 96.9 0.33 -33.6 -34.3 121.2 0.0 41 0.434 N 88.3 1 -185.3 0.33 -32 -33 101.7 0.33 -34.7 -33.1 93.3 0.33 -36.3 -37.1 136.5 0.0 42 0.441 N 89.3 1 -185.8 0.33 -34.3 -35. 4 106.8 0.33 -37.1 -35.5 83 0.33 -38.9 -39.8 137.2 0.0 43 0.438 N 90.2 1 -185.3 0.33 -36.7 -37. 8 110.7 0.33 -39.8 -38.2 104.9 0. 33 -41.5 -42.5 139.8 0.0 44 0.433 N 88.8 1 -185.2 0.33 -39 -40.2 111.5 0.33 -42 -40.5 85.7 0.33 -43.6 -44.9 125.2 0.0 45 0.398 SW 93.1 0.039 -185.7 0.33 -41.2 42.5 102.3 0.33 -44.5 -42.9 93.3 0. 33 -46.1 -47.5 136.1 2.2 46 0.341 SW 92.3 0.039 -185.3 0.33 -43.3 44.7 101.6 0.33 -46.9 -45.4 96 0. 33 -48.6 -50.1 140.2 1.8 47 0.42 SW 94.2 0.039 -185.9 0.33 -45.6 -47 108.4 0.33 -49.4 -47.8 96.8 0.33 -51 -52.6 140.9 1.6 48 0.424 SW 94.3 0.039 -185.7 0.33 -47.4 48.9 90.8 0.33 -51.5 -50 85.1 0. 33 -53.1 -54.9 130.2 2.2 49 0.375 SW 91.4 0.039 -185.9 0.33 -49.8 51.3 114.5 0.33 -53.8 -52.3 96.5 0. 33 -55.2 -57.2 130.3 2.2 50 0.401 SW 98.8 0.038 -185.7 0.33 -51.6 53.3 93.7 0.33 -55.9 -54.5 88.6 0. 33 -57.3 -59.4 130.3 2.1 51 0.385 SW 97.8 0.038 -185.7 0.33 -53.7 55.3 100.3 0.33 -58 -56.6 86.7 0. 33 -59.5 -61.7 135.3 2.9 52 0.368 SW 105.6 0.037 -185.8 0.33 -55.7 -57.4 102 0.33 -60.2 -58.7 87.4 0.33 -61.8 -64 142.5 2.4 53 0.381 SW 98.8 0.039 -185.8 0.33 -57.6 -59.4 96 0.33 -62.4 -61 97 0.33 -63.9 -66.3 139.9 2.6 54 0.389 SW 97.3 0.039 -185.8 0.33 -59.8 61.7 115.5 0.33 -64.4 -63.1 90.9 0. 33 -65.9 -68.4 135.7 2.6 55 0.388 SW 106.5 0.038 -185.3 0.33 -61.8 63.7 101.9 0.33 -66.7 -65.4 101.5 0. 33 -68.1 -70.7 146.6 4.0 56 0.366 SW 103.5 0.038 -185.9 0.33 -63.7 65.7 98.2 0.33 -68.8 -67.5 93.2 0. 33 -70.2 -72.9 142.4 4.0 57 0.453 SW 102.2 0.039 -186.2 0.33 -65.3 67.4 88.6 0.33 -70.5 -69.3 79.6 0.33 -72 -74.9 132.8 4.7 58 0.385 SW 102.8 0.039 -185.9 0.33 -67.2 69.3 98.5 0.33 -72.6 -71.4 96.4 0. 33 -73.9 -76.9 135.7 3.0 59 0.426 SW 100.8 0.039 -185.6 0.33 -69.2 71.3 106.1 0.33 -74.4 -73.3 90.2 0. 33 -75.6 -78.7 130.4 3.1 60 0.39 SW 108.3 0.038 -185.3 0.33 -71.2 73.3 106.5 0.33 -76.6 -75.5 106.5 0.33 -77.8 -80.8 151 3.6 61 0.413 SW 105.7 0.039 -185.8 0.33 -73 75.2 98.6 0.33 -78.6 -77.5 101.1 0.33 -79.7 -83 149.5 4.4 62 0.392 SW 104.5 0.039 -184.9 0.33 -74.8 77 99.3 0.33 -80.4 -79.5 95.9 0. 33 -81.3 -84.8 131.4 3.1 63 0.382 SW 103.5 0.039 -186.2 0.33 -76.5 78.8 95.6 0.33 -82.3 -81.3 91.7 0. 33 -83.2 -86.7 141.5 2.8 64 0.411 SW 104.9 0.039 -185.9 0.33 -78.3 80.7 104.7 0.33 -83.9 -83 84.2 0. 33 -84.8 -88.4 134.1 3.5 65 0.36 SW 110.8 0.039 -185.7 0.33 -80.2 -82.7 108.6 0.33 -86 -85.1 115 0. 33 -86.8 -90.4 149.6 4.0 66 0.378 SW 105 0.04 -185.9 0.33 -81.6 84.2 85.4 0.33 -87.5 -86.7 78 0. 33 -88.3 -92.1 133.1 4.0 67 0.438 SW 109.1 0.039 -186.1 0.33 -83.4 -86.1 106 0.33 -89.3 -88.5 97.9 0.33 -90 -93.8 141.1 4.1 68 0.369 SW 109 0.04 -185.9 0.33 -85.1 -87. 8 95.5 0.33 -91.2 -90.4 104.4 0. 33 -91.8 -95.7 150.4 3.9 69 0.409 SW 109.9 0.04 -186.3 0.33 -87 -89. 6 111.3 0.33 -93.2 -92.3 107.9 0. 33 -93.9 -97.8 171.9 3.1 70 0.347 SW 114.3 0.04 -185.3 0.33 -88.6 91.4 102.2 0.33 -94.7 -94.1 98.8 0. 33 -95.2 -99.4 130.9 2.2 71 0.387 SW 120 0.04 -185.8 0.33 -90.1 -93 95.2 0.33 -96. 4 -95.7 91.6 0.33 -96.9 -101.1 147.7 4.4 72 0.331 SW 115.5 0.041 -186.1 0.33 -91.4 94.3 75.9 0.33 -98 -97.4 100.3 0. 33 -98.5 -102.8 148.5 3.5 73 0.358 SW 124.3 0.04 -186 0.33 -93 -95. 9 95.5 0.33 -99.6 -99 92.4 0.33 -100.1 -104.5 151.4 3.8 74 0.34 SW 124.6 0.041 -185.9 0.33 -94.4 -97. 4 88.9 0.33 -101.1 -100.6 97.7 0.33 -101.5 -106 136.8 5.0 75 0.406 SW 118.1 0.042 -186.5 0.33 -95.7 98.8 85.4 0.33 -102.6 -102 84.8 0.33 -103.1 -107.6 152.4 3.6 76 0.395

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143EXP 12 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 123 0.041 -185.7 0.33 -97.4 -100. 5 107.3 0.33 -104.2 -103.6 101.8 0.33 -104.7 -109.3 158.5 4.4 77 0.399 SW 111.4 0.043 -185.9 0.33 -98.2 -101. 5 58.3 0.33 -104.9 -104.6 53.2 0.33 -105.4 -110.3 106.4 3.1 78 0.385 SW 120.2 0.042 -186.3 0.33 -99.8 103 93.8 0.33 -106.9 -106.4 119.7 0.33 -107.1 -111.9 156.9 1.4 79 0.357 SW 119.6 0.043 -186.5 0.33 -101.4 -104. 6 108.3 0.33 -108.3 -107.8 91.5 0.33 -108.6 -113.4 155 2.3 80 0.327 SW 124.6 0.043 -186.1 0.33 -102.4 -105. 8 69.6 0.33 -109.4 -109.1 81.7 0.33 -109.7 -114.7 133.3 2.5 81 0.335 SW 129.2 0.044 -186 0.33 -103.4 -106. 9 70.1 0.33 -110.5 -110.2 70.7 0.33 -110.9 -116 142.4 2.9 82 0.403 SW 130.1 0.045 -186.5 0.33 -104.7 108.1 83.8 0.33 -112 -111.6 98.7 0.33 -112.4 -117.4 157.5 3.6 83 0.349 SW 139.9 0.045 -185.8 0.33 -106 -109. 5 88.8 0.33 -113.2 -112.9 84.3 0.33 -113.6 -118.7 146.6 3.8 84 0.373 SW 128.7 0.047 -186.1 0.33 -106.7 110.4 56.7 0.33 -114 -113.8 55.1 0.33 -114.2 -119.6 112.1 3.6 85 0.359 SW 133.2 0.046 -186.5 0.33 -108.3 111.7 95.7 0.33 -115.6 -115.3 116 0.33 -115.6 -120.9 148.7 1.8 86 0.376 SW 131.4 0.047 -186.1 0.33 -109.1 -112. 8 66.1 0.33 -116.4 -116.2 60.6 0.33 -116.6 -122 137.8 3.3 87 0.317 SW 127.3 0.047 -185.9 0.33 -110.1 -113. 7 66.9 0.33 -117.5 -117.3 75.5 0.33 -117.7 -123.2 146.9 2.8 88 0.295 SW 133.4 0.048 -186.2 0.33 -111.4 115 88.4 0.33 -118.8 -118.6 95.4 0.33 -118.8 -124.3 146.6 2.1 89 0.328 SW 137.2 0.048 -186.1 0.33 -112.1 -115. 9 62.2 0.33 -119.6 -119.5 69.2 0.33 -119.7 -125.3 129.7 3.0 90 0.331 SW 132.3 0.05 -186.1 0.33 -113.2 116.9 65.5 0.33 -121 -120.7 93.8 0.33 -121.1 -126.7 171.6 5.8 91 0.32 SW 146.7 0.052 -186.1 0.33 -114.5 -118. 2 97.2 0.33 -122.1 -121.9 85.7 0.33 -122.2 -127.9 158.6 3.1 92 0.36 SW 147.7 0.052 -186.2 0.33 -114.9 118.9 40.3 0.33 -122.9 -122.7 60 0.33 -123.1 -128.9 139.3 2.9 93 0.328 SW 140.7 0.052 -186.2 0.33 -116 -119. 8 68.6 0.33 -124.1 -123.8 90.2 0.33 -124.3 -130 162.5 3.4 94 0.331 SW 137.6 0.053 -186 0.33 -117.2 -121 90.8 0.33 -124.9 -124.9 82.3 0.33 -124.9 -130.9 128.9 2.7 95 0.356 SW 145.9 0.053 -186.3 0.33 -117.7 -121. 7 40.6 0.33 -125.8 -125.8 71.9 0.33 -125.9 -131.8 146.6 2.9 96 0.343 SW 145.3 0.055 -186.2 0.33 -119.1 -122. 9 95.1 0.33 -127.1 -126.9 95.9 0.33 -127.2 -133 178 3.5 97 0.339 SW 143.2 0.057 -186.1 0.33 -119.4 -123. 5 35.1 0.33 -127.6 -127.6 51.1 0.33 -127.6 -133.8 122.7 6.7 98 0.334 SW 142.1 0.06 -186.2 0.33 -120.9 124.7 97.4 0.33 -129 -128.9 119.7 0.33 -129 -134.9 179.9 3.1 99 0.336 SW 152.5 0.064 -186 0.33 -121.1 -125. 3 34.8 0.33 -129.1 -129.3 24.8 0.33 -129.1 -135.4 100.2 2.6 100 0.317 SW 151.7 0.063 -186.7 0.33 -122.3 -126. 3 80.3 0.33 -130.6 -130.5 110.5 0.33 -130.6 -136.7 193.5 3.2 101 0.342 SW 137.3 0.06 -186.5 0.33 -122.9 127.1 56.4 0.33 -131 -131.1 50.7 0.33 -130.9 -137.2 112 3.2 102 0.267 SW 135.9 0.061 -185.7 0.33 -124.1 -128. 2 88.9 0.33 -132.2 -132.3 118.6 0.33 -131.7 -137.9 141.1 2.6 103 0.299 SW 144.4 0.063 -186 0.33 -124.7 -128. 9 52.6 0.33 -132.9 -133 53.9 0.33 -132.7 -139 172 3.1 104 0.36 SW 169.9 0.068 -186.4 0.33 -125.5 -129. 7 65.7 0.33 -133.4 -133.7 72.6 0.33 -133 -139.5 110.4 1.9 105 0.352 SW 154.8 0.073 -186.7 0.33 -126 -130. 3 42.7 0.33 -134.3 -134.4 65.5 0.33 -134 -140.4 167.9 7.5 106 0.284 SW 138.5 0.073 -186.3 0.33 -127.4 131.5 100.9 0.33 -135.6 -135.8 140 0.33 -135.1 -141.4 180.3 4.1 107 0.316 SW 148.9 0.078 -185.9 0.33 -127.5 132 26.8 0.33 -135.5 -136.1 25.1 0.33 -134.8 -141.5 66.7 2.4 108 0.321 SW 163.9 0.079 -186.4 0.33 -128.5 -132. 8 70.7 0.33 -136.6 -136.9 99.8 0.33 -136 -142.4 169.1 3.6 109 0.338 SW 158.3 0.078 -186.5 0.33 -129.7 133.9 101.6 0.33 -137.8 -138 115.8 0.33 -137.1 -143.5 194.8 3.1 110 0.313 SW 151.2 0.076 -186.3 0.33 -129.8 -134. 3 13.7 0.33 -137.9 -138.5 46.8 0.33 -137.2 -143.9 98.9 4.0 111 0.299 SW 144.9 0.077 -186 0.33 -130.9 -135. 2 86.4 0.33 -139.1 -139.5 113.1 0.33 -138.4 -144.9 194 1.9 112 0.313 SW 157.9 0.081 -186.2 0.33 -131.7 136.1 75 0.33 -139.7 -140.2 78.8 0.33 -138.9 -145.6 146.9 3.2 113 0.368 SW 176.4 0.084 -186.3 0.33 -132 -136. 5 28.9 0.33 -140.2 -140.8 75.8 0.33 -139.2 -146 111.3 3.0 114 0.337

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144EXP 12 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 148.3 0.079 -186.7 0.33 -133.4 -137. 8 125.3 0.33 -141.1 -141.6 88.8 0.33 -140.3 -146.9 186.9 6.0 115 0.322 SW 139.1 0.08 -186 0.33 -133.8 138.4 49 0.33 -141.7 -142.4 93 0.33 -140.6 -147.4 120.5 3.6 116 0.303 SW 157.4 0.085 -186.4 0.33 -134.3 -138. 9 38.7 0.33 -142.2 -142.9 66.6 0.33 -141.1 -147.9 139.9 3.3 117 0.375 SW 164.3 0.085 -186.3 0.33 -135.5 140 110.7 0.33 -143.2 -143.8 117.2 0.33 -142.1 -148.8 181.2 4.7 118 0.352 SW 141 0.084 -186.7 0.33 -135.9 -140. 6 47.8 0.33 -143.9 -144.5 86.2 0.33 -142.7 -149.5 168.9 6.0 119 0.308 SW 143.7 0.088 -186.3 0.33 -137 -141. 6 109.2 0.33 -144.7 -145.4 105.6 0.33 -143.5 -150.3 172.4 3.6 120 0.314 SW 146.4 0.089 -186.1 0.33 -137.1 142 23.1 0.33 -145.2 -145.9 61.3 0.33 -144.2 -151.1 174 3.2 121 0.376 SW 158.1 0.088 -186.1 0.33 -138.6 -143. 3 141.9 0.33 -146.1 -146.9 141.6 0.33 -144.7 -151.6 148.2 2.2 122 0.307 SW 147.4 0.089 -186.6 0.33 -138.9 -143. 7 33.8 0.33 -146.9 -147.8 125.8 0.33 -145.3 -152.2 160.5 2.5 123 0.314 SW 146.2 0.088 -186.1 0.33 -139.2 -144. 2 41.9 0.33 -146.9 -147.9 24.8 0.33 -145.4 -152.5 113.4 3.4 124 0.374 SW 135.9 0.083 -186.3 0.33 -140.4 -145. 2 116.8 0.33 -147.8 -148.8 133.1 0.33 -146.1 -153.1 162.8 1.9 125 0.354 SW 134.8 0.086 -186.1 0.33 -140.8 -145. 8 52.2 0.33 -148.2 -149.3 78.3 0.33 -146.4 -153.5 118.2 2.1 126 0.339 SW 135.1 0.083 -186.4 0.33 -141.6 146.5 85.4 0.33 -148.9 -150 109.3 0.33 -147 -154 154.8 3.3 127 0.39 SW 130.8 0.079 -186.6 0.33 -143 -147. 8 159.9 0.33 -150.1 -151.1 151.1 0.33 -148.3 -155.2 244.5 3.3 128 0.331 SW 129.4 0.08 -186.5 0.33 -143 -148. 1 14.6 0.33 -150.5 -151.7 104.2 0.33 -148.6 -155.8 152.7 4.0 129 0.34 SW 135.5 0.081 -186.5 0.33 -143.4 148.6 51.4 0.33 -150.5 -152 60.2 0.33 -148.4 -155.7 60.4 1.9 130 0.381 SW 126.7 0.083 -186.7 0.33 -144.7 -149. 6 137.5 0.33 -151.6 -152.9 164.2 0.33 -149.2 -156.3 169.1 3.1 131 0.349 SW 136 0.09 -186.6 0.33 -145.3 -150. 4 86.7 0.33 -152.6 -153.7 115.5 0.33 -150.7 -157.7 297.6 4.3 132 0.322 SW 137.4 0.091 -186.4 0.33 -145.2 -150. 6 11.7 0.33 -152.4 -153.9 53.9 0.33 -150.2 -157.7 51.2 2.0 133 0.338 SW 138 0.093 -186.2 0.33 -146.8 -151. 7 160.3 0.33 -154.3 -155.2 220.1 0.33 -152.2 -159.2 344.9 3.9 134 0.284 SW 143.1 0.09 -186.6 0.33 -146.5 -151. 9 3.2 0.33 -154.4 -155.6 70.2 0.33 -153.9 -161.1 492.2 5.1 135 0.297 SW 145 0.089 -186.3 0.42 -147.9 -152. 6 88.4 0.42 -161.6 -159.1 694.5 0.17 -174.7 -179.5 4661.5 4.0 136 0.275 SW 131.3 0.091 -185.9 0.42 -153.6 153.7 49.7 0.42 -180.4 -173.7 2917 0.17 -179.4 -184.2 6111.1 3.5 137 0.282 SW 145.6 0.089 -186.7 -154.4 -181 -185.4 4.7 138 0.32 SW 135.6 0.091 -186.4 -156.2 -183.1 -185.9 2.5 139 0.218 SW 137 0.092 -186.1 -158.3 -183.6 -185.3 3.4 140 0.326 SW 147.6 0.09 -186.2 -161.7 -185.2 -186.1 2.8 141 0.25 SW 139.7 0.093 -186.2 -163.9 -185.6 -186.2 2.3 142 0.308 SW 147.1 0.09 -186.3 -167 -185.5 -185.8 5.5 143 0.301 EXP 13 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 59.1 1 9.9 0.33 22.2 23.2 770.2 0.33 22.6 23.6 557.1 0.33 21.9 23.5 677.3 0.0 1 0.311 N 58.9 1 7.7 0.33 22.2 22.7 325.9 0.33 22.2 22.9 228.8 0.33 21.5 22.8 264.1 0.0 2 0.332 N 59.1 1 5.7 0.33 21.3 21. 9 302.6 0.33 21.6 22.4 252.5 0.33 20.7 22 305 0.0 3 0.308 N 59.9 1 2.9 0.33 20.6 21 302.4 0.33 21 21. 6 172.8 0.33 20.3 21.5 158.8 0.0 4 0.327

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145EXP 13 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 60.2 1 0.7 0.33 19.9 20. 3 356 0.33 20.2 21 316.1 0.33 19.4 20.6 277.2 0.0 5 0.32 N 61.6 1 -2.3 0.33 18.8 19.3 304.7 0.33 19. 1 20 248.4 0.33 18.3 19.6 297.5 0.0 6 0.279 N 61.1 1 -6 0.33 17.9 18.3 324 0.33 18.2 19 207.5 0.33 17.4 18.7 242.3 0.0 7 0.3 N 63.1 1 -8.9 0.33 16.9 17.2 361.8 0.33 17. 1 18 276.7 0.33 16.3 17.5 249.4 0.0 8 0.338 N 63.3 1 -15.6 0.33 15.4 15. 7 268.4 0.33 16 16.9 218.2 0.33 15.1 16.3 269.4 0.0 9 0.288 N 61.7 1 -16.1 0.33 14 14.3 272.3 0.33 14.5 15.5 250.3 0.33 13.6 14.9 321.5 0.0 10 0.392 N 63.2 1 -18.1 0.33 13 13.1 247.2 0.33 13.4 14.3 165.4 0.33 12.5 13.6 255.3 0.0 11 0.31 N 60.7 1 -22.8 0.33 11.8 11. 8 193.7 0.33 12.1 13 184.4 0.33 11.2 12.2 238.6 0.0 12 0.358 N 63.4 1 -27.7 0.33 10.1 10. 2 253.9 0.33 10.6 11.6 222.6 0. 33 9.7 10.7 210.7 0.0 13 0.308 N 64.7 1 -42.5 0.33 8.5 8.5 188.4 0.33 8. 7 9.9 155.7 0.33 7.6 8.7 221.5 0.0 14 0.335 SW 64 1 -58.7 0.33 6.2 6.3 209.1 0.33 6. 5 7.8 187.7 0.33 5.2 6.4 243 1.4 15 0.343 N 66.8 1 -64.1 0.33 4.5 4.5 312.4 0.33 4. 5 5.8 277.9 0.33 3.3 4.3 204.6 0.0 16 0.339 SW 67.7 0.043 -69.5 0.33 1.8 1.8 191.7 0.33 2.1 3.5 125.4 0. 33 0.9 1.8 217.3 1.9 17 0.254 N 66.7 0.044 -79.4 0.33 -0.5 -0.6 172.1 0.33 -0 .5 1 177.2 0.33 -1.7 -0.8 236.6 0.0 18 0.322 SW 66.1 0.044 -82 0.33 -2.8 -3 222.1 0.33 -2.7 -1.4 186.9 0.33 -3.8 -3.2 189.2 1.5 19 0.324 SW 71.6 0.041 -93 0.33 -5.1 -5.3 172.4 0.33 -5.3 -3.9 157.9 0.33 -6.5 -5.8 204.2 2.2 20 0.3 SW 68.4 0.043 -100.4 0.33 -7.6 -7.9 194.6 0.33 -7 .8 -6.4 176.4 0.33 -8.9 -8.4 158.5 2.0 21 0.322 N 76.4 0.04 -126 0.33 -10.7 -10. 8 129.9 0.33 -11.5 -9.7 108.7 0. 33 -12.8 -12.1 216.7 0.0 22 0.288 SW 80.6 0.039 -135 0.33 -13.7 -14 138.8 0.33 -14. 9 -13 139.2 0.33 -16.4 -15.9 167.1 2.3 23 0.285 N 82.1 0.038 -177.7 0.33 -16.7 -17. 1 150.1 0.33 -18.3 -16.3 133.3 0. 33 -19.9 -19.6 159.3 0.0 24 0.289 SW 90.9 0.036 -185.1 0.33 -19.8 20.1 139.2 0.33 -21.8 -19.7 125.5 0. 33 -23.8 -23.5 173.7 2.6 25 0.255 SW 92.8 0.036 -185.8 0.33 -22.6 23.1 128.6 0.33 -25 -22.8 115.2 0. 33 -27.2 -27.2 166.9 2.2 26 0.293 SW 92.6 0.036 -185.3 0.33 -25.6 26.1 134.6 0.33 -28.4 -26.2 130.4 0. 33 -30.6 -30.8 166.9 3.0 27 0.262 SW 92.8 0.037 -185.1 0.33 -28.5 29.1 139.2 0.33 -31.7 -29.4 121.1 0. 33 -33.9 -34.3 170.7 3.5 28 0.235 SW 92.6 0.037 -184.6 0.33 -32.6 33 150.5 0.33 -35.9 -33.4 131.5 0. 33 -38.2 -38.6 206.8 2.9 29 0.241 SW 93.9 0.037 -185.6 0.33 -35.2 36 136.1 0.33 -38.8 -36.6 124.6 0. 33 -41.1 -41.9 166.8 4.2 30 0.235 SW 95.2 0.037 -184.9 0.33 -38.3 -39.1 144 0.33 -42.2 -39.9 121.1 0.33 -44.3 -45.3 173 3.8 31 0.256 SW 98.2 0.036 -185.5 0.33 -40.8 41.8 145.9 0.33 -44.9 -42.8 139.4 0. 33 -47.2 -48.4 164.3 4.2 32 0.26 SW 95 0.037 -185.5 0.33 -43.7 44.7 120.1 0.33 -48 -45.9 116.6 0. 33 -50 -51.4 166.1 3.1 33 0.256 SW 100.1 0.036 -185 0.33 -46.5 47.5 177.4 0.33 -51 -49 159.8 0. 33 -53.1 -54.6 176 3.5 34 0.26 SW 101.3 0.037 -185.4 0.33 -49 50.2 144.6 0.33 -53.7 -51.7 112.7 0.33 -56 -57.7 172.5 2.4 35 0.293 SW 104.4 0.036 -185.3 0.33 -51.5 52.8 124.9 0.33 -56.4 -54.4 112.1 0.33 -58.4 -60.4 158 4.0 36 0.273 SW 104.7 0.037 -185.7 0.33 -54.4 55.7 134.4 0.33 -59.2 -57.4 111.8 0.33 -61 -63.1 160.8 3.3 37 0.275 SW 104 0.037 -185.3 0.33 -56.7 -58.1 146 0.33 62 -60.2 125.8 0.33 -63.8 -66 174.4 4.1 38 0.292 SW 105.9 0.037 -185.5 0.33 -59.2 60.7 124.9 0.33 -64.4 -62.8 137.9 0.33 -66.1 -68.5 158 2.5 39 0.281 SW 106.8 0.037 -185.4 0.33 -61.4 -63 130.1 0.33 -67.2 -65.4 89.7 0.33 -69 -71.4 182.8 4.4 40 0.263 SW 106.6 0.038 -185.5 0.33 -63.9 -65.5 129.5 0.33 -69.6 -68 122 0. 33 -71.2 -73.9 158.4 3.9 41 0.234 SW 107.6 0.038 -185.5 0.33 -66.5 68.1 130 0.33 -72.2 -70.6 123.1 0. 33 -73.7 -76.5 170.3 4.6 42 0.269

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146EXP 13 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 108.4 0.038 -185.5 0.33 -68.8 -70. 6 142.9 0.33 -74.7 -73.1 120.5 0.33 -76.2 -79.1 174.8 3.9 43 0.26 SW 109 0.038 -185.5 0.33 -70.9 -72. 8 122.2 0.33 -77 -75.5 120.5 0.33 -78.5 -81.5 168.5 3.8 44 0.3 SW 111.2 0.038 -185.6 0.33 -73.2 75.2 119.1 0.33 -79.5 -78 112.4 0.33 -81 -84.2 182.2 4.8 45 0.251 SW 114.6 0.038 -185.5 0.33 -75.5 -77. 5 129.3 0.33 -81.8 -80.4 107.7 0.33 -83.1 -86.4 162.8 3.8 46 0.242 SW 118.1 0.039 -185.7 0.33 -77.4 -79. 6 115.3 0.33 -83.9 -82.5 98.9 0.33 -85.4 -88.8 175.1 3.3 47 0.254 SW 117 0.04 -185.8 0.33 -79.3 -81. 5 134 0.33 -86.2 -84.8 131.1 0.33 -87.6 -91.1 175.8 3.2 48 0.248 SW 124.7 0.04 -185.8 0.33 -81.4 -83. 6 137.8 0.33 -88.5 -87.1 108.7 0.33 -89.8 -93.5 181.6 4.0 49 0.253 SW 123.9 0.041 -185.1 0.33 -83.5 -85. 8 92.1 0.33 -90.7 -89.3 103.8 0.33 -92.1 -95.9 186.2 3.8 50 0.254 SW 129.1 0.042 -185.7 0.33 -85.1 -87. 5 121.9 0.33 -92.6 -91.2 81.5 0.33 -94.1 -98 175.9 3.6 51 0.276 SW 128.8 0.042 -185.6 0.33 -86.9 89.4 131.4 0.33 -94.3 -93 117.9 0.33 -95.7 -99.8 157.1 4.1 52 0.24 SW 130.1 0.042 -185.7 0.33 -88.7 -91. 2 116.8 0.33 -96.3 -95.1 109.3 0.33 -97.6 -101.8 172.8 3.4 53 0.311 SW 131.3 0.043 -185.6 0.33 -90.4 93 126.3 0.33 -98.1 -96.9 111.4 0.33 -99.6 -103.9 182.1 4.1 54 0.274 SW 126.4 0.044 -185 0.33 -92.3 -94. 8 112.1 0.33 -100.1 -98.9 119.4 0.33 -101.5 -105.9 182.6 4.7 55 0.251 SW 129.1 0.045 -185.6 0.33 -93.7 -96. 4 106.4 0.33 -101.8 -100.6 84.6 0.33 -103.2 -107.7 170.6 3.5 56 0.268 SW 132.4 0.046 -185.6 0.33 -95.4 98.2 110 0.33 -103.5 -102.4 113.6 0.33 -104.7 -109.3 161.7 2.5 57 0.259 SW 132.6 0.047 -185.3 0.33 -97.1 -99. 9 121.8 0.33 -105.1 -104.1 88.1 0.33 -106.4 -111.1 172.8 2.9 58 0.307 SW 137.6 0.048 -186.1 0.33 -98.7 101.6 114 0.33 -106.7 -105.7 90.2 0.33 -107.9 -112.7 167.3 5.6 59 0.287 SW 133.2 0.049 -185.6 0.33 -100.4 -103. 3 120.3 0.33 -108.4 -107.5 112.2 0.33 -109.5 -114.3 173.3 2.6 60 0.342 SW 135.3 0.049 -185.6 0.33 -102 105 122.7 0.33 -110 -109.2 110.3 0.33 -110.9 -115.9 166.1 2.2 61 0.385 SW 138.8 0.05 -185.8 0.33 -103.1 -106. 3 120.3 0.33 -111.2 -110.5 105.6 0.33 -112.1 -117.2 151.2 1.8 62 0.246 SW 135.4 0.05 -185.4 0.33 -104.9 108 88.4 0.33 -113 -112.1 66.1 0.33 -113.9 -119 193 4.0 63 0.316 SW 138.6 0.049 -185.5 0.33 -106.3 109.5 133.8 0.33 -114.4 -113.7 119 0.33 -115.3 -120.5 177.2 2.5 64 0.403 SW 132.2 0.051 -185.5 0.33 -107.6 -110. 8 101.3 0.33 -115.9 -115.2 86.5 0.33 -116.5 -121.8 157.4 4.7 65 0.302 SW 139.6 0.052 -185.5 0.33 -109.3 -112. 6 130.5 0.33 -117.2 -116.7 140.2 0.33 -117.7 -123.1 162.5 6.0 66 0.358 SW 138.3 0.054 -185.6 0.33 -110.5 -113. 8 91.7 0.33 -118.9 -118.2 65.2 0.33 -119.5 -124.9 204.7 3.0 67 0.325 SW 137.7 0.056 -185.2 0.33 -111.9 -115. 3 153.8 0.33 -119.9 -119.5 103.4 0.33 -120.3 -126 143.1 4.1 68 0.382 SW 137.1 0.057 -185.8 0.33 -113.2 116.7 76.2 0.33 -121.3 -120.9 109 0.33 -121.6 -127.2 169.8 7.7 69 0.39 SW 141.9 0.059 -185.8 0.33 -114.3 117.9 89.3 0.33 -122.2 -122 64.8 0.33 -122.5 -128.3 148.3 3.0 70 0.385 SW 130.2 0.059 -185.4 0.33 -116 -119. 5 129 0.33 -123.9 -123.6 114.5 0.33 -123.8 -129.5 164.9 2.4 71 0.389 SW 133.3 0.06 -185.8 0.33 -116.9 120.6 90.7 0.33 -124.8 -124.7 98 0.33 -124.8 -130.6 156.2 2.7 72 0.375 SW 136.3 0.063 -185.5 0.33 -118.4 -122. 1 111.8 0.33 -126.3 -126.1 68.9 0.33 -126.2 -131.9 184 2.5 73 0.318 SW 132.1 0.064 -185.8 0.33 -119.5 123.4 157 0.33 -127.3 -127.3 164.3 0.33 -126.9 -132.9 144.6 3.6 74 0.454 SW 129.9 0.065 -185.7 0.33 -120.8 -124. 7 120.1 0.33 -128.6 -128.6 101.5 0.33 -128.2 -134.1 178.7 2.1 75 0.405 SW 132 0.065 -185.7 0.33 -121.8 -125. 8 142.9 0.33 -129.5 -129.7 132.6 0.33 -129 -135.1 148.5 3.2 76 0.516 SW 134.6 0.066 -186 0.33 -123 -127 73.6 0.33 -130.8 -131 80.1 0.33 -130.2 -136.2 168 2.8 77 0.477 SW 128.6 0.066 -185.7 0.33 -124.3 -128. 3 142.8 0.33 -131.8 -132.1 100.5 0.33 -131.1 -137.3 161.6 4.1 78 0.531 SW 126.6 0.066 -185.9 0.33 -125.5 129.6 119.5 0.33 -133 -133.3 99.1 0.33 -132.2 -138.4 171.9 3.1 79 0.326 SW 130.5 0.067 -186 0.33 -126.5 130.7 99.3 0.33 -134 -134.4 28 0.33 -133.1 -139.4 165.1 4.6 80 0.46

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147EXP 13 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 130.5 0.068 -185.6 0.33 -127.9 132 78.3 0.33 -135.5 -135.9 131.1 0.33 -134.4 -140.6 196 3.0 81 0.462 SW 132 0.07 -185 0.33 -129.1 -133.4 158.4 0.33 -136.2 -136.8 159.5 0.33 -135 -141.4 141.7 3.1 82 0.361 SW 132.7 0.071 -185.8 0.33 -130.2 134.6 124.1 0.33 -137.3 -138 124.8 0.33 -135.8 -142.3 147.9 1.7 83 0.467 SW 132.6 0.074 -186 0.33 -130.9 -135. 5 176.7 0.33 -138.1 -138.8 130.2 0.33 -136.8 -143.2 168 3.1 84 0.42 SW 143.3 0.084 -185.7 0.33 -132.1 136.5 100.1 0.33 -139.4 -140 105.4 0.33 -138.1 -144.4 201.6 6.7 85 0.474 SW 141.5 0.088 -185.8 0.33 -133.3 137.8 124.7 0.33 -140.4 -141.1 81 0.33 -138.9 -145.4 175.9 3.3 86 0.483 SW 141.1 0.089 -185.8 0.33 -134.1 -138. 7 66.7 0.33 -141.1 -141.9 27.1 0.33 -139.7 -146.3 161.5 3.5 87 0.505 SW 141 0.091 -185.5 0.33 -135.4 -139. 9 157.4 0.33 -142.4 -143.3 230.5 0.33 -140.7 -147.3 183.3 3.3 88 0.442 SW 139.3 0.092 -185.8 0.33 -136.3 141 120.8 0.33 -143.4 -144.3 31.1 0.33 -141.5 -148.2 174 2.8 89 0.479 SW 135.9 0.092 -185.6 0.33 -137.2 -141. 9 75.2 0.33 -144.3 -145.3 140.4 0.33 -142.5 -149.2 189.5 7.2 90 0.403 SW 134.6 0.093 -185.9 0.33 -137.8 -142. 7 185.5 0.33 -144.8 -145.8 62.5 0.33 -143.2 -150 167 3.9 91 0.335 SW 135.8 0.093 -185.9 0.33 -138.9 -143. 8 42.2 0.33 -145.8 -146.8 8.4 0.33 -144 -150.8 174.3 3.5 92 0.406 SW 133.8 0.092 -185.5 0.33 -139.8 -144. 7 126.7 0.33 -146.9 -147.9 242.9 0.33 -145 -151.8 206.2 3.1 93 0.467 SW 132.4 0.093 -185.6 0.33 -140.7 -145. 7 202.8 0.33 -147.8 -148.8 66.2 0.33 -145.9 -152.8 205.1 4.2 94 0.49 SW 133.8 0.093 -185.8 0.33 -141.6 146.6 50 0.33 -148.3 -149.6 61.1 0.33 -146.3 -153.3 137.1 3.3 95 0.471 SW 136.3 0.092 -185.8 0.33 -142.2 -147. 3 76.3 0.33 -149.2 -150.5 138.3 0.33 -147 -154 169.4 2.9 96 0.41 SW 133.7 0.092 -185.8 0.33 -143.2 148.2 221 0.33 -150.1 -151.3 220.7 0.33 -148.1 -155 225.6 3.8 97 0.407 SW 133.8 0.092 -185.5 0.33 -143.9 149 153.1 0.33 -151 -152.3 64.4 0.33 -148.6 -155.7 169.5 4.3 98 0.543 SW 131.9 0.091 -185.5 0.33 -144.6 -149. 8 48.4 0.33 -151.3 -152.8 38.3 0.33 -148.9 -156.1 126.4 3.6 99 0.525 SW 130.8 0.09 -185.5 0.33 -145.7 -150. 9 196.1 0.33 -152.3 -153.6 279.3 0.33 -150 -157.1 237 2.8 100 0.387 SW 132.3 0.089 -185.7 0.33 -146.2 -151. 4 179.9 0.33 -153.1 -154.5 53.3 0.33 -150.7 -157.8 189.2 4.2 101 0.498 SW 126.6 0.087 -185.8 0.33 -147.1 -152. 3 106.9 0.33 -153.8 -155.2 32.1 0.33 -151.3 -158.6 190.1 2.8 102 0.505 SW 112.5 0.08 -186.1 0.33 -147.7 -153. 1 55.8 0.33 -154.1 -155.8 214.9 0.33 -151.3 -158.7 97.8 3.5 103 0.507 SW 123.7 0.089 -185.9 0.33 -148.4 153.7 252.8 0.33 -155.3 -156.8 97 0.33 -152.6 -159.8 265.2 3.4 104 0.438 SW 129.4 0.091 -185.7 0.33 -149.6 154.8 82.2 0.33 -156 -157.6 66.6 0.33 -153.3 -160.6 206.8 3.1 105 0.358 SW 130.9 0.038 -186 0.42 -150.1 -155. 5 166.8 0.42 -158.9 -158.4 1254.8 0.17 -169.6 -175.2 3724.1 2.7 106 0.327 SW 123.5 0.038 -185.6 0.42 -152 -156 13.5 0.42 -171.3 -167.7 4871.3 0.17 -177.6 -183.2 6916.5 2.6 107 0.274 SW 130.2 0.091 -185.4 -157.2 -180 -184.8 2.6 108 0.321 SW 128.3 0.092 -185.7 -158.8 -183.2 -184.8 4.8 109 0.533 SW 129.3 0.092 -185.6 -162.4 -185 -185.5 4.7 110 0.465 SW 125.9 0.094 -185.8 -166.4 -185.3 -185.8 4.8 111 0.318 EXP 14 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 59.4 1 10.5 0.33 21.8 22.7 770.2 0.33 22.4 23.1 557.1 0. 33 22 23.4 394.5 0.0 1 0.339 N 60.2 1 8 0.33 21.4 21.9 325. 9 0.33 21.8 22.4 228.8 0.33 21.2 22.6 363.5 0.0 2 0.345

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148EXP 14 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 60.2 1 6 0.33 20.7 21.1 302. 6 0.33 21.2 21.7 252.5 0.33 20.7 21.9 217.1 0.0 3 0.331 N 60.9 1 3.3 0.33 19.9 20.3 302.4 0.33 20.4 21.1 172.8 0.33 19.8 21.1 294.3 0.0 4 0.346 N 61.5 1 0 0.33 18.7 19.2 356 0.33 19.3 20 316.1 0.33 18.8 20.1 287.9 0.0 5 0.352 N 62.2 1 -3.4 0.33 17.8 18.2 304.7 0.33 18. 4 19 248.4 0.33 17.9 19.2 237.3 0.0 6 0.338 N 62.2 1 -7.1 0.33 16.6 17 324 0.33 17. 3 18 207.5 0.33 16.7 18 306.2 0.0 7 0.325 N 61.8 1 -10.4 0.33 15.2 15. 5 361.8 0.33 16 16.7 276.7 0.33 15.6 16.8 252.5 0.0 8 0.385 N 62.2 1 -14.2 0.33 14 14.2 268.4 0.33 14.7 15.4 218.2 0.33 14.2 15.4 280.7 0.0 9 0.385 N 65.8 1 -19.9 0.33 12.5 12.8 272.3 0.33 13.1 13.9 250.3 0.33 12.8 14 245 0.0 10 0.348 N 63.7 1 -27.5 0.33 10.8 11 247.2 0.33 11.6 12.4 165.4 0.33 11.2 12.3 215.3 0.0 11 0.328 N 63.9 1 -41.4 0.33 8.8 9.1 193.7 0.33 9. 4 10.4 184.4 0.33 8.9 10.2 208.2 0.0 12 0.357 N 68.5 1 -63.6 0.33 6.6 6.9 253.9 0.33 7. 2 8.1 222.6 0.33 6.9 8 230.3 0.0 13 0.388 N 65.6 0.489 -56.6 0.33 4.7 4. 8 188.4 0.33 5.1 6.1 155.7 0. 33 4.5 5.7 208.4 0.0 14 0.283 N 67.2 0.301 -74.4 0.33 2.1 2.3 209.1 0.33 2.4 3.6 187.7 0.33 1.9 3 215.8 0.0 15 0.395 N 69 0.215 -84.1 0.33 -0.7 -0.5 312.4 0.33 -0 .5 0.7 277.9 0.33 -0.9 0.2 301.9 0.0 16 0.353 N 66 0.175 -65 0.33 -2.9 -3.1 191.7 0.33 -2.6 -1.4 125.4 0.33 -3.5 -2.6 210.4 0.0 17 0.306 N 73.7 0.134 -95.8 0.33 -5.4 -5.5 172.1 0.33 -5.4 -4.2 177.2 0.33 -5.8 -5.1 169.3 0.0 18 0.303 SW 72.5 0.029 -107.3 0.33 -8.7 -8.7 222.1 0.33 -8 .8 -7.3 186.9 0.33 -9.4 -8.6 236.6 3.3 19 0.346 SW 75.2 0.028 -111.6 0.33 -11.3 11.6 172.4 0.33 -11.7 -10.3 157.9 0. 33 -12.5 -11.9 202.9 1.8 20 0.326 SW 78.1 0.027 -125.8 0.33 -14.7 14.8 194.6 0.33 -15.2 -13.7 176.4 0. 33 -15.9 -15.4 207.5 2.5 21 0.296 SW 79.2 0.027 -133.8 0.33 -17.6 18 129.9 0.33 -18.3 -16.8 108.7 0. 33 -19.3 -18.9 149.9 2.5 22 0.285 SW 93.9 0.025 -184.3 0.33 -20.9 21.2 138.8 0.33 -22.3 -20.5 139.2 0. 33 -23.4 -23.1 178.9 3.1 23 0.304 SW 95.4 0.025 -184.8 0.33 -24.3 24.8 150.1 0.33 -25.9 -24.1 133.3 0.33 -27.1 -27 171.9 3.7 24 0.317 SW 94.3 0.025 -185.3 0.33 -27.4 28 139.2 0.33 -29.4 -27.5 125.5 0. 33 -30.8 -30.9 177.7 3.7 25 0.308 SW 95.4 0.025 -185.3 0.33 -30.2 31 128.6 0.33 -32.6 -30.7 115.2 0. 33 -34.3 -34.7 173.2 4.3 26 0.295 SW 96.4 0.025 -185.3 0.33 -33.2 34 134.6 0.33 -36.1 -34.1 130.4 0. 33 -37.8 -38.3 174.8 3.1 27 0.284 SW 96.4 0.026 -185.3 0.33 -36.2 37.1 139.2 0.33 -39 -37.2 121.1 0. 33 -40.5 -41.4 151.6 3.1 28 0.264 SW 95.9 0.026 -185.5 0.33 -39.5 -40.4 150.5 0.33 -42.5 -40.6 131. 5 0.33 -44.1 -45 183 2.4 29 0.267 SW 97.4 0.026 -185.1 0.33 -42.3 43.4 136.1 0.33 -45.5 -43.7 124.6 0.33 -47.2 -48.3 170 2.6 30 0.249 SW 96.7 0.026 -185.2 0.33 -45.2 -46.4 144 0.33 -48.5 -46.7 121.1 0.33 -50 -51.4 161.4 3.7 31 0.281 SW 100.2 0.026 -185.7 0.33 -48.3 49.5 145.9 0.33 -51.9 -50.1 139.4 0. 33 -53.3 -54.7 182.2 3.5 32 0.275 SW 101.6 0.026 -185.7 0.33 -50.6 52.1 120.1 0.33 -54.6 -52.9 116.6 0. 33 -56.1 -57.8 167.6 3.5 33 0.268 SW 107 0.026 -185.4 0.33 -54.4 55.6 177.4 0.33 -58.5 -56.5 159.8 0.33 -60 -61.6 212.9 4.1 34 0.287 SW 105.9 0.026 -185.3 0.33 -56.9 58.6 144.6 0.33 -60.8 -59.3 112.7 0. 33 -62.3 -64.4 159.9 3.3 35 0.27 SW 108 0.026 -185.3 0.33 -59.2 61.1 124.9 0.33 -63.3 -61.9 112.1 0.33 -64.7 -67 158.4 3.6 36 0.276 SW 109.5 0.026 -185.5 0.33 -61.8 63.7 134.4 0.33 -65.9 -64.5 111.8 0. 33 -67.3 -69.7 164.5 3.1 37 0.29 SW 109.8 0.027 -185.5 0.33 -64.5 66.5 146 0.33 -68.6 -67.3 125.8 0. 33 -69.8 -72.3 165.5 4.2 38 0.301 SW 109.9 0.027 -185.8 0.33 -66.8 68.9 124.9 0.33 -71.5 -70.2 137.9 0. 33 -72.6 -75.2 183.5 4.8 39 0.304 SW 112.8 0.027 -185.4 0.33 -69 -71. 3 130.1 0.33 -73.5 -72.3 89.7 0. 33 -74.9 -77.7 162.4 3.6 40 0.305

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149EXP 14 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 114.1 0.027 -185.6 0.33 -71.4 73.6 129.5 0.33 -76.1 -74.8 122 0.33 -77.3 -80.3 171.5 3.2 41 0.242 SW 112.1 0.028 -185.3 0.33 -73.7 76 130 0.33 -78.6 -77.4 123.1 0.33 -79.6 -82.7 164.4 3.5 42 0.316 SW 111.5 0.028 -185.9 0.33 -76.2 78.5 142.9 0.33 -81 -79.9 120.5 0.33 -82 -85.2 177.9 2.4 43 0.305 SW 117.5 0.028 -185.7 0.33 -78.2 -80. 7 122.2 0.33 -83.4 -82.3 120.5 0.33 -84.5 -87.7 179.5 4.2 44 0.308 SW 117.9 0.028 -186 0.33 -80.2 -82. 8 119.1 0.33 -85.5 -84.5 112.4 0.33 -86.5 -90 163.1 4.4 45 0.248 SW 123.6 0.029 -185.3 0.33 -82.3 85 129.3 0.33 -87.7 -86.7 107.7 0.33 -88.6 -92.2 169 3.4 46 0.28 SW 126.5 0.029 -185.8 0.33 -84.1 -86. 9 115.3 0.33 -89.7 -88.7 98.9 0.33 -90.9 -94.5 180.7 4.1 47 0.258 SW 128.7 0.03 -185.4 0.33 -86.4 89.1 134 0.33 -92.1 -91.1 131.1 0.33 -93 -96.9 181.7 4.5 48 0.287 SW 130.5 0.03 -185 0.33 -88.5 -91. 4 137.8 0.33 -94.1 -93.2 108.7 0.33 -94.9 -98.9 168.4 4.6 49 0.278 SW 135.6 0.031 -185.5 0.33 -89.9 92.9 92.1 0.33 -96 -95.1 103.8 0.33 -96.9 -101 177.1 4.6 50 0.293 SW 131.1 0.031 -185 0.33 -91.7 -94. 8 121.9 0.33 -97.7 -96.7 81.5 0.33 -98.9 -103.1 180.6 5.0 51 0.255 SW 129.9 0.032 -185.5 0.33 -93.7 -96. 9 131.4 0.33 -99.6 -98.8 117.9 0.33 -100.5 -104.9 157 5.3 52 0.261 SW 136.9 0.032 -185.3 0.33 -95.5 -98. 7 116.8 0.33 -101.5 -100.7 109.3 0.33 -102.3 -106.7 170.9 4.4 53 0.24 SW 135.9 0.033 -185.7 0.33 -97.3 -100. 6 126.3 0.33 -103.6 -102.7 111.4 0.33 -104.5 -108.9 202.3 5.6 54 0.3 SW 133.7 0.034 -185.5 0.33 -99 -102. 3 112.1 0.33 -105.5 -104.7 119.4 0.33 -106.2 -110.8 174.7 2.6 55 0.294 SW 136.2 0.035 -185.6 0.33 -100.4 -103. 9 106.4 0.33 -106.8 -106.2 84.6 0.33 -107.4 -112.3 148.8 4.4 56 0.232 SW 138.8 0.036 -185.5 0.33 -102.1 105.5 110 0.33 -108.6 -108 113.6 0.33 -109.1 -113.9 168 4.0 57 0.26 SW 142.4 0.036 -185.8 0.33 -103.7 107.2 121.8 0.33 -110 -109.5 88.1 0.33 -110.5 -115.4 162.9 5.6 58 0.302 SW 139.2 0.037 -185.4 0.33 -105.2 108.8 114 0.33 -111.4 -111 90.2 0.33 -111.9 -116.9 158.7 5.3 59 0.289 SW 141.7 0.037 -185.4 0.33 -106.8 -110. 5 120.3 0.33 -113.2 -112.7 112.2 0.33 -113.6 -118.6 182.5 5.8 60 0.222 SW 137.4 0.038 -185.2 0.33 -108.4 -112. 1 122.7 0.33 -114.6 -114.4 110.3 0.33 -114.7 -120 152.2 2.3 61 0.221 SW 145.8 0.039 -185.9 0.33 -109.9 113.7 120.3 0.33 -116.4 -116 105.6 0.33 -116.6 -121.8 198.9 2.0 62 0.289 SW 142 0.039 -185.7 0.33 -110.9 -114. 9 88.4 0.33 -117.2 -117.1 66.1 0.33 -117.4 -122.8 130.9 4.4 63 0.257 SW 142.2 0.04 -185.5 0.33 -112.7 116.6 133.8 0.33 -118.9 -118.7 119 0.33 -118.8 -124.2 169.1 2.9 64 0.259 SW 144.5 0.04 -185.6 0.33 -113.8 -117. 9 101.3 0.33 -120.1 -120.1 86.5 0.33 -120.1 -125.6 168.5 5.9 65 0.258 SW 143.1 0.042 -185.5 0.33 -115.5 -119. 5 130.5 0.33 -122.1 -121.9 140.2 0.33 -122 -127.4 208.1 2.5 66 0.259 SW 143.8 0.043 -185.7 0.33 -116.4 -120. 7 91.7 0.33 -122.8 -122.9 65.2 0.33 -122.6 -128.4 135.9 3.4 67 0.277 SW 144.3 0.044 -185.6 0.33 -118.3 -122. 4 153.8 0.33 -124.2 -124.3 103.4 0.33 -123.8 -129.5 158 6.4 68 0.27 SW 139.2 0.046 -185.5 0.33 -119.1 123.4 76.2 0.33 -125.5 -125.7 109 0.33 -125 -130.7 163.1 2.7 69 0.263 SW 144.9 0.047 -185.5 0.33 -120 -124. 4 89.3 0.33 -126.5 -126.6 64.8 0.33 -126.2 -132 176.3 3.3 70 0.249 SW 141.1 0.046 -185.4 0.33 -121.5 125.8 129 0.33 -127.8 -128 114.5 0.33 -127.2 -133.1 156.8 3.6 71 0.245 SW 142.3 0.048 -185.3 0.33 -122.4 126.9 90.7 0.33 -129 -129.2 98 0.33 -128.5 -134.4 181.5 3.8 72 0.257 SW 142.9 0.05 -185.5 0.33 -123.6 -128. 1 111.8 0.33 -129.8 -130.2 68.9 0.33 -129.2 -135.3 145.4 4.8 73 0.248 SW 143.2 0.05 -185.8 0.33 -125.4 129.8 157 0.33 -131.8 -132 164.3 0.33 -131 -136.9 222.5 3.4 74 0.278 SW 133.8 0.051 -185.8 0.33 -126.5 -131. 1 120.1 0.33 -132.7 -133.2 101.5 0.33 -131.7 -137.9 149.1 6.8 75 0.319 SW 139.5 0.052 -185.9 0.33 -128 -132. 5 142.9 0.33 -133.9 -134.6 132.6 0.33 -132.5 -138.8 144.5 2.5 76 0.296 SW 138.9 0.052 -185.9 0.33 -128.5 -133. 3 73.6 0.33 -134.7 -135.5 80.1 0.33 -133.5 -139.7 158.6 6.0 77 0.305 SW 134.7 0.053 -185.9 0.33 -130 -134. 7 142.8 0.33 -135.6 -136.5 100.5 0.33 -133.9 -140.3 114.2 6.9 78 0.258

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150EXP 14 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 114.1 0.027 -185.6 0.33 -71.4 73.6 129.5 0.33 -76.1 -74.8 122 0.33 -77.3 -80.3 171.5 3.2 41 0.242 SW 112.1 0.028 -185.3 0.33 -73.7 76 130 0.33 -78.6 -77.4 123.1 0.33 -79.6 -82.7 164.4 3.5 42 0.316 SW 111.5 0.028 -185.9 0.33 -76.2 78.5 142.9 0.33 -81 -79.9 120.5 0.33 -82 -85.2 177.9 2.4 43 0.305 SW 117.5 0.028 -185.7 0.33 -78.2 -80. 7 122.2 0.33 -83.4 -82.3 120.5 0.33 -84.5 -87.7 179.5 4.2 44 0.308 SW 117.9 0.028 -186 0.33 -80.2 -82. 8 119.1 0.33 -85.5 -84.5 112.4 0.33 -86.5 -90 163.1 4.4 45 0.248 SW 123.6 0.029 -185.3 0.33 -82.3 85 129.3 0.33 -87.7 -86.7 107.7 0.33 -88.6 -92.2 169 3.4 46 0.28 SW 126.5 0.029 -185.8 0.33 -84.1 -86. 9 115.3 0.33 -89.7 -88.7 98.9 0.33 -90.9 -94.5 180.7 4.1 47 0.258 SW 128.7 0.03 -185.4 0.33 -86.4 89.1 134 0.33 -92.1 -91.1 131.1 0.33 -93 -96.9 181.7 4.5 48 0.287 SW 130.5 0.03 -185 0.33 -88.5 -91. 4 137.8 0.33 -94.1 -93.2 108.7 0.33 -94.9 -98.9 168.4 4.6 49 0.278 SW 135.6 0.031 -185.5 0.33 -89.9 92.9 92.1 0.33 -96 -95.1 103.8 0.33 -96.9 -101 177.1 4.6 50 0.293 SW 131.1 0.031 -185 0.33 -91.7 -94. 8 121.9 0.33 -97.7 -96.7 81.5 0.33 -98.9 -103.1 180.6 5.0 51 0.255 SW 129.9 0.032 -185.5 0.33 -93.7 -96. 9 131.4 0.33 -99.6 -98.8 117.9 0.33 -100.5 -104.9 157 5.3 52 0.261 SW 136.9 0.032 -185.3 0.33 -95.5 -98. 7 116.8 0.33 -101.5 -100.7 109.3 0.33 -102.3 -106.7 170.9 4.4 53 0.24 SW 135.9 0.033 -185.7 0.33 -97.3 -100. 6 126.3 0.33 -103.6 -102.7 111.4 0.33 -104.5 -108.9 202.3 5.6 54 0.3 SW 133.7 0.034 -185.5 0.33 -99 -102. 3 112.1 0.33 -105.5 -104.7 119.4 0.33 -106.2 -110.8 174.7 2.6 55 0.294 SW 136.2 0.035 -185.6 0.33 -100.4 -103. 9 106.4 0.33 -106.8 -106.2 84.6 0.33 -107.4 -112.3 148.8 4.4 56 0.232 SW 138.8 0.036 -185.5 0.33 -102.1 105.5 110 0.33 -108.6 -108 113.6 0.33 -109.1 -113.9 168 4.0 57 0.26 SW 142.4 0.036 -185.8 0.33 -103.7 107.2 121.8 0.33 -110 -109.5 88.1 0.33 -110.5 -115.4 162.9 5.6 58 0.302 SW 139.2 0.037 -185.4 0.33 -105.2 108.8 114 0.33 -111.4 -111 90.2 0.33 -111.9 -116.9 158.7 5.3 59 0.289 SW 141.7 0.037 -185.4 0.33 -106.8 -110. 5 120.3 0.33 -113.2 -112.7 112.2 0.33 -113.6 -118.6 182.5 5.8 60 0.222 SW 137.4 0.038 -185.2 0.33 -108.4 -112. 1 122.7 0.33 -114.6 -114.4 110.3 0.33 -114.7 -120 152.2 2.3 61 0.221 SW 145.8 0.039 -185.9 0.33 -109.9 113.7 120.3 0.33 -116.4 -116 105.6 0.33 -116.6 -121.8 198.9 2.0 62 0.289 SW 142 0.039 -185.7 0.33 -110.9 -114. 9 88.4 0.33 -117.2 -117.1 66.1 0.33 -117.4 -122.8 130.9 4.4 63 0.257 SW 142.2 0.04 -185.5 0.33 -112.7 116.6 133.8 0.33 -118.9 -118.7 119 0.33 -118.8 -124.2 169.1 2.9 64 0.259 SW 144.5 0.04 -185.6 0.33 -113.8 -117. 9 101.3 0.33 -120.1 -120.1 86.5 0.33 -120.1 -125.6 168.5 5.9 65 0.258 SW 143.1 0.042 -185.5 0.33 -115.5 -119. 5 130.5 0.33 -122.1 -121.9 140.2 0.33 -122 -127.4 208.1 2.5 66 0.259 SW 143.8 0.043 -185.7 0.33 -116.4 -120. 7 91.7 0.33 -122.8 -122.9 65.2 0.33 -122.6 -128.4 135.9 3.4 67 0.277 SW 144.3 0.044 -185.6 0.33 -118.3 -122. 4 153.8 0.33 -124.2 -124.3 103.4 0.33 -123.8 -129.5 158 6.4 68 0.27 SW 139.2 0.046 -185.5 0.33 -119.1 123.4 76.2 0.33 -125.5 -125.7 109 0.33 -125 -130.7 163.1 2.7 69 0.263 SW 144.9 0.047 -185.5 0.33 -120 -124. 4 89.3 0.33 -126.5 -126.6 64.8 0.33 -126.2 -132 176.3 3.3 70 0.249 SW 141.1 0.046 -185.4 0.33 -121.5 125.8 129 0.33 -127.8 -128 114.5 0.33 -127.2 -133.1 156.8 3.6 71 0.245 SW 142.3 0.048 -185.3 0.33 -122.4 126.9 90.7 0.33 -129 -129.2 98 0.33 -128.5 -134.4 181.5 3.8 72 0.257 SW 142.9 0.05 -185.5 0.33 -123.6 -128. 1 111.8 0.33 -129.8 -130.2 68.9 0.33 -129.2 -135.3 145.4 4.8 73 0.248 SW 143.2 0.05 -185.8 0.33 -125.4 129.8 157 0.33 -131.8 -132 164.3 0.33 -131 -136.9 222.5 3.4 74 0.278 SW 133.8 0.051 -185.8 0.33 -126.5 -131. 1 120.1 0.33 -132.7 -133.2 101.5 0.33 -131.7 -137.9 149.1 6.8 75 0.319 SW 139.5 0.052 -185.9 0.33 -128 -132. 5 142.9 0.33 -133.9 -134.6 132.6 0.33 -132.5 -138.8 144.5 2.5 76 0.296 SW 138.9 0.052 -185.9 0.33 -128.5 -133. 3 73.6 0.33 -134.7 -135.5 80.1 0.33 -133.5 -139.7 158.6 6.0 77 0.305 SW 134.7 0.053 -185.9 0.33 -130 -134. 7 142.8 0.33 -135.6 -136.5 100.5 0.33 -133.9 -140.3 114.2 6.9 78 0.258

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151EXP 14 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 136.2 0.053 -185.8 0.33 -131 -135. 9 119.5 0.33 -136.6 -137.5 99.1 0.33 -134.9 -141.3 158.6 3.2 79 0.33 SW 134 0.054 -185.5 0.33 -131.6 136.8 99.3 0.33 -136.9 -138 28 0.33 -135.6 -142 137.2 4.2 80 0.254 SW 135.1 0.055 -185.4 0.33 -132.4 -137. 5 78.3 0.33 -138.2 -139.2 131.1 0.33 -136.6 -143 165.2 5.7 81 0.271 SW 138.8 0.057 -185.6 0.33 -134 -138. 9 158.4 0.33 -140 -140.7 159.5 0.33 -138.4 -144.7 256.6 2.9 82 0.297 SW 140.6 0.057 -185.6 0.33 -135 -140 124.1 0.33 -140.8 -141.9 124.8 0.33 -138.9 -145.5 139.7 3.0 83 0.293 SW 135.3 0.058 -186 0.33 -136.5 -141. 5 176.7 0.33 -141.8 -143 130.2 0.33 -139.6 -146.3 149.7 2.6 84 0.278 SW 140.2 0.059 -186 0.33 -137.2 -142. 4 100.1 0.33 -142.7 -143.9 105.4 0.33 -140.6 -147.2 171.5 2.6 85 0.291 SW 140.8 0.066 -185.6 0.33 -138.1 143.4 124.7 0.33 -143.1 -144.6 81 0.33 -140.8 -147.6 98.1 5.8 86 0.272 SW 143.3 0.066 -185.8 0.33 -138.3 -143. 9 66.7 0.33 -143.4 -144.9 27.1 0.33 -141.3 -148.1 117.1 2.4 87 0.343 SW 145.4 0.069 -186 0.33 -139.9 -145 157.4 0.33 -145.8 -146.7 230.5 0.33 -143.7 -150.1 336.8 5.9 88 0.296 SW 140.5 0.071 -185.2 0.33 -140.5 146 120.8 0.33 -145.5 -147.1 31.1 0.33 -143.2 -150 53.2 2.8 89 0.272 SW 147.3 0.074 -185.8 0.33 -141.1 -146. 5 75.2 0.33 -147.1 -148.2 140.4 0.33 -145.2 -151.8 285.9 4.1 90 0.249 SW 143.4 0.075 -185.7 0.33 -142.3 -147. 8 185.5 0.33 -147.2 -148.8 62.5 0.33 -144.9 -151.5 79.1 5.8 91 0.256 SW 140.4 0.076 -185.6 0.33 -142.3 147.6 42.2 0.33 -147.4 -149 8.4 0.33 -145.4 -152.5 133 3.3 92 0.241 SW 144.5 0.076 -185.9 0.33 -143.5 -148. 9 126.7 0.33 -149.5 -150.6 242.9 0.33 -147.2 -153.9 280.6 3.4 93 0.273 SW 143.4 0.077 -185.5 0.33 -144.7 -150. 3 202.8 0.33 -149.5 -151.2 66.2 0.33 -146.8 -153.9 67.8 4.7 94 0.297 SW 141.9 0.076 -185.5 0.33 -144.8 150.6 50 0.33 -149.9 -151.6 61.1 0.33 -147.4 -154.5 142.3 2.9 95 0.282 SW 139.9 0.076 -185.4 0.33 -145.4 -151. 1 76.3 0.33 -151.2 -152.6 138.3 0.33 -148.8 -155.7 258.6 6.0 96 0.281 SW 142.2 0.076 -186 0.33 -147.1 152.5 221 0.33 -152.5 -154 220.7 0.33 -149.7 -156.7 216.8 2.5 97 0.259 SW 140 0.077 -185.9 0.33 -147.7 -153. 5 153.1 0.33 -152.4 -154.5 64.4 0.33 -149.4 -156.8 56.5 5.1 98 0.295 SW 138.6 0.076 -185.6 0.33 -147.7 -153. 2 48.4 0.33 -152.6 -154.5 38.3 0.33 -149.7 -157 106.8 3.6 99 0.297 SW 136.8 0.076 -185.8 0.33 -149.3 -154. 9 196.1 0.33 -154.9 -156.3 279.3 0.33 -152.2 -159 400.9 4.0 100 0.256 SW 140.7 0.076 -185.8 0.33 -150 -155. 9 179.9 0.33 -154.8 -156.8 53.3 0.33 -151.9 -158.9 105.4 2.5 101 0.263 SW 130.5 0.074 -185.4 0.33 -150.3 155.9 106.9 0.33 -155 -156.5 32.1 0.33 -152.1 -158.7 115.8 2.6 102 0.256 SW 132.8 0.075 -185.7 0.33 -150.8 -156. 7 55.8 0.33 -156.4 -158.1 214.9 0.33 -153.4 -160.6 260.7 2.2 103 0.295 SW 138.5 0.076 -185.8 0.33 -152.1 158 252.8 0.33 -156.7 -158.7 97 0.33 -153.5 -160.3 123.4 2.3 104 0.289 SW 129.4 0.074 -185.9 0.33 -152.2 -157. 6 82.2 0.33 -157.3 -159.1 66.6 0.33 -154.6 -161.9 266.6 2.8 105 0.23 SW 135.3 0.052 -185.6 0.42 -154.1 -159. 3 166.8 0.42 -166.8 -164.7 1254.8 0.17 -175 -179.5 4428.8 3.7 106 0.167 SW 140.6 0.095 -185.5 0.42 -156.8 -158. 9 13.5 0.42 -181.8 -178.7 4871.3 0.17 -177.8 -183.3 10622.9 3.2 107 0.265 SW 139.8 0.076 -185.8 -162 -184.7 -185.6 5.4 108 0.246 SW 138.3 0.077 -185.6 -166 -185.1 -184.4 6.0 109 0.188 SW 136.8 0.078 -185.4 -171.6 -185.4 -185.3 4.6 110 0.226 SW 135.4 0.078 -185.7 -179.4 -185.7 -184.8 5.2 111 0.23

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152EXP 15 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 83.3 1 8.2 0.33 21.73 22.4 497.6 0.33 22.33 22.9 282.7 0.33 21.95 23.2 142.2 0.0 1 0.317 N 83.7 1 5.7 0.33 20.99 21.5 348 0.33 21.5 22.2 220.6 0.33 20.84 22.2 367.2 0.0 2 0.31 N 84.2 1 3.3 0.33 20.27 20.8 255.7 0.33 20.6 21.2 320.6 0.33 20.15 21.5 249.7 0.0 3 0.282 N 88.5 1 0.6 0.33 19.35 19.8 325 0.33 19.97 20.6 159.3 0.33 19.4 20.7 232.3 0.0 4 0.295 N 88.6 1 -2.9 0.33 18.23 18.7 300 0.33 18. 66 19.5 267.3 0.33 18 19.4 337.3 0.0 5 0.328 N 90.5 1 -7.9 0.33 16.62 17.1 375.5 0.33 17. 34 18.1 298.3 0.33 16.95 18.2 250 0.0 6 0.336 N 91.7 1 -13.1 0.33 15.08 15. 5 374.1 0.33 15.85 16.7 261.7 0. 33 15.3 16.7 340.4 0.0 7 0.38 SW 90.7 1 -16.3 0.33 13.81 14. 1 297.9 0.33 14.61 15.4 218.7 0. 33 14.06 15.3 262.6 3.4 8 0.328 SW 93.2 1 -20.8 0.33 12.21 12. 5 296.4 0.33 12.84 13.7 271.9 0. 33 12.34 13.6 298.9 3.0 9 0.362 SW 92.4 1 -26.1 0.33 10.15 10. 5 294.1 0.33 11.1 11.9 219.2 0. 33 10.78 11.9 216.5 3.9 10 0.375 SW 97.3 1 -41 0.33 8.157 8.4 253.3 0.33 9. 003 9.9 199 0.33 8.528 9.8 252.2 4.1 11 0.355 SW 95.6 0.015 -51.5 0.33 5.558 5.8 335 0.33 6.331 7.5 281.7 0. 33 5.852 7.1 327.3 5.1 12 0.377 SW 97.1 0.014 -49.1 0.33 3.559 3.6 211.6 0.33 4.253 5.2 181.6 0. 33 3.835 4.9 205.2 4.1 13 0.306 SW 102.2 0.014 -70.9 0.33 0.387 0.6 334.7 0.33 0.994 2.3 285.2 0. 33 0.538 1.8 333.3 4.5 14 0.402 SW 92.9 0.014 -64.3 0.33 -2.01 -2.1 295.7 0.33 -1 .25 -0.2 209.3 0.33 -1.84 -0.9 276.7 4.8 15 0.382 SW 99.6 0.014 -67.2 0.33 -5.17 -5.3 375.5 0.33 -4 .38 -3.2 300.5 0.33 -4.87 -4 346.5 5.5 16 0.394 SW 96.9 0.014 -64.7 0.33 -7.29 -7.7 224.3 0.33 -6 .77 -5.7 198.9 0.33 -7.2 -6.6 233.6 5.8 17 0.398 SW 101.3 0.014 -83.4 0.33 -10.3 10.6 257.5 0.33 -9.65 -8.6 212.1 0. 33 -9.88 -9.3 229.8 5.6 18 0.363 SW 103.4 0.013 -92.8 0.33 -13.5 13.9 252.5 0.33 -13.2 -11.9 216.5 0. 33 -13.6 -12.9 275.6 5.2 19 0.355 SW 104 0.013 -104.6 0.33 -16.5 -17 216.1 0.33 -16. 2 -15 184.1 0.33 -16.5 -16.1 212.4 7.0 20 0.336 SW 106.2 0.013 -118.5 0.33 -19.8 20.3 208 0.33 -19.8 -18.5 185.9 0. 33 -20.1 -19.7 218.7 6.3 21 0.346 SW 109.2 0.013 -133.1 0.33 -23.2 23.7 151.5 0.33 -23.5 -22.2 148.6 0. 33 -23.7 -23.5 165.5 5.7 22 0.361 SW 118.4 0.013 -178.7 0.33 -27 27.6 169.2 0.33 -27.4 -26 144.7 0. 33 -27.7 -27.5 175.7 4.3 23 0.382 SW 104 0.014 -186.4 0.33 -30.2 -31 151 0.33 -30.8 -29.6 135.3 0.33 -31.1 -31.2 162.8 6.7 24 0.374 SW 113.6 0.013 -185.4 0.33 -33.2 34.2 141.9 0.33 -34.1 -33 133.9 0. 33 -34.3 -34.7 153.9 5.9 25 0.328 SW 114 0.013 -186.4 0.33 -37.2 -38.1 178 0.33 -38. 1 -36.8 157.8 0.33 -38.3 -38.7 185.9 5.7 26 0.421 SW 121.1 0.013 -185.3 0.33 -40.6 41.6 166.2 0.33 -41.7 -40.5 151.2 0.33 -41.9 -42.5 179 5.5 27 0.318 SW 113.1 0.013 -185.2 0.33 -43.8 45.1 160.2 0.33 -45.3 -44.1 147.3 0. 33 -45.5 -46.3 182.1 6.3 28 0.363 SW 118.7 0.014 -186.1 0.33 -48.2 49.2 201.9 0.33 -49.9 -48.5 193.1 0. 33 -49.9 -50.7 217.6 5.5 29 0.342 SW 123.2 0.013 -186.1 0.33 -51.6 -53 178.2 0.33 -53.5 -52.3 166 0. 33 -53.5 -54.7 197 5.0 30 0.394 SW 121.8 0.013 -186.1 0.33 -54.8 56.4 168.3 0.33 -56.9 -55.9 156 0. 33 -56.8 -58.3 184.7 5.7 31 0.421 SW 126.9 0.013 -185.9 0.33 -57.8 59.6 160.4 0.33 -60 -59.1 143.5 0. 33 -60.1 -61.8 183.4 5.3 32 0.316 SW 127.8 0.013 -186.4 0.33 -60.8 62.7 160.9 0.33 -63.4 -62.5 154.6 0. 33 -63.4 -65.2 190.4 4.9 33 0.421 SW 132.5 0.014 -185.9 0.33 -63.7 -65.8 165.3 0.33 -66 -65.3 124.9 0.33 -66 -68.2 165 5.7 34 0.349 SW 133.5 0.014 -186.5 0.33 -66.6 68.7 154 0.33 -69.3 -68.5 156.1 0. 33 -69.1 -71.4 180.7 6.2 35 0.369 SW 134.3 0.014 -186.1 0.33 -69.4 71.6 161.2 0.33 -71.8 -71.4 140.1 0. 33 -71.4 -73.9 151.4 6.0 36 0.378 SW 133.9 0.014 -185.8 0.33 -71.8 74.2 141.4 0.33 -74.9 -74.2 135.3 0. 33 -74.8 -77.3 202.2 4.5 37 0.391 SW 138 0.014 -186.4 0.33 -74.9 77.3 175.3 0.33 -77.7 -77.2 150.6 0.33 -77.3 -80 167.6 2.7 38 0.398

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153EXP 15 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 137.8 0.014 -186.6 0.33 -77 -79. 7 135.4 0.33 -80.6 -79.9 134.6 0. 33 -80.6 -83.4 212.4 4.5 39 0.364 SW 137.3 0.014 -186 0.33 -79.7 -82. 4 159.6 0.33 -82.9 -82.5 132.3 0. 33 -82.6 -85.8 154.7 4.9 40 0.381 SW 138.6 0.014 -186.6 0.33 -82.3 85.1 164.9 0.33 -85.4 -85.2 146.6 0.33 -84.6 -88 148.7 4.3 41 0.398 SW 141.5 0.014 -186.3 0.33 -84.9 87.6 153.9 0.33 -88.4 -88.2 170.9 0. 33 -87.5 -90.8 190.6 5.8 42 0.419 SW 142 0.014 -186.2 0.33 -87.3 90.3 161.5 0.33 -91 -90.6 128.7 0. 33 -90.6 -94 216.9 2.9 43 0.413 SW 145 0.015 -186.5 0.33 -89.5 -92. 5 141.3 0.33 -93.5 -93.3 156.3 0. 33 -92.7 -96.4 168.2 5.4 44 0.399 SW 146 0.015 -186.4 0.33 -91.8 94.9 157.2 0.33 -95.4 -95.4 120 0. 33 -94.6 -98.5 157.8 5.0 45 0.411 SW 147.3 0.015 -186.2 0.33 -93.9 97.2 145.5 0.33 -97.8 -97.7 135.1 0.33 -97 -100.9 181.8 5.7 46 0.417 SW 151.7 0.015 -186 0.33 -96.1 99.4 150.1 0.33 -100 -100.1 146.7 0. 33 -99.4 -103.4 190.6 6.3 47 0.373 SW 150.2 0.015 -186.4 0.33 -98.7 -102 181.1 0.33 -103 -102.8 175.4 0.33 -101 -105.5 161 3.9 48 0.388 SW 149.8 0.015 -185.6 0.33 -100 103.9 125.6 0.33 -104 -104.3 87.2 0.33 -103 -107.5 163 5.5 49 0.381 SW 154.5 0.016 -186.2 0.33 -103 106.1 159.3 0.33 -107 -107 188.5 0. 33 -105 -109.8 189.9 2.7 50 0.378 SW 152.6 0.016 -186.4 0.33 -104 -107.8 119.6 0.33 -109 -109 134.1 0.33 -107 -112 184.5 5.0 51 0.397 SW 156.3 0.016 -186.2 0.33 -106 -109.7 149 0.33 110 -110.3 73.2 0.33 -109 -113.4 128.7 3.0 52 0.393 SW 159.4 0.016 -186.1 0.33 -108 111.8 157.7 0.33 -113 -112.9 202.4 0. 33 -111 -115.5 190.1 6.5 53 0.356 SW 161.7 0.017 -186.4 0.33 -109 113.2 101.9 0.33 -114 -114.5 109.4 0. 33 -112 -117.3 154.6 4.5 54 0.408 SW 163.8 0.017 -186.2 0.33 -111 114.9 130.1 0.33 -115 -115.8 86.3 0. 33 -114 -118.9 156.3 5.5 55 0.351 SW 166.9 0.017 -186 0.33 -113 -116.8 154.9 0.33 117 -117.5 125.4 0.33 -116 -120.7 172.1 5.3 56 0.32 SW 167.3 0.018 -186.2 0.33 -114 118.5 140.9 0.33 -119 -119.2 125.9 0.33 -117 -122.2 155 5.9 57 0.367 SW 165.3 0.018 -186.2 0.33 -116 120.2 140.4 0.33 -120 -121 138.8 0. 33 -119 -124.1 194.2 4.9 58 0.382 SW 168.9 0.018 -186.6 0.33 -117 121.9 144.4 0.33 -122 -122.5 114.6 0. 33 -120 -125.4 135.4 4.6 59 0.359 SW 170.4 0.019 -186.6 0.33 -119 123.4 130.8 0.33 -124 -124.3 146.3 0. 33 -122 -127.1 174.7 5.1 60 0.372 SW 172.3 0.019 -186.8 0.33 -120 124.7 118.7 0.33 -125 -125.7 118.6 0. 33 -123 -128.4 144.9 6.0 61 0.304 SW 178.7 0.02 -186.3 0.33 -121 -126 121 0.33 126 -127 103.4 0.33 -125 -130.2 198.7 4.9 62 0.331 SW 176.3 0.02 -186.5 0.33 -123 127.5 144.5 0.33 -127 -128.3 103 0. 33 -125 -131.3 129.8 3.1 63 0.327 SW 182.4 0.02 -186 0.33 -124 -128.4 83.9 0.33 128 -129.4 91.4 0.33 -127 -132.5 156.6 6.3 64 0.302 SW 177 0.021 -186.3 0.33 -125 -129.6 115.6 0.33 130 -130.6 100.9 0.33 -128 -133.7 152.7 6.1 65 0.323 SW 183.9 0.022 -186.5 0.33 -127 131.4 184.8 0.33 -132 -132.6 202.8 0. 33 -130 -135.5 215.4 6.2 66 0.342 SW 183.6 0.023 -186.4 0.33 -127 132.5 100.8 0.33 -132 -133.2 32.9 0. 33 -130 -136.2 101.3 4.7 67 0.308 SW 186.3 0.023 -186.2 0.33 -128 133.4 101.4 0.33 -133 -134.5 125.2 0. 33 -131 -137.3 156.9 3.0 68 0.327 SW 187.2 0.023 -186.5 0.33 -130 134.6 129.8 0.33 -134 -135.5 88.7 0. 33 -133 -138.7 179.1 6.3 69 0.341 SW 185.6 0.024 -186.4 0.33 -131 136.3 176.7 0.33 -136 -137.2 173.8 0. 33 -134 -140.3 212.7 6.1 70 0.337 SW 181.3 0.024 -186.5 0.33 -132 137.2 96.3 0.33 -136 -138 64.3 0. 33 -134 -140.7 82.1 4.0 71 0.36 SW 182.8 0.025 -186.3 0.33 -133 137.9 81.6 0.33 -138 -138.9 94.1 0. 33 -136 -141.9 181.8 6.5 72 0.362 SW 179.6 0.025 -186.5 0.33 -134 139.3 164.9 0.33 -139 -140.3 153 0. 33 -137 -143.2 190.6 5.6 73 0.376 SW 185.3 0.026 -186.3 0.33 -135 140.4 135.7 0.33 -139 -141.1 73.1 0. 33 -137 -143.6 75.5 4.3 74 0.368 SW 181.4 0.026 -186.5 0.33 -137 141.6 134.4 0.33 -142 -142.9 215.8 0. 33 -139 -145.5 277.5 4.5 75 0.373 SW 184.2 0.027 -186.6 0.33 -138 143.3 212.8 0.33 -143 -144.3 157.6 0. 33 -140 -146.6 170.4 4.9 76 0.345

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154EXP 15 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 183.5 0.027 -186.5 0.33 -139 144.6 147.4 0.33 -144 -145.6 168.4 0. 33 -141 -147.6 158.3 3.8 77 0.399 SW 182.4 0.027 -186.4 0.33 -140 145.5 120.5 0.33 -145 -146.6 113.7 0.33 -142 -148.7 185 6.5 78 0.374 SW 184.8 0.028 -186.8 0.33 -141 146.5 135.1 0.33 -145 -146.8 26 0. 33 -142 -148.5 45.7 5.4 79 0.395 SW 176.5 0.027 -186.6 0.33 -141 146.8 45.8 0.33 -145 -147.4 77.7 0. 33 -142 -149.2 103.8 2.8 80 0.37 SW 180.2 0.028 -186.8 0.33 -142 147.8 157.4 0.33 -146 -148.3 132.3 0. 33 -143 -150.1 161.7 8.5 81 0.399 SW 181.9 0.028 -186.4 0.33 -144 -149.4 228.1 0.33 -148 -149.6 176. 1 0.33 -144 -151 155 4.1 82 0.396 SW 190.5 0.03 -186.4 0.33 -145 150.2 112.7 0.33 -149 -151.1 197.8 0. 33 -146 -152.8 302.8 4.5 83 0.38 SW 192 0.031 -186.6 0.33 -146 -151.9 248.3 0.33 150 -152.4 192.3 0.33 -147 -153.7 148.2 4.8 84 0.369 SW 194.2 0.033 -186.9 0.33 -147 -153 167.3 0.33 151 -153.4 149.3 0.33 -147 -154.4 144.3 6.6 85 0.395 SW 195.4 0.034 -186.9 0.33 -147 153.1 35.2 0.33 -151 -152.6 34.3 0. 33 -148 -153.4 85.5 5.8 86 0.396 SW 194.1 0.034 -186.8 0.33 -149 154.9 286.5 0.33 -153 -155.2 275.4 0. 33 -149 -155.8 207.4 3.0 87 0.367 SW 192.2 0.035 -186.5 0.33 -149 155.3 59.6 0.33 -154 -156.3 188.5 0. 33 -150 -157.3 265.9 6.0 88 0.376 SW 190.8 0.036 -187 0.33 -150 -155.6 77.5 0.33 154 -155.2 57.6 0.33 -150 -155.9 65 6.4 89 0.386 SW 188.6 0.036 -186.8 0.33 -150 156.3 125.9 0.33 -154 -156.3 95.4 0.33 -151 -156.5 94 6.1 90 0.407 SW 191.5 0.036 -186.7 0.33 -150 156.5 58.1 0.33 -155 -156.3 50 0. 33 -151 -157.1 59.4 4.7 91 0.392 SW 188.6 0.036 -186.6 0.33 -151 156.5 53.8 0.33 -155 -157.5 79.8 0. 33 -152 -158.9 219.3 4.1 92 0.376 SW 187.8 0.02 -186.3 0.42 -152 158.1 260.7 0.42 -159 -159.5 344.2 0.17 -166 -171.4 2829 6.7 93 0.356 SW 180.7 0.038 -186.8 0.42 -157 160.7 435.4 0.42 -173 -169.8 2383.5 0. 17 -176 -181.2 4374.8 5.0 94 0.417 SW 186.9 0.035 -186.4 -160.7 -180.7 -183.5 5.5 95 0.371 SW 188.6 0.035 -186.6 -161.4 -181.4 -182.7 4.5 96 0.396 SW 181.9 0.035 -186.4 -168.3 -185.3 -184.7 3.6 97 0.395 SW 183.6 0.036 -187 -176.8 -184.5 -182.4 6.2 98 0.379 SW 183.1 0.036 -186.7 -185.3 -186 -183.5 5.1 99 0.386 SW 183.7 0.036 -186.6 -185.6 -185.7 -184.7 4.3 100 0.392 SW 182.2 0.036 -186.9 -188.1 -187.3 -185.2 4.5 101 0.394 SW 180.3 0.037 -186.9 -185.7 -183.4 -181.3 4.5 102 0.37 SW 180.3 0.037 -187.1 -187.7 -185.3 -182.7 7.1 103 0.389 SW 179.3 0.037 -186.8 -187.4 -186.3 -184.6 6.2 104 0.384 SW 180.1 0.037 -186.7 -186.1 -184.8 -183.2 5.2 105 0.375 SW 179.3 0.037 -186.7 -186.3 -185.2 -183.6 6.1 106 0.369 SW 176 0.037 -186.7 -186.3 -185 -183.6 4.5 107 0.343 SW 175.5 0.037 -186.4 -186.6 -185 -183.2 7.2 108 0.39 SW 171.1 0.037 -186.7 -187 -186 -184.7 6.1 109 0.36 SW 169.4 0.037 -187.3 -187.7 -185.8 -183.9 3.0 110 0.353 SW 165.6 0.038 -187 -186.5 -184.8 -183.3 6.9 111 0.348 SW 166.4 0.038 -186.9 -187.7 -186.8 -185.3 6.2 112 0.32 SW 167.2 0.038 -187 -187.5 -185.7 -183.3 6.9 113 0.314

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155EXP 16 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 83.7 1 12.2 0.33 22.94 23.7 656 0.33 23. 27 24.1 401 0.33 22.48 24 508.5 0.0 1 0.377 N 84.1 1 9.2 0.33 22.47 23 255 0.33 22.56 23.4 243 0.33 21.66 23.1 356.4 0.0 2 0.311 N 81.9 1 5.2 0.33 21.34 21. 9 385 0.33 21.46 22.5 274 0.33 20.42 21.9 416.9 0.0 3 0.382 N 88.9 1 1.4 0.33 20.25 20. 8 354 0.33 20.44 21.4 280 0.33 19.5 20.9 313.1 0.0 4 0.355 N 84.3 1 -2.3 0.33 18.83 19.4 400 0.33 19. 15 20.2 275 0.33 18.17 19.6 361.8 0.0 5 0.382 N 90.8 1 -6.6 0.33 17.32 17.8 376 0.33 17. 49 18.7 305 0.33 16.38 17.8 422.3 0.0 6 0.373 N 87.4 1 -11.6 0.33 15.44 16 401 0.33 15.78 16.9 347 0.33 15.01 16.3 317.9 0.0 7 0.413 N 93.5 1 -17 0.33 13.5 13.9 374 0.33 13.98 15.2 238 0.33 12.93 14.3 362.6 0.0 8 0.421 N 93.5 1 -25.9 0.33 11.34 11.7 396 0.33 11. 78 13.1 311 0.33 10.73 12.1 391 0.0 9 0.444 N 94.6 1 -28.3 0.33 9.008 9.3 414 0.33 9. 401 10.8 314 0.33 8.23 9.6 428.6 0.0 10 0.395 N 96.4 1 -32.2 0.33 6.43 6.6 408 0.33 6. 981 8.4 296 0.33 5.845 7.1 376.3 0.0 11 0.44 N 97 1 -40.1 0.33 3.416 3.6 458 0.33 3. 974 5.6 339 0.33 2.743 4 452.7 0.0 12 0.443 N 97.1 1 -43.8 0.33 -0.11 0.1 411 0.33 0. 55 2.3 315 0.33 -0.61 0.6 387.2 0.0 13 0.466 N 103.1 1 -61.2 0.33 -3.55 -3.6 348 0.33 -2. 79 -1.1 258 0.33 -3.95 -2.8 327.6 0.0 14 0.43 N 100.7 1 -77.6 0.33 -7.02 -7.2 296 0.33 -6. 37 -4.6 230 0.33 -7.58 -6.6 298.5 0.0 15 0.379 N 106.4 1 -94.6 0.33 -11.3 -11.4 347 0.33 -11. 1 -9 305 0.33 -12.3 -11.1 376.1 0.0 16 0.42 N 103.1 1 -96.4 0.33 -15.1 -15.5 320 0.33 -14. 8 -13 252 0.33 -15.8 -15.1 307.7 0.0 17 0.382 N 104.2 1 -104.1 0.33 -19.2 -19.6 286 0.33 -19. 3 -17.3 253 0.33 -20.3 -19.6 311.4 0.0 18 0.411 N 111.7 1 -120.5 0.33 -23.4 -23.9 319 0.33 -23. 7 -21.7 269 0.33 -24.8 -24.3 342.5 0.0 19 0.383 N 105 1 -116.8 0.33 -27.5 -28.1 279 0.33 -28.1 -26.2 258 0.33 -29.1 -28.8 305.8 0.0 20 0.35 SW 111 1 -129.9 0.33 -31.7 -32.4 277 0.33 -32. 7 -30.8 248 0.33 -33.7 -33.6 312.3 3.7 21 0.397 SW 109.9 0.022 -137.7 0.33 -36 -36.7 199 0.33 37.2 -35.3 184 0.33 -38 -38.1 212.2 4.4 22 0.356 SW 111.7 0.022 -183.2 0.33 -40 -41 197 0.33 -41. 3 -39.6 170 0.33 -42 -42.5 206.7 2.3 23 0.365 SW 113.1 0.022 -184.7 0.33 -44.4 -45.4 210 0.33 -46.1 -44.2 193 0. 33 -46.8 -47.3 234 2.9 24 0.4 SW 111.9 0.022 -185.6 0.33 -48.1 -49.4 193 0.33 -49.9 -48.4 171 0. 33 -50.4 -51.4 202.3 1.9 25 0.35 SW 111.9 0.022 -185.3 0.33 -52.3 -53.6 209 0.33 -54.2 -52.6 184 0. 33 -54.7 -55.8 228.8 3.3 26 0.374 SW 115.7 0.022 -184.7 0.33 -56 -57.6 198 0.33 -58. 3 -56.8 184 0.33 -58.8 -60.1 228.2 3.3 27 0.348 SW 112.8 0.022 -185.2 0.33 -60.3 -61.9 223 0.33 -62.4 -61.1 200 0. 33 -62.5 -64.1 217 3.3 28 0.384 SW 123.8 0.022 -184.7 0.33 -64 -65.8 205 0.33 66.8 -65.4 205 0.33 -67 -68.6 252.4 2.8 29 0.414 SW 123.2 0.022 -184.7 0.33 -68 -69.8 220 0.33 71 -69.6 197 0.33 -71.4 -73.2 262.1 2.6 30 0.385 SW 120.8 0.022 -185 0.33 -71.5 -73.6 204 0.33 74.8 -73.5 195 0.33 -75 -77.2 235.9 3.4 31 0.432 SW 123.7 0.022 -185.3 0.33 -75.6 -77.7 234 0.33 -78.8 -77.7 219 0. 33 -78.5 -81 228.7 3.8 32 0.417 SW 125.5 0.023 -185.4 0.33 -79.4 -81.6 228 0.33 -82.7 -81.7 204 0. 33 -82.6 -85.1 262.1 3.6 33 0.422 SW 128.2 0.022 -185.4 0.33 -82.4 -85.1 203 0.33 -85.9 -85 173 0. 33 -86 -88.9 244.5 3.6 34 0.434 SW 131.3 0.022 -184.8 0.33 -86 -88.6 215 0.33 -89. 7 -88.9 223 0.33 -89.3 -92.4 239.9 3.4 35 0.436 SW 135.7 0.023 -184.9 0.33 -88.9 -91.7 197 0.33 -93.1 -92.3 190 0. 33 -92.8 -96.1 255 3.7 36 0.393 SW 139.7 0.023 -185.1 0.33 -92.1 -95 210 0.33 -96. 1 -95.6 191 0.33 -95.7 -99.2 226.1 4.1 37 0.418 SW 141.5 0.023 -185.2 0.33 -94.9 -97.9 189 0.33 -99.6 -98.9 200 0. 33 -99.2 -102.8 264.6 3.3 38 0.379

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156EXP 16 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 141.5 0.024 -186 0.33 -98.1 -101.1 215 0.33 103 -102.3 222 0.33 -102 -105.9 233.4 3.7 39 0.367 SW 144.3 0.024 -185 0.33 -100 -103.5 165 0.33 105 -104.7 144 0.33 -105 -108.7 227.8 3.6 40 0.38 SW 146.2 0.024 -185.2 0.33 -103 -105.9 172 0.33 108 -107.4 191 0.33 -107 -111.1 203.5 4.3 41 0.361 SW 151.4 0.025 -183.8 0.33 -105 -108.6 196 0.33 111 -110.6 227 0.33 -110 -114.2 269.4 3.4 42 0.373 SW 154.4 0.025 -184.8 0.33 -108 -111 173 0.33 113 -112.8 148 0.33 -112 -116.6 213.6 3.7 43 0.37 SW 153.9 0.026 -185.4 0.33 -110 -113.4 174 0.33 -115 -115.1 165 0.33 -114 -119 222.1 4.0 44 0.328 SW 150.5 0.026 -185.2 0.33 -112 -115.6 172 0.33 -117 -117.2 159 0.33 -116 -121.3 219 3.5 45 0.354 SW 158.7 0.027 -185.4 0.33 -114 -117.9 183 0.33 120 -119.8 202 0.33 -119 -123.6 228.5 4.5 46 0.355 SW 164.2 0.027 -185.4 0.33 -116 -120 164 0.33 122 -121.8 160 0.33 -120 -125.5 197.4 4.0 47 0.369 SW 163.5 0.028 -184.9 0.33 -118 -122 166 0.33 124 -124.1 186 0.33 -123 -127.8 242.8 4.1 48 0.377 SW 163.6 0.028 -185.3 0.33 -120 -124.1 184 0.33 126 -126.1 175 0.33 -124 -129.8 217.6 4.3 49 0.404 SW 165.2 0.028 -184.7 0.33 -122 -126.1 171 0.33 128 -128.2 187 0.33 -126 -131.8 223.4 5.9 50 0.393 SW 162.9 0.029 -185.2 0.33 -124 -128.2 189 0.33 130 -130.2 179 0.33 -128 -133.5 201.1 3.4 51 0.411 SW 162.6 0.029 -185.1 0.33 -126 -130.2 180 0.33 131 -132.1 184 0.33 -130 -135.4 236.4 4.0 52 0.431 SW 161.3 0.029 -185.3 0.33 -128 -132.1 179 0.33 -133 -134.1 202 0.33 -131 -137 201.7 4.5 53 0.42 SW 164.6 0.029 -185.4 0.33 -130 -134.2 215 0.33 135 -136.4 244 0.33 -133 -138.7 211.1 4.9 54 0.408 SW 162.1 0.03 -184.9 0.33 -131 -135.8 155 0.33 136 -137.6 126 0.33 -134 -140.1 182.4 6.0 55 0.424 SW 163.3 0.03 -185.2 0.33 -133 -137.5 175 0.33 139 -139.5 225 0.33 -136 -142.1 275.5 4.3 56 0.406 SW 162.2 0.03 -184.8 0.33 -134 -139.2 188 0.33 -140 -141 169 0.33 -137 -143.1 147.5 4.9 57 0.417 SW 167.3 0.031 -184.9 0.33 -136 -140.7 169 0.33 141 -142.3 149 0.33 -139 -145.1 285.2 4.9 58 0.413 SW 163.9 0.031 -185 0.33 -137 -141.9 138 0.33 143 -144.1 239 0.33 -139 -146 133.3 4.1 59 0.418 SW 161.9 0.032 -185.2 0.33 -139 -143.6 196 0.33 144 -145.3 151 0.33 -141 -147.5 234.1 4.0 60 0.418 SW 166.7 0.034 -186 0.33 -140 -145.1 177 0.33 145 -146.5 160 0.33 -142 -148.6 178.5 4.9 61 0.398 SW 174.7 0.035 -185.1 0.33 -141 -146.3 155 0.33 147 -148.1 233 0.33 -144 -150.1 245.6 4.4 62 0.403 SW 177 0.038 -184.8 0.33 -142 -147.2 121 0.33 147 -149 120 0.33 -144 -151.1 189.4 3.8 63 0.376 SW 182.9 0.04 -185 0.33 -143 -148.5 170 0.33 149 -150.5 238 0.33 -146 -152.6 251.4 4.2 64 0.368 SW 185.5 0.043 -185.4 0.33 -144 -149.7 166 0.33 -150 -151.5 146 0.33 -147 -153.8 224 5.2 65 0.369 SW 192.5 0.046 -185.1 0.33 -145 -150.7 146 0.33 151 -152.6 187 0.33 -148 -154.8 196.2 3.4 66 0.398 SW 197.3 0.047 -185 0.33 -146 -151.5 118 0.33 152 -153.7 189 0.33 -149 -155.9 232.6 4.9 67 0.396 SW 186 0.044 -185 0.33 -147 -152.7 175 0.33 153 -154.8 195 0.33 -150 -157 237.5 4.5 68 0.386 SW 179.8 0.042 -184.9 0.42 -149 -153.9 184 0.42 -156 -156.1 89 0.17 -167 -171.8 3424 4.4 69 0.412 SW 179.8 0.042 -184.9 0.42 -152 -155.1 137 0.42 -176 -171.4 3435 0.17 -176 -180.8 4652 4.6 70 0.373 SW 192.6 0.068 -185 -157.3 -180.7 -181.7 4.3 71 0.323 SW 192 0.05 -184.8 -166.4 -182.3 -182.3 5.2 72 0.343 SW 191.1 0.051 -185.2 -180.4 -183.4 -182.7 3.5 73 0.379 SW 197 0.055 -184.9 -182.4 -183.7 -182.9 3.6 74 0.315 SW 197.1 0.057 -184.7 -182.7 -184 -183.1 5.7 75 0.297 SW 191.7 0.057 -185 -183.1 -184.1 -183.1 3.3 76 0.358

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157EXP 16 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 184.7 0.058 -185.3 -183.5 -184.3 -183.2 4.1 77 0.301 SW 184.3 0.058 -185 -183.3 -184.4 -183.5 3.7 78 0.402 SW 184.6 0.058 -185 -183.6 -184.8 -183.8 5.5 79 0.284 SW 178.8 0.058 -185.3 -183.9 -185.2 -184.3 3.9 80 0.296 SW 174.5 0.059 -185.2 -183.9 -185.1 -184.3 5.1 81 0.27 SW 178 0.059 -185.5 -184.6 -185.3 -184 5.7 82 0.231 SW 170.7 0.06 -185.3 -184.6 -185.6 -184.5 4.5 83 0.262 SW 174.6 0.06 -185.4 -184.8 -185.5 -184.5 6.1 84 0.267 EXP 17 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 81.3 1 8.8 0.33 22.85 23.7 572 0.33 23. 11 24 433 0.33 22.46 24 437.2 0.0 1 0.360 N 82.1 1 6.6 0.33 22.29 22. 9 281 0.33 22.37 23.3 198 0.33 21.39 22.9 400.8 0.0 2 0.297 N 85.8 1 3.3 0.33 21.48 22 298 0.33 21.8 22.6 174 0.33 20.91 22.2 207.7 0.0 3 0.380 N 82.4 1 0.5 0.33 20.29 20.8 367 0.33 20. 57 21.6 267 0.33 19.56 21 384 0.0 4 0.373 N 86.9 1 -2.3 0.33 19.42 19.9 262 0.33 19. 57 20.5 235 0.33 18.6 19.9 289.9 0.0 5 0.301 N 88.3 1 -6.3 0.33 18.04 18.5 349 0.33 18. 43 19.4 228 0.33 17.5 18.8 281.2 0.0 6 0.363 N 88.2 1 -10.4 0.33 16.77 17.1 305 0.33 17. 14 18.2 218 0.33 16.13 17.4 302.4 0.0 7 0.399 N 87.3 1 -15.3 0.33 15.02 15.4 364 0.33 15. 37 16.5 281 0.33 14.33 15.7 364.4 0.0 8 0.385 N 94.7 1 -19 0.33 13.63 13.9 250 0.33 14.12 15.1 171 0.33 13.12 14.3 218.7 0.0 9 0.399 N 94 1 -31.6 0.33 11.58 11.9 318 0.33 11.84 13.3 233 0.33 10.47 11.9 381.4 0.0 10 0.405 N 92.4 1 -34.6 0.33 9.337 9.6 332 0.33 10. 02 11.2 229 0.33 8.978 10.1 246.2 0.0 11 0.387 N 91 1 -41.2 0.33 6.997 7.1 361 0.33 7. 494 8.9 275 0.33 6.288 7.5 382 0.0 12 0.427 SW 95.7 0.036 -41 0.33 4.909 4.8 290 0.33 5. 61 6.9 183 0.33 4.369 5.4 262.9 3.7 13 0.407 SW 95.2 0.036 -53.4 0.33 2. 175 2.1 378 0.33 2.831 4.4 271 0. 33 1.513 2.6 378 4.4 14 0.426 SW 98.4 0.035 -50.3 0.33 -0.23 -0.4 269 0. 33 0.194 1.6 233 0.33 -0.94 0 277.1 2.3 15 0.376 SW 98.8 0.035 -67.7 0.33 -2.94 -3.2 250 0.33 -2 .34 -0.9 171 0.33 -3.53 -2.7 235.5 2.9 16 0.413 SW 94.1 0.036 -85.4 0.33 -5.74 -6 203 0.33 -5. 43 -3.9 171 0.33 -6.6 -5.8 217.9 1.9 17 0.410 SW 107 0.033 -107.7 0.33 -9.2 -9.4 265 0.33 -9. 03 -7.3 213 0.33 -10.3 -9.4 282.2 3.3 18 0.407 SW 97.3 0.035 -102.2 0.33 -12.5 -12.8 211 0.33 -12.5 -10.8 177 0. 33 -13.7 -13 221.3 3.3 19 0.410 SW 107.6 0.034 -127.1 0.33 -15.6 -16.1 204 0.33 -16 -14.2 176 0.33 -17.2 -16.7 232.4 3.3 20 0.336 SW 104.8 0.034 -129.3 0.33 -19. 4 -19.9 246 0.33 -20 -18 200 0. 33 -21.4 -20.9 277 2.8 21 0.371 SW 107.1 0.034 -128.1 0.33 -23 -23.6 237 0.33 23.8 -21.9 208 0.33 -25 -24.8 250.6 2.6 22 0.379 SW 107 0.034 -132.4 0.33 -26.4 -27.1 157 0.33 -27. 5 -25.7 140 0.33 -28.8 -28.7 180.2 3.4 23 0.403 SW 109.3 0.034 -181.6 0.33 -29.8 -30.7 157 0.33 -31 -29.3 134 0.33 -32.2 -32.5 169.6 3.8 24 0.341 SW 103.4 0.035 -186.2 0.33 -33.2 -34.2 157 0.33 -34.5 -32.8 129 0. 33 -35.7 -36.2 172.4 3.6 25 0.379

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158EXP 17 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 114.1 0.034 -185.6 0.33 -36.9 -37.9 170 0.33 -38.2 -36.6 151 0. 33 -39.2 -39.8 171.9 3.6 26 0.387 SW 108.5 0.034 -186 0.33 -40.3 -41.5 166 0.33 -42. 1 -40.4 147 0.33 -43.1 -43.7 193.2 3.4 27 0.361 SW 109.3 0.035 -186.9 0.33 -43.7 -45 166 0.33 -45. 7 -44.1 152 0.33 -46.6 -47.5 186.9 3.7 28 0.390 SW 115.9 0.034 -186.1 0.33 -47 -48.4 167 0.33 49 -47.6 142 0.33 -49.7 -50.9 170.7 4.1 29 0.384 SW 114.6 0.034 -185.4 0.33 -50.5 -52 177 0.33 -52. 7 -51.2 152 0.33 -53.5 -54.7 202.3 3.3 30 0.357 SW 114.2 0.034 -185 0.33 -53.8 -55.5 173 0.33 56 -54.7 148 0.33 -56.7 -58.3 186.8 3.7 31 0.367 SW 118.3 0.035 -185.1 0.33 -56.8 -58.6 158 0.33 -59.7 -58.3 158 0.33 -60.4 -62 203 3.6 32 0.343 SW 121.1 0.034 -185.8 0.33 -60 -61.8 168 0.33 -62. 8 -61.6 146 0.33 -63.4 -65.3 187.2 4.3 33 0.383 SW 124.7 0.034 -185.6 0.33 -62.7 -64.8 152 0.33 -66 -64.7 137 0.33 -66.7 -68.8 199.2 3.4 34 0.390 SW 127.1 0.035 -185.4 0.33 -65.7 -67.8 161 0.33 -69.3 -68.1 161 0. 33 -69.9 -72.1 196 3.7 35 0.364 SW 128.1 0.035 -185.6 0.33 -68.4 -70.6 153 0.33 -72.1 -71 135 0.33 -72.8 -75.3 189.8 4.0 36 0.395 SW 130.9 0.035 -185.2 0.33 -71.1 -73.3 151 0.33 -75.1 -74 144 0.33 -75.6 -78.3 189.3 3.5 37 0.368 SW 130.1 0.036 -185.6 0.33 -73.6 -75.9 146 0.33 -77.9 -76.8 143 0. 33 -78.4 -81.2 188.6 4.5 38 0.369 SW 133.6 0.036 -185.2 0.33 -76.3 -78.6 154 0.33 -80.9 -79.8 150 0. 33 -81.4 -84.3 206.2 4.0 39 0.364 SW 133.9 0.036 -185.2 0.33 -78.7 -81.2 145 0.33 -83.4 -82.5 141 0. 33 -83.7 -86.9 176.8 4.1 40 0.378 SW 135.5 0.037 -185.3 0.33 -81.4 -83.9 157 0.33 -86.1 -85.3 151 0. 33 -86.3 -89.6 185.9 4.3 41 0.371 SW 137.2 0.037 -185.1 0.33 -83.9 -86.5 156 0.33 -88.8 -88 151 0. 33 -89 -92.4 197.7 5.9 42 0.364 SW 137.4 0.037 -185.1 0.33 -86.3 -88.9 149 0.33 -91.3 -90.6 147 0.33 -91.5 -95 196 3.4 43 0.351 SW 140.1 0.038 -184.1 0.33 -88.4 -91.2 137 0.33 -93.7 -93 138 0.33 -93.8 -97.6 189.5 4.0 44 0.397 SW 140.3 0.038 -185.1 0.33 -90.9 -93.7 159 0.33 -96.1 -95.5 146 0. 33 -96.1 -100 191.4 4.5 45 0.363 SW 143.4 0.038 -185 0.33 -92.9 -95.9 135 0.33 -98. 4 -97.9 143 0.33 -98.3 -102.3 181.8 4.9 46 0.378 SW 142.7 0.039 -185.3 0.33 -95. 1 -98.1 142 0.33 -101 -100.1 138 0.33 -100 -104.5 181 6.0 47 0.380 SW 145.1 0.039 -185.3 0.33 -97.1 -100.2 137 0.33 -103 -102.4 148 0. 33 -103 -106.8 194.3 4.3 48 0.344 SW 147.9 0.04 -185.1 0.33 -100 -103 192 0.33 105 -105 174 0.33 -105 -109.4 216.3 4.9 49 0.369 SW 148.9 0.04 -185.3 0.33 -102 -105 130 0.33 107 -107.2 139 0.33 -107 -111.7 195.9 4.9 50 0.360 SW 150.3 0.041 -185.4 0.33 -103 -106.8 120 0.33 109 -109.2 134 0.33 -109 -113.5 166.3 4.1 51 0.341 SW 153.5 0.042 -185.5 0.33 -105 -108.7 140 0.33 -111 -111 133 0.33 -111 -115.4 182.6 4.0 52 0.324 SW 154.9 0.042 -185.1 0.33 -107 -110.7 141 0.33 -113 -113 138 0.33 -113 -117.5 200 4.9 53 0.373 SW 158.7 0.043 -185.3 0.33 -109 -112.5 136 0.33 -115 -114.9 135 0.33 -114 -119.2 173 4.4 54 0.303 SW 160.2 0.044 -185.2 0.33 -111 -114.3 127 0.33 117 -116.8 151 0.33 -116 -121.2 203.3 3.8 55 0.376 SW 161.6 0.045 -185.4 0.33 -112 -116 128 0.33 118 -118.5 119 0.33 -118 -123 187.3 4.2 56 0.340 SW 163.6 0.045 -185.4 0.33 -114 -117.4 111 0.33 120 -120.1 127 0.33 -119 -124.7 183.7 5.2 57 0.292 SW 164.7 0.046 -185.5 0.33 -115 -119 122 0.33 122 -121.7 129 0.33 -121 -126.3 176.9 3.4 58 0.307 SW 169.1 0.047 -185.3 0.33 -117 -120.5 122 0.33 123 -123.1 113 0.33 -122 -127.7 165.5 4.9 59 0.287 SW 171 0.048 -185.3 0.33 -118 -122.1 126 0.33 125 -124.8 138 0.33 -124 -129.2 184.3 4.5 60 0.314 SW 169.7 0.049 -185.2 0.33 -120 -123.7 133 0.33 126 -126.4 139 0.33 -125 -130.7 181.6 4.4 61 0.310 SW 172.8 0.049 -185.1 0.33 -121 124.7 83.4 0.33 -127 -127.7 112 0. 33 -126 -132.2 186.8 4.6 62 0.302 SW 176.1 0.051 -185.1 0.33 -122 -126.4 149 0.33 129 -129.3 155 0.33 -128 -133.8 201.7 4.3 63 0.313

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159EXP 17 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 175.2 0.052 -185.3 0.33 -123 -127.6 102 0.33 130 -130.6 109 0.33 -129 -135.1 174.8 5.2 64 0.292 SW 174.6 0.052 -185.3 0.33 -125 -129 117 0.33 131 -131.8 121 0.33 -130 -136.3 174 3.5 65 0.329 SW 176.9 0.053 -185.2 0.33 -126 -130.3 115 0.33 -133 -133.4 155 0.33 -131 -137.5 168 3.6 66 0.309 SW 176.6 0.054 -185.5 0.33 -127 -131.5 113 0.33 134 -134.4 96.1 0.33 -133 -138.7 189.2 5.7 67 0.328 SW 176.2 0.055 -185.1 0.33 -128 -132.9 133 0.33 135 -135.6 130 0.33 -134 -139.8 163.4 3.3 68 0.301 SW 176.1 0.056 -185.4 0.33 -130 -134.2 128 0.33 -136 -137 147 0.33 -135 -140.9 179.6 4.1 69 0.361 SW 178.7 0.057 -185.2 0.33 -131 -135.4 114 0.33 137 -138.2 127 0.33 -136 -142.1 180.4 3.7 70 0.303 SW 174.5 0.058 -185.3 0.33 -132 -136.6 122 0.33 -138 -139.3 127 0.33 -137 -143 152.2 5.5 71 0.350 SW 178.2 0.06 -185.2 0.33 -133 -137.9 128 0.33 140 -140.5 131 0.33 -138 -144.2 200.7 3.9 72 0.340 SW 178.3 0.062 -185.2 0.33 -134 -139.2 143 0.33 141 -141.6 128 0.33 -139 -145.3 178.4 5.1 73 0.332 SW 180.2 0.062 -185.1 0.33 -136 -140.4 134 0.33 142 -142.9 157 0.33 -140 -146.3 182.6 5.7 74 0.310 SW 179.6 0.064 -185 0.33 -137 -141.5 116 0.33 143 -144.1 151 0.33 -141 -147.4 195.3 4.5 75 0.358 SW 182.6 0.065 -185.3 0.33 -138 -142.5 117 0.33 144 -145.1 142 0.33 -142 -148.4 177.9 6.1 76 0.389 SW 182.3 0.066 -185.2 0.33 -139 -143.7 135 0.33 145 -146.2 147 0.33 -143 -149.6 214.6 4.3 77 0.353 SW 184.6 0.067 -185.1 0.33 -140 -144.9 142 0.33 146 -147.3 144 0.33 -144 -150.5 185.9 5.5 78 0.344 SW 181.9 0.067 -185.1 0.33 -141 -145.8 115 0.33 147 -148.4 166 0.33 -145 -151.7 218.4 5.9 79 0.371 SW 180.6 0.067 -185 0.33 -142 -147.1 168 0.33 148 -149.4 138 0.33 -146 -152.5 175.4 4.9 80 0.377 SW 181.4 0.069 -185.5 0.33 -143 -148.2 133 0.33 149 -150.5 167 0.33 -147 -153.5 200.1 4.2 81 0.387 SW 175.9 0.069 -185.2 0.33 -144 -149.3 143 0.33 150 -151.5 150 0.33 -147 -154.2 171.1 5.1 82 0.348 SW 180.8 0.071 -185.6 0.33 -145 -149.9 82.1 0.33 -151 -152.3 141 0.33 -148 -155 173.8 6.3 83 0.362 SW 182.5 0.071 -185.1 0.33 -146 -151.3 204 0.33 -152 -153.5 195 0.33 -149 -156 224.6 4.3 84 0.369 SW 179.7 0.073 -185.4 0.33 -147 -152.3 135 0.33 -153 -154.5 172 0.33 -150 -157 216.3 3.2 85 0.374 SW 177.7 0.072 -185.1 0.33 -148 -153.2 139 0.33 -154 -155.5 180 0.33 -151 -158 238.3 3.7 86 0.370 SW 175.3 0.071 -185.4 0.33 -149 -154.3 161 0.33 -155 -156.4 153 0.33 -152 -159 224.7 5.1 87 0.372 SW 181.8 0.073 -185.3 0.42 -150 -155.1 126 0.42 158 -157.5 69.5 0.17 -170 -175.3 3998 4.3 88 0.391 SW 175.3 0.069 -185.5 0.42 -153 -156.1 107 0.42 -175 -171.2 3143 0.17 -176 -181.5 5182 4.2 89 0.416 SW 171.1 0.069 -185.6 -157.5 -180.9 -182.2 3.7 90 0.405 SW 165.8 0.069 -185.5 -163.5 -183.5 -183.3 5.9 91 0.423 SW 164.9 0.07 -185.5 -176 -184.1 -183.5 4.6 92 0.412 SW 169.2 0.072 -185.6 -182.2 -184.2 -183.6 3.4 93 0.402 SW 179.9 0.08 -185.5 -183.4 -184.7 -184 5.0 94 0.431 SW 182.7 0.087 -185.6 -184.2 -185.3 -184.3 4.8 95 0.390 SW 187.8 0.091 -185.4 -184.3 -185.5 -184.4 4.6 96 0.349 SW 185.2 0.093 -185.3 -184.7 -185.2 -184.5 4.6 97 0.328 SW 183.5 0.094 -185.3 -184.2 -185 -184.3 3.6 98 0.356 SW 184 0.094 -185.6 -184.4 -185.3 -184.5 6.0 99 0.317 SW 184.3 0.095 -185.5 -184.4 -185.3 -184.4 4.9 100 0.285

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160EXP 18 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 52.1 1 12.3 0.33 22.3 23.3 972 0.33 22.3 23.4 927.4 0.33 21.8 23.5 875.8 0.0 1 0.123 N 54 1 11.1 0.33 22.3 22.8 184. 2 0.33 22.6 23.1 49.4 0.33 22.1 23.2 33.3 0.0 2 0.213 N 50.1 1 9.7 0.33 22 22.5 188. 5 0.33 22.4 22.9 57.1 0.33 21.6 22.9 191.3 0.0 3 0.278 N 56.3 1 8 0.33 21.3 21.8 340. 4 0.33 21.6 22.3 270.3 0.33 20.9 22.2 309.2 0.0 4 0.277 N 51.8 1 7.4 0.33 21.2 21.5 132.6 0.33 21.5 22 43.9 0.33 20.7 21.9 161.2 0.0 5 0.157 N 57.9 1 6.1 0.33 20.6 21 231.9 0.33 20.9 21.5 232.1 0. 33 20.2 21.4 223 0.0 6 0.304 N 51.7 1 5 0.33 20 20.4 266 0.33 20.3 20. 9 209.4 0.33 19.7 20.9 202 0.0 7 0.211 N 54.7 1 3.8 0.33 19.5 19.9 233.7 0.33 19.9 20.4 150.5 0.33 19.3 20.4 189.3 0.0 8 0.244 N 52.4 1 2.5 0.33 18.8 19.1 287.4 0.33 19.1 19.8 223.4 0.33 18.4 19.7 291.8 0.0 9 0.307 N 58.8 1 0.1 0.33 18.3 18.6 210.4 0.33 18.7 19.3 115.6 0.33 18.1 19.1 177.3 0.0 10 0.354 N 54.2 1 -0.8 0.33 17.5 17.8 276.9 0.33 18. 1 18.6 186.2 0.33 17.4 18.5 211.7 0.0 11 0.246 N 55.1 1 -2.4 0.33 16.9 17.1 242.6 0.33 17.4 18 158 0.33 16.7 17.8 236.6 0.0 12 0.299 N 53.8 1 -4.3 0.33 16.1 16.3 275.9 0.33 16. 7 17.4 141.8 0.33 15.9 17 266.5 0.0 13 0.395 N 57 1 -6.5 0.33 15.5 15.7 204.5 0.33 15.9 16.5 210.1 0.33 15.2 16. 3 208.6 0.0 14 0.377 N 57.9 1 -8.4 0.33 14.8 14.9 213.4 0.33 15. 1 15.8 164.6 0.33 14.4 15.5 231.8 0.0 15 0.367 N 57 1 -10.9 0.33 13.9 14 258.2 0.33 14.4 15 147.7 0.33 13.7 14.7 201.6 0.0 16 0.413 N 57.9 1 -13.1 0.33 12.9 13 259 0.33 13.4 14.1 164.9 0.33 12.4 13. 5 297.2 0.0 17 0.378 N 58.9 1 -16.8 0.33 11.8 11. 9 256.4 0.33 12.5 13.1 162.3 0. 33 11.7 12.6 203.4 0.0 18 0.382 N 58.1 1 -19.5 0.33 10.7 10. 8 251.9 0.33 11.5 12.1 168.8 0. 33 10.8 11.7 209.7 0.0 19 0.398 N 59.4 1 -22.7 0.33 9.7 9.7 179.3 0.33 10. 3 11 136.7 0.33 9.4 10.4 205.4 0.0 20 0.407 N 61.6 1 -36.8 0.33 8.4 8.4 195.5 0.33 9 9.7 150.4 0.33 8.2 9. 1 195.1 0.0 21 0.41 N 60.5 1 -39.7 0.33 6.9 6.9 244.5 0.33 7. 4 8.3 161.6 0.33 6.3 7.3 275.6 0.0 22 0.412 N 60.7 1 -40.8 0.33 5.7 5.5 196.4 0.33 6. 3 7.1 124.8 0.33 5.1 5.9 208.9 0.0 23 0.414 N 61.2 1 -43.3 0.33 3.9 3.8 317.6 0.33 4. 6 5.5 210.1 0.33 3.5 4.2 296.5 0.0 24 0.413 N 59.4 1 -37.9 0.33 2.6 2.3 233.5 0.33 3. 1 3.9 189.8 0.33 2 2.7 258.5 0.0 25 0.41 N 61.9 1 -41.6 0.33 0.9 0.6 299.3 0.33 1. 6 2.4 185.7 0.33 0.7 1.2 258.1 0.0 26 0.374 N 58.7 1 -41.8 0.33 -0.6 -1 231.4 0.33 -0.1 0.7 196.3 0.33 -1 -0.4 242.4 0.0 27 0.412 N 59.7 1 -50.8 0.33 -1.7 -2.2 137.7 0.33 -1.3 -0.6 95.9 0.33 -2.3 -1.9 161.2 0.0 28 0.388 N 61.4 1 -69.8 0.33 -3.4 -3.9 159.5 0.33 -3.4 -2.3 121.9 0.33 -4.8 -4.2 225.4 0.0 29 0.377 N 61.7 1 -82 0.33 -5.3 -5.7 155.2 0.33 -5.5 -4.3 136.8 0.33 -6.8 -6.4 193.7 0.0 30 0.37 N 62.7 1 -90.8 0.33 -7.1 -7.5 149.1 0.33 -7.6 -6.3 121.4 0.33 -9.4 -8.9 219.4 0.0 31 0.353 N 64.7 1 -97.1 0.33 -8.9 -9.3 142.3 0.33 -10 -8.4 132.6 0.33 -12.1 -11.7 234.6 0.0 32 0.382 N 64.3 1 -100.7 0.33 -10.6 -11. 1 135 0.33 -11.9 -10.3 105.1 0.33 -14.4 -14.2 205.2 0.0 33 0.344 N 66.5 1 -105.9 0.33 -12.7 -13. 1 151.2 0.33 -14.6 -12.7 146.6 0. 33 -17.1 -17 230.7 0.0 34 0.314 N 65.8 1 -108.7 0.33 -14.4 -14. 9 126.2 0.33 -16.6 -14.8 116.5 0. 33 -19.3 -19.4 200.5 0.0 35 0.337 N 67.7 1 -113.5 0.33 -16.5 -16. 9 136.4 0.33 -19.3 -17.2 139.9 0. 33 -22.2 -22.3 235.6 0.0 36 0.331 N 67.4 1 -116.8 0.33 -18.4 -18. 9 139.7 0.33 -21.4 -19.4 124.3 0. 33 -24.4 -24.8 217.6 0.0 37 0.343 N 70.2 1 -114.9 0.33 -20.3 -20. 8 136.4 0.33 -23.7 -21.5 118.1 0. 33 -27.2 -27.6 249.9 0.0 38 0.32

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161EXP 18 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 68.1 1 -116 0.33 -22.3 -22.8 150 0.33 -25.8 -23.7 127.6 0.33 -29.1 -29.8 209.9 0.0 39 0.317 SW 70.2 0.036 -114.6 0.33 -24.2 24.8 141.1 0.33 -28.2 -25.9 124.9 0. 33 -31.9 -32.5 264.4 2.7 40 0.3 SW 68.5 0.036 -115.7 0.33 -25.9 -26.5 118.2 0.33 -30.5 -28.1 139. 8 0.33 -34 -34.9 229 1.9 41 0.326 SW 71.7 0.035 -119.1 0.33 -28.1 28.6 151.1 0.33 -32.7 -30.3 120 0. 33 -36.5 -37.5 244.4 2.0 42 0.321 SW 71.5 0.035 -122.1 0.33 -29.8 30.5 118.7 0.33 -34.8 -32.4 115.3 0. 33 -38.6 -39.8 218.3 2.7 43 0.3 SW 72.3 0.035 -128 0.33 -31.8 -32.4 134 0.33 -37. 1 -34.7 139.3 0.33 -40.9 -42.1 231.4 3.7 44 0.284 SW 69.2 0.036 -125.7 0.33 -33.8 34.4 136.4 0.33 -39.1 -36.7 118.3 0.33 -42.8 -44.3 217 2.8 45 0.31 SW 70.2 0.036 -127.3 0.33 -35.6 36.4 130.2 0.33 -41.2 -38.8 112.2 0.33 -45 -46.5 229.8 2.9 46 0.319 SW 71.2 0.035 -129.4 0.33 -37.6 38.4 103.4 0.33 -43.5 -41 104.9 0. 33 -47.3 -48.9 175.6 3.3 47 0.327 SW 70.3 0.036 -158.5 0.33 -39.3 -40.1 76.3 0.33 -45.4 -43 78.3 0.33 -49.3 -51 147.8 3.7 48 0.266 SW 68.3 0.036 -175.9 0.33 -41.3 42.1 93.3 0.33 -47.5 -45.1 85.1 0. 33 -51.1 -53.1 138.9 4.3 49 0.35 SW 65.7 0.037 -176.5 0.33 -43.1 -44 84.5 0.33 -49.1 -47 73.1 0. 33 -52.5 -54.6 116.5 3.7 50 0.323 SW 63.8 0.038 -176.2 0.33 -44.8 -45.8 82 0.33 -50.8 -48.8 74.6 0.33 -54 -56.2 122 5.1 51 0.317 SW 64.4 0.037 -176.6 0.33 -46.5 47.5 79.7 0.33 -52.9 -50.8 88.9 0.33 -56 -58.1 138.2 3.1 52 0.315 SW 67.3 0.036 -176.3 0.33 -48.2 49.3 83.6 0.33 -54.5 -52.4 64.7 0. 33 -57.8 -60.1 141.1 3.7 53 0.215 SW 64.6 0.037 -176.6 0.33 -49.9 51.1 83.4 0.33 -56.1 -54.1 71.1 0. 33 -59.4 -61.8 132.9 4.1 54 0.2 SW 65.3 0.037 -177 0.33 -51.3 -52. 6 70.5 0.33 -57.7 -55.8 73.3 0. 33 -60.8 -63.3 118.5 3.3 55 0.267 SW 67.2 0.036 -177.1 0.33 -53 54.3 79.5 0.33 -59.5 -57.6 82.7 0.33 -62.4 -65 131.8 2.7 56 0.222 SW 63.3 0.038 -177.6 0.33 -54.5 55.9 75.4 0.33 -61.1 -59.2 67.4 0. 33 -64.3 -66.9 143.5 3.1 57 0.228 SW 64.4 0.037 -177.5 0.33 -56 -57.5 73 0.33 -62. 7 -60.9 77.6 0.33 -65.5 -68.3 115.6 3.2 58 0.206 SW 66.2 0.036 -177.3 0.33 -57.5 -59 75.6 0.33 -64.2 -62.4 64.3 0.33 -67.2 -70 136.8 3.2 59 0.195 SW 64.1 0.037 -177.7 0.33 -59 -60. 6 73.8 0.33 -65.6 -63.9 66.1 0. 33 -68.5 -71.5 126.6 3.7 60 0.189 SW 64.8 0.037 -177.8 0.33 -60.5 62.1 74.2 0.33 -67.3 -65.6 76.5 0.33 -70.2 -73.1 136 4.3 61 0.202 SW 62.4 0.038 -178.4 0.33 -61.7 63.4 62.2 0.33 -68.5 -66.9 57.3 0. 33 -71.4 -74.6 124.5 3.8 62 0.198 SW 64.9 0.037 -177.8 0.33 -63.3 64.9 76.7 0.33 -70.4 -68.6 88.9 0. 33 -73.1 -76.2 140.5 3.5 63 0.176 SW 66 0.036 -178.3 0.33 -64.4 66.1 57.1 0.33 -71.6 -70 63.1 0. 33 -74.4 -77.6 127.2 2.9 64 0.144 SW 67.2 0.036 -177.8 0.33 -65.6 67.4 58.1 0.33 -73.3 -71.5 74.2 0. 33 -76.2 -79.4 155.1 3.6 65 0.148 SW 72.6 0.034 -178.3 0.33 -66.8 68.6 60.3 0.33 -74.4 -72.7 57.9 0. 33 -77.4 -80.9 130.4 3.6 66 0.151 SW 81.3 0.032 -177.9 0.33 -68.3 70.1 74.7 0.33 -76.1 -74.2 68.5 0. 33 -79.5 -82.8 174.2 3.8 67 0.166 SW 78.4 0.033 -178.2 0.33 -69.5 71.3 60.8 0.33 -77.8 -75.8 88.5 0. 33 -81.1 -84.6 157.9 3.2 68 0.178 SW 83 0.032 -177.7 0.33 -70.7 -72. 6 59.8 0.33 -79.3 -77.2 66.3 0. 33 -82.8 -86.4 169.8 4.0 69 0.163 SW 81 0.033 -178.8 0.33 -72.1 -73. 9 67.7 0.33 -80.9 -78.7 73.1 0. 33 -84.8 -88.4 182.6 3.8 70 0.164 SW 79.4 0.033 -178.8 0.33 -73.2 75.1 56.7 0.33 -82.2 -80.1 67.9 0.33 -86 -89.9 153.2 2.9 71 0.195 SW 89.9 0.031 -178.6 0.33 -74.4 76.3 53.3 0.33 -83.6 -81.5 67.4 0. 33 -87.5 -91.4 165.5 3.5 72 0.193 SW 85.9 0.032 -178.4 0.33 -75.7 -77.6 64.2 0.33 -85.1 -82.9 75. 6 0.33 -89 -93 165.3 2.9 73 0.196 SW 91.9 0.031 -178.2 0.33 -76.5 78.5 37.9 0.33 -86.6 -84.3 73.3 0.33 -90.6 -94.6 176 3.7 74 0.166 SW 78.9 0.033 -178.5 0.33 -78.1 -79.9 75.2 0.33 -87.9 -85.7 71. 8 0.33 -91.8 -96 162 2.6 75 0.192 SW 98 0.03 -178.2 0.33 -79.3 81.2 62.5 0.33 -89.4 -87.1 77 0. 33 -93.5 -97.6 182.6 3.3 76 0.149

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162EXP 18 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 88 0.032 -178.9 0.33 -80.4 -82. 4 57.7 0.33 -90.4 -88.1 44 0.33 -94.6 -99 162 2.6 77 0.23 SW 82.6 0.033 -178.5 0.33 -81.4 83.5 48 0.33 -91.6 -89.3 62.5 0.33 -95.9 -100.3 172.4 3.1 78 0.168 SW 108.1 0.03 -177.9 0.33 -82.7 -84. 7 58.9 0.33 -93.4 -90.8 79.7 0.33 -97.9 -102.2 217.9 2.3 79 0.155 SW 81.4 0.034 -179 0.33 -83.6 -85. 7 47.8 0.33 -94.1 -91.8 42.9 0.33 -98.5 -103.2 146 3.3 80 0.228 SW 100.6 0.03 -177.9 0.33 -84.8 -86. 8 53.5 0.33 -95.7 -93.2 77.5 0.33 -100.4 -104.9 214.4 2.1 81 0.108 SW 101.1 0.031 -178.2 0.33 -86 -88. 1 64.6 0.33 -96.8 -94.3 54.1 0.33 -101.4 -106.2 177.5 2.2 82 0.218 SW 104.1 0.031 -177.7 0.33 -87.2 -89. 3 60.7 0.33 -98.1 -95.6 69.3 0.33 -102.7 -107.5 192.5 3.5 83 0.161 SW 91.4 0.033 -178.3 0.33 -88.4 90.5 61.8 0.33 -99.4 -97 76.2 0.33 -103.8 -108.7 175.6 2.0 84 0.242 SW 93.5 0.032 -178.6 0.33 -89.3 91.6 48.8 0.33 -100.3 -98 46.6 0.33 -104.9 -109.9 183.5 2.1 85 0.164 SW 98.4 0.031 -178.2 0.33 -90.5 -92. 7 57.1 0.33 -101.7 -99.3 75.6 0.33 -106.1 -111.1 189.6 2.4 86 0.137 SW 100.3 0.031 -178 0.33 -91.6 -93. 9 57.5 0.33 -102.8 -100.4 58.9 0.33 -107.5 -112.5 210.3 2.2 87 0.176 SW 96.8 0.032 -178.1 0.33 -92.9 -95. 2 68.5 0.33 -104.2 -101.8 88.1 0.33 -108.5 -113.6 184 4.8 88 0.168 SW 104.5 0.031 -178.8 0.33 -93.6 96 38.1 0.33 -104.8 -102.6 33.7 0.33 -109.2 -114.5 168.7 2.6 89 0.223 SW 95.2 0.032 -178 0.33 -94.7 -97. 1 51.3 0.33 -106.1 -103.8 70.8 0.33 -110.5 -115.7 200.7 2.2 90 0.17 SW 108 0.031 -178.2 0.33 -95.6 98 45.4 0.33 -107.2 -105 75.7 0.33 -111.4 -116.7 180.3 5.5 91 0.202 SW 98.5 0.032 -178.3 0.33 -97 -99. 4 78.4 0.33 -108.4 -106.1 66.1 0.33 -112.6 -117.9 210.5 3.2 92 0.171 SW 105.2 0.031 -177.9 0.33 -97.9 -100. 3 42.3 0.33 -109.5 -107.4 87.4 0.33 -113.3 -118.8 171.8 3.2 93 0.197 SW 89.9 0.033 -178.2 0.33 -99 -101. 6 69.8 0.33 -110.2 -108 22.9 0.33 -114.4 -119.9 201.7 2.3 94 0.099 SW 104.4 0.032 -178.2 0.33 -100 -102. 6 54.9 0.33 -111.1 -109 58.1 0.33 -115.3 -120.8 187.8 2.4 95 0.187 SW 99.2 0.032 -178.2 0.33 -100.8 103.5 43.7 0.33 -112.3 -110.2 73 0.33 -116.4 -122 210.5 6.2 96 0.16 SW 106.7 0.032 -178.4 0.33 -101.8 104.5 56.7 0.33 -113.1 -111 42.5 0.33 -117.3 -122.9 197.9 2.6 97 0.211 SW 105.2 0.032 -177.8 0.33 -102.9 105.6 60.1 0.33 -114.4 -112.2 83 0.33 -118.5 -124.1 226.2 3.2 98 0.166 SW 110.1 0.031 -178 0.33 -103.7 -106. 6 50.4 0.33 -115 -112.9 26.7 0.33 -119.3 -125 197.7 5.2 99 0.141 SW 100.6 0.032 -178.4 0.33 -104.7 107.5 54.2 0.33 -116.1 -114 73.6 0.33 -120.2 -126 209.9 2.7 100 0.202 SW 113.9 0.031 -177.8 0.33 -105.4 108.4 44.2 0.33 -117.1 -115 56.1 0.33 -121.3 -127.1 234.5 3.0 101 0.206 SW 108.8 0.032 -177.6 0.33 -106.8 109.7 83.3 0.33 -118 -116 67.8 0.33 -121.9 -127.8 190.8 2.9 102 0.188 SW 98.2 0.032 -177.7 0.33 -107.5 -110. 6 50.7 0.33 -118.8 -116.9 56.3 0.33 -122.5 -128.5 187.4 4.1 103 0.171 SW 125.4 0.03 -177.2 0.33 -108.7 111.7 69.8 0.33 -120 -118.2 92.4 0.33 -123.6 -129.5 222.1 5.6 104 0.228 SW 87.3 0.035 -178.2 0.33 -109.7 112.8 66 0.33 -120.9 -119.2 74.1 0.33 -124.1 -130.2 189.6 3.6 105 0.23 SW 101.4 0.031 -177.8 0.33 -110.7 -113. 8 66.7 0.33 -121.7 -120.1 62.7 0.33 -125 -131.1 209.3 4.1 106 0.142 SW 91.6 0.033 -178.6 0.33 -111.4 -114. 6 40.8 0.33 -122.3 -120.9 62.4 0.33 -125.1 -131.3 136.1 6.1 107 0.203 SW 95.3 0.032 -178.4 0.33 -112.7 115.8 83.8 0.33 -123.5 -122 87.2 0.33 -126.3 -132.3 230.2 3.8 108 0.179 SW 98.6 0.032 -178.4 0.33 -113.4 116.8 59.9 0.33 -124 -122.6 26.9 0.33 -127 -133.2 202.5 3.9 109 0.159 SW 100 0.032 -178.8 0.33 -114 -117.5 36.4 0.33 -124.7 -123.4 64.5 0.33 -127.5 -133.8 180.7 5.6 110 0.177 SW 93.3 0.033 -178.9 0.33 -115.1 -118. 5 71.6 0.33 -125.8 -124.4 80.4 0.33 -128.5 -134.6 218.3 2.9 111 0.142 SW 98.8 0.032 -179 0.33 -115.7 -119. 2 43.4 0.33 -126.2 -125 35.6 0.33 -129 -135.3 190.2 6.0 112 0.131 SW 106.8 0.031 -179.3 0.33 -116.4 -119. 9 40.8 0.33 -127.1 -125.8 57.4 0.33 -130 -136.2 222.9 6.2 113 0.119 SW 93.4 0.033 -179.3 0.33 -117.4 121 77.5 0.33 -127.9 -126.6 62.9 0.33 -130.5 -136.9 200.2 4.4 114 0.128

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163EXP 18 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 106.4 0.031 -179 0.33 -117.8 -121. 5 24 0.33 -128.4 -127.1 17.7 0.33 -131.5 -137.8 236.7 4.7 115 0.172 SW 109.4 0.032 -179.5 0.33 -118.8 122.4 70.9 0.33 -129.3 -128 67.1 0.33 -132.2 -138.6 216.6 5.1 116 0.115 SW 106.3 0.032 -179.9 0.33 -119.3 -123. 2 47.4 0.33 -129.5 -128.5 19.6 0.33 -132.2 -138.8 155.8 4.3 117 0.217 SW 104.9 0.032 -178.5 0.33 -120.3 -124. 1 69.5 0.33 -130.7 -129.4 67.2 0.33 -133.6 -139.9 278.2 6.5 118 0.223 SW 122.7 0.031 -179.6 0.33 -120.5 124.5 14 0.33 -131.2 -130 39.8 0.33 -134 -140.5 201.4 5.1 119 0.233 SW 85.2 0.036 -180.1 0.33 -121.1 125 31.1 0.33 -131.6 -130.6 44.6 0.33 -134.2 -140.8 165 5.0 120 0.132 SW 101.7 0.032 -179.7 0.33 -122.2 -126 84 0.33 -132.6 -131.3 52 0.33 -135.5 -141.9 286 3.8 121 0.088 SW 109.2 0.032 -179.8 0.33 -122.7 126.6 42 0.33 -133.4 -132.1 44.4 0.33 -136.7 -143.1 296.9 5.6 122 0.15 SW 101.3 0.033 -180.3 0.33 -123 -127 19.1 0.33 -133.7 -132.5 16.3 0.33 -136.8 -143.6 198.2 3.5 123 0.122 SW 113.2 0.032 -179.7 0.33 -124 -127. 9 70.8 0.33 -134.5 -133.4 73.4 0.33 -137 -143.8 170.3 3.5 124 0.137 SW 110.8 0.033 -180.5 0.33 -124.6 -128. 5 39.8 0.33 -135.7 -134.3 89.5 0.33 -138.5 -145 327.6 3.2 125 0.169 SW 99.2 0.033 -180.1 0.33 -125.6 129.6 92.1 0.33 -135.9 -135 38.2 0.33 -138.3 -145.2 164.4 4.5 126 0.161 SW 117.4 0.032 -179.8 0.33 -125.7 -129. 9 8.5 0.33 -136.3 -135.3 6.3 0.33 -139 -145.8 233.2 4.9 127 0.175 SW 96.6 0.035 -180.4 0.33 -126.2 -130. 3 22.5 0.33 -137.3 -136.1 80.9 0.33 -139.9 -146.7 272.9 3.5 128 0.13 SW 97.8 0.034 -180.3 0.33 -126.9 131 56.8 0.33 -137.2 -136.5 15.2 0.33 -139.3 -146.4 96.7 4.2 129 0.113 SW 98 0.033 -180 0.33 -127.5 -131.7 50.3 0.33 -137.9 -136.9 24.9 0.33 -140.4 -147.2 281 3.4 130 0.136 SW 100.2 0.034 -179.8 0.33 -128.2 -132. 3 43.4 0.33 -139.2 -138.1 128.4 0.33 -141.6 -148.3 318.3 4.9 131 0.162 SW 110.6 0.034 -180.6 0.33 -128.7 -132. 8 40.4 0.33 -139.2 -138.4 11.6 0.33 -141.3 -148.4 149.9 4.1 132 0.142 SW 95 0.034 -180.7 0.42 -130.3 -134. 2 133.7 0.42 -141.3 -139.6 119.2 0.17 -149.4 -155.4 1562.9 7.8 133 0.138 SW 89.2 0.035 -180.4 0.42 -132.1 135.3 87.8 0.42 -151.7 -145.9 965 0.17 -170.9 -175 5418.9 4.8 134 0.063 SW 101.1 0.033 -180 -135.1 -154.5 -176.5 4.1 135 0.075 SW 99.4 0.033 -180.1 -136.5 -160.9 -176.3 3.4 136 0.168 SW 105.5 0.033 -180 -137.5 -164.4 -176.4 4.1 137 0.164 SW 91.9 0.036 -180.5 -140.4 -167.5 -176.7 5.8 138 0.106 SW 96.5 0.033 -180.4 -142.6 -170.4 -177.7 4.7 139 0.093 SW 101.5 0.033 -180.4 -145.3 -172.5 -177.5 5.2 140 0.129 SW 102.9 0.034 -180.6 -147.5 -172.3 -177.1 4.8 141 0.089 SW 104.9 0.035 -180.2 -150.5 -174.6 -178.4 4.4 142 0.105 SW 96.5 0.035 -180.3 -152 -174.7 -178 4.0 143 0.175 SW 116.6 0.034 -180.4 -155.4 -176 -178.1 5.4 144 0.214 SW 94.9 0.037 -180.5 -158 -177.4 -178.1 4.2 145 0.07 SW 103.5 0.035 -180.4 -160.3 -177.1 -178.5 4.6 146 0.144 SW 111.8 0.035 -180.8 -162.2 -176.7 -178.1 4.0 147 0.149 SW 98.5 0.036 -181 -164.1 -177.3 -178.2 4.6 148 0.157 SW 107.2 0.037 -180.7 -166.5 -177.8 -178.5 6.7 149 0.197 SW 112.4 0.04 -181 -168 -178.3 -179.1 4.4 150 0.21 SW 119.3 0.039 -181.2 -170.2 -178.8 -179 4.7 151 0.201 SW 114.2 0.04 -181.7 -170.7 -178.3 -178.4 4.2 152 0.135

PAGE 183

164EXP 18 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 102.7 0.036 -181.2 -176.3 -180.7 -179.5 5.7 153 0.072 SW 100.6 0.036 -181.4 -178 -180.8 -180.4 3.9 154 0.186 EXP 19 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P N 53.3 1 12.2 0.33 22.31 23 609 0.33 22.88 23.4 287 0.33 22.38 23.6 189.8 0.0 1 0.216 N 53.4 1 10.8 0.33 21.87 22. 4 294 0.33 22.34 22.9 231 0.33 21.78 23.1 267.6 0.0 2 0.285 N 57 1 8.4 0.33 21.39 21.8 275 0.33 21.93 22.4 202 0.33 21.44 22.7 175.8 0.0 3 0.304 N 56.8 1 7.4 0.33 20.84 21. 3 261 0.33 21.23 21.7 325 0.33 20.86 22.1 244.2 0.0 4 0.229 N 57.3 1 6.6 0.33 19.99 20. 4 442 0.33 20.71 21.2 186 0.33 20.24 21.5 269.5 0.0 5 0.197 N 58.9 1 5.5 0.33 19.84 20. 1 137 0.33 20.28 20.8 142 0.33 19.67 20.9 251.4 0.0 6 0.269 N 55.6 1 4.3 0.33 18.62 19. 1 495 0.33 19.29 19.9 380 0.33 18.9 20.1 301.5 0.0 7 0.233 N 57.1 1 3.1 0.33 18.1 18. 4 300 0.33 18.83 19.3 203 0.33 18.49 19.6 191.1 0.0 8 0.303 N 58.9 1 1.6 0.33 17.76 17.9 204 0.33 18.5 18.9 92.6 0.33 18.05 19.1 172.7 0.0 9 0.284 N 56.6 1 0.2 0.33 16.84 17.1 317 0.33 17. 37 18 326 0.33 16.96 18.2 340.2 0.0 10 0.259 N 56.2 1 -1.8 0.33 15.69 15.9 451 0.33 16. 56 17.1 231 0.33 16.09 17.2 303.4 0.0 11 0.339 N 59.4 1 -3.7 0.33 15.22 15.3 206 0.33 15. 79 16.3 255 0.33 15.45 16.5 227.1 0.0 12 0.368 N 59.1 0.428 -5.4 0.33 14 14.2 408 0.33 14. 77 15.3 291 0.33 14.51 15.6 287.4 0.0 13 0.309 N 59.3 0.249 -6.8 0.33 13.41 13.5 262 0.33 14. 1 14.6 180 0.33 13.72 14.7 257.2 0.0 14 0.331 N 57.6 0.178 -8.2 0.33 12.51 12.5 320 0.33 13.36 13.8 187 0.33 13.01 14 223.7 0.0 15 0.342 N 59.7 0.127 -9.6 0.33 11.63 11.6 286 0.33 12.33 12.8 263 0.33 12.06 13 264.4 0.0 16 0.39 N 60.5 0.096 -11.7 0.33 10.58 10.6 324 0.33 11.34 11.8 266 0.33 11.22 12.1 237.7 0.0 17 0.417 N 60.5 0.076 -13.7 0.33 9.749 9.7 249 0.33 10.33 10.8 222 0. 33 10.13 11 268.4 0.0 18 0.417 N 59.8 0.054 -17 0.33 8.481 8.5 324 0.33 9. 283 9.7 215 0.33 9.122 10 236.1 0.0 19 0.415 N 60.3 0.054 -20.7 0.33 7.354 7.2 197 0.33 8.248 8.7 118 0.33 7.958 8.8 168.8 0.0 20 0.414 N 62.4 0.129 -40.3 0.33 5.602 5.6 240 0.33 6.128 6.9 248 0.33 5.911 6.9 264.7 0.0 21 0.418 N 62.8 0.078 -43.5 0.33 4.077 4 232 0.33 4. 433 5.2 193 0.33 3.996 5 267.6 0.0 22 0.407 N 62.7 0.069 -46.7 0.33 2.119 2.1 267 0.33 2.608 3.4 207 0.33 2.228 3.1 239.8 0.0 23 0.421 N 62.8 0.064 -51.4 0.33 0. 213 0.1 326 0.33 0.703 1.6 236 0.33 0.171 1 322 0.0 24 0.408 N 62.4 0.059 -44.5 0.33 -1.19 -1.6 267 0.33 -0 .66 0 197 0.33 -1.1 -0.6 237.1 0.0 25 0.393 N 62.4 0.055 -45.2 0.33 -2.91 -3.4 302 0.33 -2 .26 -1.6 203 0.33 -2.69 -2.2 261 0.0 26 0.405 N 62.4 0.052 -46.7 0.33 -4.43 -5 212 0.33 -3. 91 -3.2 158 0.33 -4.4 -4 216.1 0.0 27 0.422 SW 63.7 0.044 -62 0.33 -6.36 -6.9 197 0.33 -5. 97 -5.2 170 0.33 -6.35 -5.9 195.8 2.2 28 0.408 SW 63.6 0.044 -77.5 0.33 -8.48 -8.9 184 0.33 -8 .6 -7.4 162 0.33 -9.37 -8.8 247 1.8 29 0.404 SW 64.9 0.043 -91.5 0.33 -10.5 -11.1 172 0.33 -10.9 -9.6 139 0. 33 -11.8 -11.4 211.2 1.6 30 0.399 SW 67.8 0.042 -100.4 0.33 -12.5 -13.1 153 0.33 -13.6 -12 144 0. 33 -15 -14.6 243.6 2.2 31 0.367

PAGE 184

165EXP 19 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 70.6 0.04 -106.9 0.33 -14.9 -15.4 167 0.33 -16.3 -14.5 142 0. 33 -18 -17.7 231.4 2.2 32 0.371 SW 71.6 0.04 -114.8 0.33 -17.3 -17.8 173 0.33 -19.2 -17.3 153 0. 33 -21.3 -21.1 249.6 2.1 33 0.341 SW 72.8 0.039 -117.6 0.33 -19.3 -19.9 141 0.33 -21.9 -19.8 130 0. 33 -24.4 -24.4 246.8 2.9 34 0.373 SW 76.7 0.038 -122.3 0.33 -21.5 -22.1 144 0.33 -24.6 -22.4 136 0. 33 -27.3 -27.6 230 2.4 35 0.327 SW 77.5 0.038 -127 0.33 -23.8 -24.4 152 0.33 -27. 3 -24.9 138 0.33 -30.1 -30.5 234.6 2.6 36 0.345 SW 76.1 0.038 -125 0.33 -26.1 -26.7 157 0.33 -30. 1 -27.6 136 0.33 -33.3 -33.8 255.1 2.6 37 0.331 SW 75.3 0.039 -128.4 0.33 -28.4 -29 151 0.33 -32. 7 -30.1 136 0.33 -35.9 -36.7 232.3 4.0 38 0.321 SW 76.4 0.038 -129.6 0.33 -30.5 31.2 100 0.33 -35.1 -32.6 91.7 0. 33 -38.4 -39.4 153.4 4.0 39 0.336 SW 79.6 0.037 -174.9 0.33 -32.8 -33.5 107 0.33 -37.8 -35.1 93 0. 33 -41.3 -42.3 173.6 4.7 40 0.296 SW 79.7 0.037 -174.7 0.33 -35.1 -35.9 112 0.33 -40.2 -37.5 84.6 0.33 -43.8 -45 161.9 3.0 41 0.343 SW 77.8 0.038 -175 0.33 -37.1 -38 99.3 0.33 -42. 3 -39.7 78.6 0.33 -46 -47.5 151.3 3.1 42 0.355 SW 75.7 0.038 -174.9 0.33 -39.4 -40.3 109 0.33 -45 -42.2 97.2 0. 33 -48.6 -50.1 168.2 3.6 43 0.378 SW 74.5 0.039 -175.5 0.33 -41.6 42.6 109 0.33 -47.3 -44.7 92.2 0. 33 -50.9 -52.6 160.1 4.4 44 0.342 SW 74 0.039 -175.4 0.33 -43.5 -44. 6 98.8 0.33 -49.2 -46.8 77.1 0. 33 -52.6 -54.6 135.7 3.1 45 0.414 SW 72.4 0.039 -175.8 0.33 -45.9 -46.9 112 0.33 -51.8 -49.3 104 0. 33 -55.1 -57 164.9 2.8 46 0.397 SW 69.4 0.04 -176 0.33 -47.7 -49 101 0.33 -53.7 -51.3 71.7 0.33 -57.1 -59.3 151.8 3.5 47 0.419 SW 69.9 0.04 -176.3 0.33 -49.5 50.9 93.5 0.33 -55.5 -53.2 74.4 0. 33 -58.8 -61.1 133.4 4.0 48 0.374 SW 72.4 0.039 -175.8 0.33 -51.9 -53.1 112 0.33 -58 -55.7 110 0. 33 -61 -63.3 158.1 4.0 49 0.379 SW 73.7 0.039 -176.1 0.33 -53.4 55 90.6 0.33 -59.6 -57.4 58.5 0. 33 -62.8 -65.3 147.8 4.1 50 0.365 SW 71.5 0.039 -176.5 0.33 -55.2 56.8 89.6 0.33 -61.7 -59.5 90.8 0. 33 -64.8 -67.3 150.5 3.9 51 0.296 SW 71.1 0.04 -176.8 0.33 -57.2 -58.7 102 0.33 -63.6 -61.4 79 0. 33 -66.7 -69.4 153.6 3.1 52 0.256 SW 68.2 0.041 -177.1 0.33 -58.9 60.5 93.3 0.33 -65.5 -63.3 74.6 0. 33 -68.7 -71.4 157.5 2.2 53 0.249 SW 75.1 0.038 -177.3 0.33 -60.2 -62 73.7 0.33 -67.2 -65 69.8 0. 33 -70.4 -73.3 149.6 4.4 54 0.225 SW 75.1 0.038 -177.6 0.33 -62.1 63.8 94.4 0.33 -69.2 -66.9 75.7 0. 33 -72.6 -75.5 171.5 3.5 55 0.216 SW 79 0.037 -177.6 0.33 -63.6 -65.4 83 0.33 -71 -68.7 77.8 0.33 -74.3 -77.4 155.5 3.8 56 0.212 SW 83.2 0.037 -177.9 0.33 -65 66.9 73.5 0.33 -72.6 -70.3 63 0. 33 -76.1 -79.3 161.6 5.0 57 0.247 SW 89.7 0.036 -177.8 0.33 -66.5 68.5 83.7 0.33 -74.5 -71.9 63.5 0. 33 -78.3 -81.5 182.9 3.6 58 0.175 SW 82 0.037 -178 0.33 -68.1 -70 81.8 0.33 -76.4 -73.8 74.4 0.33 -80.4 -83.7 188.1 4.4 59 0.21 SW 86.1 0.036 -178 0.33 -69.2 71.2 62.3 0.33 -77.7 -75.2 48.2 0.33 -81.7 -85.3 152 3.1 60 0.17 SW 90.7 0.036 -177.9 0.33 -70.8 72.8 82.6 0.33 -79.6 -76.9 69.7 0. 33 -83.8 -87.3 189.2 1.4 61 0.179 SW 92.8 0.036 -177.5 0.33 -72.5 74.5 91.4 0.33 -81.7 -78.8 82.7 0.33 -86 -89.6 208.2 2.3 62 0.183 SW 104.4 0.034 -177.3 0.33 -73.8 -75.9 74 0.33 -83.2 -80.2 47.9 0.33 -88 -91.7 203.4 2.5 63 0.204 SW 101.2 0.035 -176.9 0.33 -75 -77 60.5 0.33 -85 -81.9 67.6 0.33 -89.9 -93.7 205.4 2.9 64 0.217 SW 109.6 0.035 -176.5 0.33 -76.7 78.7 94.3 0.33 -86.8 -83.6 65.4 0. 33 -91.9 -95.8 218.4 3.6 65 0.189 SW 108.7 0.035 -176.9 0.33 -78.1 80.2 81.6 0.33 -88.4 -85.2 59.2 0. 33 -93.7 -97.8 215.2 3.8 66 0.262 SW 109.9 0.035 -176.8 0.33 -79.3 -81.5 69 0.33 -90 -86.6 47.8 0. 33 -95.6 -99.8 222.7 3.6 67 0.191 SW 124.8 0.035 -176.7 0.33 -80.7 -82.9 74 0.33 -92 -88.3 57.5 0.33 -98 -102.2 262 1.8 68 0.222 SW 107.8 0.037 -176.9 0.33 -82.3 84.5 90.7 0.33 -93.5 -89.9 58.3 0.33 -99.5 -104 220.5 3.3 69 0.223

PAGE 185

166EXP 19 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 111.1 0.036 -177.3 0.33 -83.5 85.8 74.2 0.33 -94.7 -91.3 44.6 0.33 -100 -105.2 180.2 2.8 70 0.193 SW 125.3 0.036 -176.7 0.33 -84.8 87.1 73.5 0.33 -96.5 -92.8 50.8 0.33 -103 -107.2 256.9 2.1 71 0.232 SW 122.6 0.037 -176.6 0.33 -86.2 -88.5 76 0.33 -97.8 -94.3 57.8 0.33 -104 -108.6 202 3.0 72 0.244 SW 106.5 0.038 -176.9 0.33 -87.7 -90 88.8 0.33 -99.3 -95.8 56. 2 0.33 -105 -110 218 5.8 73 0.179 SW 121.9 0.037 -176.4 0.33 -88. 5 -91 53.4 0.33 -100 -97 34.5 0.33 -106 -111 178.1 3.1 74 0.194 SW 119.9 0.038 -177 0.33 -90.5 -92.7 105 0.33 103 -98.9 93.7 0.33 -108 -113.1 291.5 2.9 75 0.211 SW 111.9 0.038 -176.9 0.33 -91.3 -93.8 54.5 0.33 -104 -100.2 44.8 0.33 -109 -114.4 205.4 3.4 76 0.221 SW 121.7 0.038 -177.2 0.33 -93.1 -95.5 104 0.33 -105 -101.7 59.7 0.33 -111 -115.9 242 2.7 77 0.193 SW 114.5 0.039 -176.8 0.33 -94.1 -96.7 71.9 0.33 -106 -102.7 30.1 0.33 -111 -116.5 147.5 2.9 78 0.223 SW 118.6 0.039 -176.9 0.33 -95.4 -98.1 79.3 0.33 -107 -104.1 53.2 0.33 -113 -118 249.7 3.5 79 0.205 SW 119.6 0.04 -176.9 0.33 -96.5 -99.2 65.1 0.33 -109 -105.5 59.4 0.33 -114 -119.4 240.5 6.7 80 0.222 SW 122 0.04 -176.9 0.33 -98.2 -100.8 101 0.33 110 -106.9 68.8 0.33 -115 -120.7 230.6 3.1 81 0.203 SW 111.3 0.042 -177.7 0.33 -99.3 -102.1 78.3 0.33 -111 -108.2 45.8 0.33 -116 -121.9 219.1 2.6 82 0.22 SW 117.3 0.041 -177 0.33 -100 -103.1 58 0.33 -112 -109.3 44.4 0.33 -117 -122.6 180.9 3.2 83 0.197 SW 112.9 0.042 -177 0.33 -101 -104 51.6 0.33 -113 -110.4 43.9 0.33 -118 -123.7 235.1 3.2 84 0.174 SW 134.4 0.04 -176.4 0.33 -103 -105.5 105 0.33 114 -111.5 47.6 0.33 -119 -125 246.3 2.6 85 0.198 SW 112.6 0.044 -176.9 0.33 -103 106.4 43.2 0.33 -115 -112.5 26.5 0. 33 -120 -125.7 185.5 3.1 86 0.207 SW 129.5 0.041 -176.4 0.33 -105 -107.8 100 0.33 117 -114.1 99.6 0.33 -122 -127.2 274.1 1.9 87 0.222 SW 122.1 0.043 -177.6 0.33 -106 -109 81.7 0.33 -118 -115 19.9 0.33 -122 -128.1 214 7.5 88 0.243 SW 116.5 0.043 -176.3 0.33 -107 -110 60.6 0.33 118 -115.8 25.1 0.33 -123 -128.7 178.6 4.1 89 0.138 SW 130.7 0.042 -176.8 0.33 -108 -111.1 72 0.33 120 -117 67.7 0.33 -124 -129.8 252.2 2.4 90 0.226 SW 114.1 0.043 -176.4 0.33 -109 -112.3 88 0.33 121 -118.3 63.6 0.33 -125 -130.8 242.1 3.6 91 0.172 SW 110.5 0.044 -176.4 0.33 -110 113.5 81.9 0.33 -122 -119.6 80.8 0. 33 -126 -131.7 221.7 3.1 92 0.224 SW 110.7 0.044 -176.9 0.33 -112 -114.9 109 0.33 122 -120.5 40.2 0.33 -126 -132.3 179.5 4.0 93 0.276 SW 98.5 0.047 -177.1 0.33 -113 -116 70.6 0.33 123 -121.5 61.7 0.33 -126 -132.7 171.9 1.9 94 0.184 SW 106.8 0.044 -177.1 0.33 -113 -116.9 71 0.33 124 -122.5 49.9 0.33 -127 -133.6 227.1 3.2 95 0.183 SW 105.6 0.045 -177.1 0.33 -115 -118.2 101 0.33 126 -123.7 84.7 0.33 -129 -134.7 240.3 3.0 96 0.183 SW 110.6 0.046 -178.2 0.33 -115 118.9 37.2 0.33 -126 -124.2 3.8 0. 33 -129 -135.5 213.7 6.0 97 0.26 SW 113.9 0.045 -177.6 0.33 -116 -120 91.9 0.33 127 -125.3 57.5 0.33 -131 -136.7 270.8 3.6 98 0.179 SW 110.6 0.047 -177.8 0.33 -117 120.9 68.2 0.33 -127 -125.8 1.23 0. 33 -131 -137.2 185.3 3.3 99 0.18 SW 113.7 0.046 -177.5 0.33 -117 121.2 14.1 0.33 -128 -126.1 26.3 0. 33 -131 -137.4 151.7 4.7 100 0.176 SW 129.2 0.046 -177.9 0.33 -119 -123 161 0.33 -130 -127.9 99.1 0.33 -134 -139.6 417.9 6.0 101 0.218 SW 107 0.05 -178 0.33 -119 -123.5 28.3 0.33 130 -128 15.9 0.33 -133 -139.7 132.2 3.6 102 0.129 SW 121.5 0.047 -177.5 0.33 -120 -123.9 27.6 0.33 -131 -129 23.9 0.33 -135 -141 318.9 3.2 103 0.166 SW 131 0.049 -178.2 0.33 -122 -125.4 137 0.33 133 -130.7 106 0.33 -136 -142.4 320.4 2.2 104 0.202 SW 120.4 0.05 -178.3 0.33 -122 126.3 75.9 0.33 -133 -130.9 20.7 0. 33 -136 -142.3 151.8 2.5 105 0.149 SW 114.4 0.052 -178 0.33 -122 -126.6 2.77 0.33 133 -131.2 13.3 0.33 -136 -143.1 219.5 3.4 106 0.12 SW 129.3 0.052 -178.7 0.33 -123 -127.6 94 0.33 134 -132.5 5.15 0.33 -138 -144.2 317.4 1.9 107 0.208

PAGE 186

167EXP 19 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t P SW 115.4 0.054 -178.6 0.33 -124 128.1 37.9 0.33 -135 -132.9 20.1 0. 33 -138 -144.6 198.3 2.1 108 0.184 SW 117.2 0.055 -178.5 0.33 -125 -129.5 138 0.33 -136 -134.3 68 0.33 -140 -146 365.8 3.3 109 0.191 SW 126.2 0.057 -178.9 0.33 -126 130.3 73.4 0.33 -136 -134.8 17.9 0. 33 -139 -146.1 148.2 3.3 110 0.238 SW 129 0.059 -178.6 0.33 -126 -130.3 12.4 0.33 137 -135.1 1.72 0.33 -140 -146.5 227.7 4.0 111 0.247 SW 114.6 0.06 -178.8 0.33 -127 -131.7 121 0.33 137 -136.1 31.6 0.33 -140 -146.9 210.3 1.9 112 0.146 SW 112.1 0.075 -178.2 0.33 -128 -131.3 19 0.33 138 -136 15.1 0.33 -140 -146.9 214.4 3.1 113 0.106 SW 118 0.043 -178.5 0.33 -130 -134.2 248 0.33 141 -139.5 363 0.33 -144 -150 661.7 4.3 114 0.145 SW 115.7 0.02 -178.4 0.42 -130 -133.6 5.34 0. 42 -143 -139.5 106 0.17 -158 -163 3224 2.0 115 0.125 SW 106 0.061 -178.9 0.42 -133 -135.5 65.4 0.42 -157 -148 903 0.17 -168 -172.5 4065 3.9 116 0.137 SW 106 0.061 -178.7 -135.7 -155.2 -172.7 5.1 117 0.193 SW 117.3 0.063 -178.5 -137.4 -162.6 -173.2 4.0 118 0.145 SW 126.7 0.066 -178.9 -139.6 -166.8 -173.2 3.5 119 0.195 SW 116.9 0.065 -178.8 -142.4 -167.5 -173.2 4.7 120 0.135 SW 112.6 0.065 -178.6 -145 -169.9 -173.6 2.5 121 0.146 SW 126.2 0.071 -178.7 -148.1 -171 -173.4 3.4 122 0.172 SW 125.1 0.068 -179 -151.2 -172.5 -173.9 2.8 123 0.2 SW 126.9 0.074 -178.7 -156.4 -175.8 -175.5 2.3 124 0.241 SW 135.9 0.081 -179.2 -159.7 -176.5 -175.8 5.5 125 0.235 SW 126.3 0.081 -179.7 -160.5 -174.6 -174.1 2.0 126 0.141 SW 123.1 0.085 -179.6 -167.5 -176.6 -175.2 2.2 127 0.169 SW 126.6 0.084 -179.5 -169.9 -175.6 -175.1 4.7 128 0.238 SW 133.1 0.087 -180.3 -177.4 -178.6 -174.8 1.9 129 0.268 SW 119.3 0.089 -179.8 -178.1 -179 -176.8 4.1 130 0.206 SW 127.4 0.089 -179.8 -178.2 -177.1 -174.7 4.0 131 0.255 SW 127.5 0.089 -180.8 -179.1 -177.8 -176.2 3.1 132 0.211 SW 111.2 0.091 -180 -176.9 -176.5 -176.4 2.7 133 0.131 SW 120.7 0.089 -180.2 -178.8 -177.3 -176 3.3 134 0.189 EXP 20 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P N 120.2 1 7.2 0.33 22.9 23.7 609 0.33 23.8 24.5 258 0.33 23.2 24.7 246 0.0 0.0 1 0.151 N 123.6 1 2.8 0.33 19.7 20.9 862 0.33 20.3 21. 6 910 0.33 20.1 22.2 760. 4 0.0 0.0 2 0.261 N 129.8 1 -1 0.33 19 19.5 371 0.33 19.7 20. 4 278 0.33 19.4 20.8 318. 7 0.0 0.0 3 0.2 N 130 1 -4.6 0.33 17.5 18.1 390 0.33 17.6 18. 7 388 0.33 16.9 18.6 582. 2 0.0 0.0 4 0.226 N 129.4 1 -8.4 0.33 15.9 16.3 452 0.33 16.8 17.6 223 0.33 16.1 17.4 261.5 0.0 0.0 5 0.273 N 132.1 1 -11.8 0.33 14.1 14.5 423 0.33 15 15. 8 362 0.33 14.6 15.9 330. 7 0.0 0.0 6 0.272

PAGE 187

168EXP 20 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P N 133.1 1 -15.9 0.33 11.6 12.1 526 0.33 12 13. 3 484 0.33 11.3 12.9 623. 4 0.0 0.0 7 0.268 N 133.5 1 -20.1 0.33 9 9.4 559 0.33 10.1 11 406 0.33 9.8 11 346.3 0.0 0.0 8 0.265 N 132.4 1 -24.9 0.33 7.1 7.3 387 0.33 7.8 8.7 363 0.33 7.4 8.7 407.4 0.0 0.0 9 0.283 N 136.9 1 -30.9 0.33 4.5 4.6 453 0.33 5.6 6.6 290 0.33 5.1 6.3 372.7 0.0 0.0 10 0.413 N 137 1 -37.8 0.33 0.1 0.6 680 0.33 1 2. 6 597 0.33 0.6 2.2 663. 9 0.0 0.0 11 0.411 N 137.9 1 -40.4 0.33 -1.9 -2.1 391 0.33 -0.8 0.2 269 0.33 -1.2 -0.4 338.5 0.0 0.0 12 0.377 N 140.5 1 -49 0.33 -6.6 -6.4 477 0.33 -5.4 -4 396 0.33 -5.4 -4.2 401.3 0.0 0.0 13 0.425 N 142.4 1 -71.2 0.33 -10.9 -10.9 422 0.33 -9.4 -8.4 378 0.33 -8.7 -7.8 311.9 0.0 0.0 14 0.416 N 141.8 1 -83.1 0.33 -14.8 -15. 1 350 0.33 -13.3 -12.2 262 0.33 13.2 -12.2 351.1 0.0 0.0 15 0.433 N 143.2 1 -98.6 0.33 -20.7 -20. 7 427 0.33 -19.2 -17.8 386 0.33 18.6 -17.4 371.7 0.0 0.0 16 0.419 N 143.9 1 -111.6 0.33 -24 -24.7 297 0.33 -23.3 -22 267 0.33 -23.1 -22. 4 350.3 0.0 0.0 17 0.4 N 143.5 1 -114.6 0.33 -29.1 -29. 7 383 0.33 -28.3 -26.9 329 0.33 27.9 -27.4 363.1 0.0 0.0 18 0.39 N 145.2 1 -117.8 0.33 -33.9 -34. 6 338 0.33 -33.4 -32 310 0.33 -32. 9 -32.6 336.6 0.0 0.0 19 0.377 N 146.4 1 -132.5 0.33 -38.5 -39. 3 230 0.33 -38.6 -37.1 225 0.33 38.2 -38 259.8 0.0 0.0 20 0.39 N 151.5 1 -176.2 0.33 -43.2 -44. 1 237 0.33 -43.7 -42.4 240 0.33 43 -43.2 248.3 0.0 0.0 21 0.418 N 157 1 -176.4 0.33 -49 -49.7 293 0.33 -50.2 48.3 279 0.33 -50 -49.9 345.4 0.0 0.0 22 0.433 N 159.4 1 -176.7 0.33 -57.1 -57. 4 408 0.33 -58.4 -56.1 388 0.33 57.7 -57.6 407.9 0.0 0.0 23 0.42 N 160.1 1 -177.2 0.33 -62.2 -63. 2 309 0.33 -63.8 -62.2 304 0.33 63.1 -63.9 332.5 0.0 0.0 24 0.43 A 162.4 0.038 -177.4 0.33 -66 -67. 7 244 0.33 -68.8 -67.2 252 0.33 68.7 -69.9 345.9 0.0 2.5 25 0.424 A 159.9 1 -177.3 0.33 -71.3 -72. 8 301 0.33 -74.3 -72.7 301 0.33 74 -75.6 339.5 0.0 2.0 26 0.432 A 159.4 1 -177.3 0.33 -75.5 -77. 4 271 0.33 -78.5 -77.5 264 0.33 77.7 -79.9 269 0.0 1.8 27 0.432 A 156.7 0.032 -177.9 0.33 -80.6 -82. 5 318 0.33 -83.4 -82.5 298 0.33 82.3 -84.6 307.4 0.0 1.8 28 0.429 A 159.1 0.032 -177.6 0.33 -83.8 86.2 235 0.33 -87.1 -86.4 230 0.33 -86.3 -89 296 0.0 1.8 29 0.427 N 159.9 1 -177.9 0.33 -89.4 -91. 6 367 0.33 -92.1 -91.3 313 0.33 90.9 -93.6 330.6 0.0 0.0 30 0.433 A 161.2 0.04 -177.7 0.33 -92.6 -95. 4 251 0.33 -95.8 -95.6 280 0.33 94.2 -97.5 273.9 0.6 2.2 31 0.43 A 163.1 0.04 -178.6 0.33 -97.8 -100. 3 360 0.33 -101.2 -100.5 342 0.33 99.7 -102.7 402.8 0.4 2.4 32 0.43 A 164.4 0.04 -178.5 0.33 -99.6 -102. 9 181 0.33 -103.4 -103.6 212 0.33 101.7 -105.7 226.9 0.3 2.9 33 0.433 A 166.2 0.039 -178.3 0.33 -103.5 -106. 8 314 0.33 -106.5 -106.6 213 0.33 104.9 -108.9 275.3 0.4 2.1 34 0.426 A 169.8 0.04 -178.4 0.33 -106.6 -110 254 0.33 -110 110.3 290 0.33 -107.9 -112. 1 276.4 0.6 4.0 35 0.42 A 178.4 0.041 -178.4 0.33 -112.4 -115. 2 441 0.33 -115.6 -115.8 474 0.33 112.4 -116.3 375.3 0.3 2.5 36 0.4 A 184.4 0.042 -178.9 0.33 -112.4 116.6 98 0.33 -117.3 -117.6 123 0.33 -116 -120.3 381.5 0.4 3.7 37 0.381 A 190.6 0.042 -177.8 0.33 -115.8 -119. 6 280 0.33 -119.9 -120.4 254 0.33 117.8 -122.7 229.5 0.4 2.9 38 0.405 A 195.8 0.043 -178.6 0.33 -117.7 -121. 8 204 0.33 -121.8 -122.7 207 0.33 119.5 -124.7 211.2 0.5 2.9 39 0.377 A 198.3 0.043 -179 0.33 -122.1 -126 419 0.33 -124.7 -126 333 0.33 -121.2 -126. 5 195.1 0.3 1.8 40 0.38 A 201.6 0.043 -178.8 0.33 -124.7 129 300 0.33 -128.1 -129.1 314 0.33 124.9 -129.9 378.3 0.4 2.3 41 0.39 A 206.3 0.044 -179 0.33 -125.5 -130. 2 118 0.33 -129.8 -131.2 220 0.33 126.8 -132.2 256.1 0.4 2.2 42 0.38 A 211.1 0.044 -179.5 0.33 -127 -131. 9 200 0.33 -130.3 -132.1 102 0.33 127.2 -133.1 114.5 0.3 2.2 43 0.378 A 218.5 0.045 -178.9 0.33 -130.9 -134. 9 356 0.33 -135.4 -136.2 493 0.33 132.1 -137.1 500.6 0.4 3.0 44 0.391 A 217.5 0.045 -179.4 0.33 -132.4 137.1 256 0.33 -136.8 -138 197 0.33 134.2 -139.8 341.9 0.3 1.8 45 0.395 A 219.5 0.044 -179.1 0.33 -133.1 137.9 77.3 0.33 -137.8 -140 298 0.33 -133.5 -140 13.94 0.4 1.4 46 0.376

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169EXP 20 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P A 223.7 0.045 -179.4 0.33 -133.3 -138. 2 42.7 0.33 -139.8 -140.7 95.8 0.33 -137.8 -143.4 497.4 0.3 2.0 47 0.375 A 229.9 0.046 -179.9 0.33 -135.6 -140. 6 313 0.33 -139.6 -141.3 50.5 0.33 137.1 -142.7 54.6 0.4 1.6 48 0.35 A 232.4 0.045 -179.7 0.33 -137.9 142.8 294 0.33 -141.9 -143.5 320 0.33 -138.6 -143.9 214 0.3 2.1 49 0.344 A 239 0.046 -180.2 0.33 -138.1 -142.5 90.1 0.33 -142.1 -143.3 126 0.33 138.4 -145.1 52.5 0.4 2.4 50 0.345 A 239.2 0.046 -180.4 0.33 -140.5 145.9 354 0.33 -143.1 -145.5 181 0.33 -139 -145.6 103.3 0.4 2.0 51 0.371 A 243.7 0.047 -180.2 0.33 -142.7 148.2 366 0.33 -145.3 -147.4 302 0.33 -141 -147.3 286.7 0.4 2.7 52 0.358 A 247.9 0.047 -179.7 0.33 -143.5 149 129 0.33 -147.8 -149.8 414 0.33 143.6 -149.7 396.9 0.4 3.7 53 0.366 A 247.6 0.046 -180 0.33 -144.8 -150. 3 231 0.33 -148.7 -151 189 0.33 -144. 7 -151.3 263.2 0.4 2.7 54 0.374 A 243.3 0.046 -180.5 0.33 -148.2 152 271 0.33 -165.1 -161.9 2415 0.33 -166.7 -169.4 3519 0.1 5.1 55 0.37 A 254.3 0.049 -180.4 -152.1 171.6 -170.8 0.1 3.3 56 0.362 A 265.8 0.054 -180.3 -154.3 176.9 -175.8 0.2 2.7 57 0.361 A 270.7 0.058 -181.1 -160.3 178.7 -178.4 0.4 2.1 58 0.356 A 279 0.061 -181.5 -165.2 178.7 -178.5 0.4 3.4 59 0.319 A 271.7 0.063 -181.2 -172.2 -174.3 -172 0.2 1.6 60 0.346 A 265.3 0.065 -181 -176 -176 -174.4 0.3 2.6 61 0.323 A 264.8 0.065 -181.6 -176.7 178.7 -178.4 0.3 2.4 62 0.329 A 255.9 0.064 -181.3 -178.5 177.6 -175.7 0.5 3.7 63 0.302 A 246.8 0.064 -182 -181.4 182.8 -180.3 0.6 3.3 64 0.328 A 246.8 0.064 -181.6 -177.8 177.7 -176.6 0.4 3.0 65 0.304 A 240.1 0.064 -181.8 -175.3 176.6 -175.2 0.2 1.9 66 0.312 A 236.7 0.064 -182.4 -183.9 -183.4 -179.5 0.4 3.3 67 0.306 EXP 21 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P N 150 1 7.4 0.33 21.1 23.8 473.2 0.33 21.6 23.8 486 0.33 21.9 24.2 328 0.0 0.0 1 0.27 N 146.2 1 0.2 0.33 19.6 21.7 489.9 0.33 19.8 22.2 343 0.33 20. 1 22.6 374.8 0.0 0.0 2 0.187 N 150.7 1 -8.2 0.33 17.3 19.2 474.5 0.33 17.3 19.8 449 0.33 17.3 20.1 467.7 0.0 0.0 3 0.275 N 155.5 1 -17 0.33 13.8 16 291.9 0.33 14.3 16. 8 262 0.33 14.4 16.9 282. 1 0.0 0.0 4 0.231 N 164.8 1 -62.5 0.33 9 10.3 452.1 0.33 9.3 11.3 420 0.33 9.8 11.6 406.5 0.0 0.0 5 0.291 N 172.1 1 -79.7 0.33 4 3.9 421.1 0.33 4.3 4.7 432 0.33 4.7 5.1 427.8 0.0 0.0 6 0.4 N 179.2 1 -99.5 0.33 -3.6 -4.2 604.1 0.33 -3.8 -3.3 572 0.33 -2.8 -3.4 620.2 0.0 0.0 7 0.333 N 171.4 1 -94.3 0.33 -10.6 -11.4 538.2 0.33 -10.2 -10.1 477 0.33 -9 .7 -10.3 503.2 0.0 0.0 8 0.357 S 174.6 1 -99.1 0.33 -17.7 -18. 9 569 0.33 -17.6 -17.5 541 0.33 17.3 -17.6 541.2 0.0 1.8 9 0.336 N 173.9 1 -104.5 0.33 -25.2 -25. 6 489.9 0.33 -25.7 -23.9 437 0.33 -24.5 -24.3 480 0.0 0.0 10 0.333 N 173.9 1 -114.6 0.33 -32.3 -32. 5 325.7 0.33 -33 -31 319 0.33 -33. 3 -31.4 329.1 0.0 0.0 11 0.402 A 203.5 1 -171.1 0.33 -39.5 -40.1 372.2 0.33 -40.5 -39.2 389 0.33 40.6 -39.7 401.9 0.6 2.2 12 0.334 A 190.2 1 -173.1 0.33 -46.8 -48. 3 416.4 0.33 -48.1 -47 370 0.33 48.5 -48 418.3 0.4 2.4 13 0.365 A 213.3 0.044 -172.9 0.33 -54.8 56 406.6 0.33 -56.7 -55.4 428 0.33 -57.2 -57.1 486 0.3 2.9 14 0.409

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170EXP 21 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P A 210.5 0.043 -172.5 0.33 -62.4 -63. 5 418.5 0.33 -64.9 -63.3 419 0.33 65.6 -65.3 464.4 0.4 2.1 15 0.36 A 216.4 0.044 -173 0.33 -69.4 -70. 7 418.9 0.33 -72.2 -70.9 431 0.33 -73 -73.6 497.4 0.6 4.0 16 0.374 A 218.1 0.045 -172.6 0.33 -75.7 -77. 5 416.4 0.33 -78.6 -77.8 406 0.33 79.8 -80.5 436.4 0.3 2.5 17 0.387 A 224.2 0.046 -172.9 0.33 -81.3 -84. 2 431.4 0.33 -84.5 -84.9 455 0.33 85.3 -87.5 482.1 0.4 3.7 18 0.424 A 228.7 0.047 -172.5 0.33 -86.2 90.5 434.2 0.33 -89.7 -91.3 418 0. 33 -91 -94 468.6 0.4 2.9 19 0.429 A 220.7 0.046 -173 0.33 -91.7 -96.4 414.7 0.33 -95.1 -97.3 423 0.33 96.2 -99.6 431.5 0.5 2.9 20 0.399 A 219.2 0.045 -174.1 0.33 -96.3 -101. 9 412.1 0.33 -100.3 -103 434 0.33 100.7 -105.1 440.2 0.3 1.8 21 0.402 A 235.2 0.049 -173.9 0.33 -100.6 -106. 5 359.7 0.33 -104.5 -107.7 373 0.33 105.6 -109.8 405.3 0.4 2.3 22 0.363 A 243 0.051 -174.4 0.33 -107.7 -110. 5 337.3 0.33 -112.4 -112 367 0.33 112.4 -113.7 351.5 0.4 2.2 23 0.369 A 260.1 0.055 -174.1 0.33 -110.6 -116 492.1 0.33 -114.7 -117.5 509 0.33 114.4 -119.1 525.2 0.3 2.2 24 0.402 A 255.4 0.054 -174.5 0.33 -114 -119.7 335.9 0.33 -119.9 -121.2 344 0.33 120.5 -123.1 401.9 0.4 3.0 25 0.357 A 267.1 0.057 -174.7 0.33 -116.7 -123. 5 364.7 0.33 -121.9 -124.9 380 0.33 122.2 -126.2 342.4 0.3 1.8 26 0.393 A 269.2 0.058 -175.3 0.33 -120 -126.4 290.5 0.33 -125.6 -127.6 284 0.33 125.2 -129.3 352.6 0.4 1.4 27 0.359 A 279.2 0.061 -175.8 0.33 -122.7 -129. 5 340.4 0.33 -128.4 -130.9 388 0.33 128.6 -132.5 393.6 0.3 2.0 28 0.353 A 284.9 0.062 -175.4 0.33 -125.2 131.6 227.1 0.33 -131 -132.8 218 0.33 -130.9 -134.2 204 0.4 1.6 29 0.352 A 298.7 0.067 -176.6 0.33 -127.4 -134. 2 326.4 0.33 -134.1 -135.6 367 0.33 133.9 -136.6 339.1 0.3 2.1 30 0.345 A 315.3 0.072 -176 0.33 -128.9 -136 210.1 0.33 -134.6 -137.4 230 0.33 134.8 -138.4 247.4 0.4 2.4 31 0.343 A 335.6 0.079 -177 0.33 -130.8 -138. 1 270 0.33 -134.8 -139.8 341 0.33 134.7 -141.2 402.2 0.4 2.0 32 0.338 A 354.9 0.086 -177.2 0.33 -132.7 -140 241.9 0.33 -136.9 -141.3 203 0.33 136.5 -142.3 163.3 0.4 2.7 33 0.337 A 356.8 0.088 -177.3 0.33 -134 -141.9 264.1 0.33 -139.4 -143.4 322 0.33 139.8 -144.5 349.6 0.4 3.7 34 0.294 A 352.2 0.086 -178.3 0.33 -135.9 -142. 4 55.9 0.33 -140.2 -144.2 140 0.33 139.3 -145.5 177.1 0.4 2.7 35 0.276 A 349 0.085 -177.4 0.33 -137.3 -145.2 433.9 0.33 -142.7 -146.9 461 0.33 141.6 -147.6 375.2 0.4 3.4 36 0.293 A 345.3 0.044 -177.7 0.33 -138.8 -146. 6 124.4 0.33 -144.9 -157.8 2029 0. 33 -143.9 -163 2808 0.1 4.7 37 0.295 A 344.2 0.044 -177.8 0.33 -139.5 -147. 7 9.4 0.33 -145.6 -168.9 3913 0.33 -144.3 -169.3 2524 0.1 4.7 38 0.285 A 345.8 0.084 -178.1 -152.7 173.5 -171.6 0.3 2.1 39 0.315 A 333.1 0.084 -177.9 -158.9 172.5 -171.1 0.2 2.7 40 0.319 A 335.3 0.086 -179.2 -172.4 -174.8 -173 0.4 2.1 41 0.301 A 314.1 0.086 -179 -175.7 174.2 -170.7 0.4 3.4 42 0.288 A 318.2 0.087 -178.7 -176.8 176.2 -173.3 0.2 1.6 43 0.298 A 319.4 0.086 -179.1 -178.9 176.6 -172.2 0.3 2.6 44 0.336 A 303.1 0.086 -179.5 -174.3 174.1 -172.7 0.3 2.4 45 0.267 A 318.4 0.086 -179.6 -175.8 -173 -168.5 0.5 3.7 46 0.274 A 291.8 0.087 -180.1 -175.9 175.3 -174.1 0.6 3.3 47 0.213 A 304.4 0.086 -180.6 -178.9 175.2 -171.6 0.4 3.0 48 0.28 A 284.8 0.088 -179.8 -177.6 -179.3 -178 0.2 1.9 49 0.235 A 278.8 0.088 -180.3 -175.5 172.3 -167.6 0.4 3.3 50 0.292 A 282.3 0.087 -180.2 -177.2 -177.2 -176 0.3 2.3 51 0.24 A 260.6 0.089 -181.2 -179.4 178.4 -174.8 0.4 3.0 52 0.272 A 292.4 0.086 -181.4 -176.7 -174.5 -172.7 0.4 2.0 53 0.256

PAGE 190

171EXP 22 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P N 104.1 1 1.9 0.33 20.1 21.5 668 0.33 20.8 22.2 491 0.33 21.1 22.5 439 0.0 0.0 1 0.211 N 126.1 1 -10.3 0.33 17.6 18. 8 396 0.33 18.2 19.6 355 0.33 18. 1 19.6 421 0.0 0.0 2 0.217 N 140.5 1 -28.3 0.33 11.3 13. 2 542 0.33 12.5 14.7 447 0.33 12. 8 14.9 434 0.0 0.0 3 0.243 N 152.8 1 -60.6 0.33 2.8 5.2 611 0.33 3.5 6.7 594 0.33 4.2 7.3 567 0.0 0.0 4 0.373 N 170.3 1 -85.2 0.33 -7.9 -5.1 726 0.33 -8.1 -4.2 755 0.33 -7.9 -3.8 772 0.0 0.0 5 0.352 N 169.8 1 -99.1 0.33 -18.7 -16. 3 549 0.33 -17.8 -14.3 470 0.33 17.6 -14.1 488 0.0 0.0 6 0.296 N 175.4 1 -151.3 0.33 -29 -27.1 506 0.33 -29.6 -25.9 538 0.33 -29.2 25.5 528 0.0 0.0 7 0.314 N 181.9 3.139 -164.9 0.33 -40.8 39.1 600 0.33 -41 -37.5 553 0.33 41.4 -37.9 609 0.0 0.0 8 0.34 A 173.3 0.074 -165.9 0.33 -48.6 48.4 465 0.33 -49.2 -46.9 446 0.33 -50 -47.7 487 0.2 2.8 9 0.34 A 198.8 0.076 -170.1 0.33 -58.5 58.4 553 0.33 -60.1 -57.6 580 0.33 -60.6 -58.2 575 0.2 2.7 10 0.322 A 236.3 0.065 -168.9 0.33 -67.9 68.1 567 0.33 -70.6 -68.3 616 0.33 -71.7 -69.4 658 0.1 3.0 11 0.314 A 225.8 0.103 -170 0.33 -76.6 -77.5 577 0.33 -79. 6 -77.9 585 0.33 -81 -79.4 629 0.2 2.4 12 0.356 A 214.1 0.083 -170.4 0.33 -84.8 86.2 578 0.33 -88.4 -87.2 612 0.33 -89.6 -88.6 623 0.2 2.7 13 0.36 A 211.7 0.05 -170.8 0.33 -91.7 93.8 535 0.33 -95.8 -95.1 573 0.33 -96.8 -96.4 577 0.2 3.3 14 0.356 A 234.4 0.046 -170.8 0.33 -98.3 100.9 536 0.33 -102.5 -102.3 556 0.33 -103.3 -103.4 550 0.8 1.2 15 0.362 A 252.6 0.067 -171.7 0.33 -103.8 107 490 0.33 -108.5 -108.8 549 0.33 109.5 -109.9 564 0.2 2.5 16 0.322 A 270.2 0.037 -171.5 0.33 -109.1 112.8 498 0.33 -113.8 -114.4 519 0.33 -114.5 -115.4 502 0.3 3.7 17 0.327 A 292.6 0.096 -171.9 0.33 -113.8 117.9 483 0.33 -118.1 -119.2 449 0.33 -119.6 -120.7 539 0.3 1.5 18 0.312 A 299 0.074 -172 0.33 -118.3 -122.8 488 0.33 -122.4 -123.7 451 0.33 -123.9 125.4 504 0.1 2.6 19 0.335 A 276.7 0.108 -173.1 0.33 -122.6 127.4 497 0.33 -127.1 -128.4 524 0.33 -128.2 -129.9 523 0.2 1.7 20 0.338 A 254.2 0.11 -173.3 0.33 -125.6 131 394 0.33 -130.4 -132.2 449 0.33 131.1 -133.2 412 0.3 1.5 21 0.344 A 251.4 0.069 -174.1 0.33 -129 -134. 5 441 0.33 -133.7 -135.6 449 0.33 134.3 -136.5 441 0.3 2.6 22 0.331 A 279.2 0.065 -174 0.33 -131.4 -137. 3 356 0.33 -136.3 -138.6 417 0.33 136.9 -139.2 398 0.3 2.5 23 0.32 A 318.5 0.165 -174 0.33 -133.7 -139.9 371 0.33 -137. 7 -140.3 249 0.33 -138 -140.8 241 0.2 1.1 24 0.318 A 337 0.051 -174.4 0.33 -135.8 -142. 2 349 0.33 -139.5 -142.2 325 0.33 138.3 -141.3 71 0.2 3.4 25 0.296 A 357.2 0.061 -174.6 0.33 -137.6 144.4 371 0.33 -139.9 -142.8 63 0.33 -140.2 -143 307 0.3 2.9 26 0.328 A 398.7 0.096 -174.7 0.33 -139.9 -146. 3 308 0.33 -146.6 -148.4 1005 0.33 -146.6 -148.1 860 0.3 1.8 27 0.33 A 471 0.106 -175 0.33 -140.8 -147.7 256 0.33 -146.2 -149.3 115 0.33 -147.8 150.7 469 0.2 1.9 28 0.32 A 397.4 0.081 -175.1 0.33 -144.9 -149. 8 320 0.33 -161.8 -161.8 2788 0.33 -167.6 -166.7 3566 0.3 1.6 29 0.354 A 501.7 0.129 -175.6 0.33 -147.3 -151. 5 125 0.33 -167.5 -169.8 4993 0.33 -166.2 -169.1 1492 0.3 2.6 30 0.323 A 582.5 0.104 -175.4 -155.7 184.5 -178.9 0.3 2.1 31 0.349 A 599.5 0.061 -176.4 -161.1 -172.7 -171 0.3 2.9 32 0.349 A 599.8 0.057 -176.2 -169.2 177.9 -174.3 0.2 3.0 33 0.306 A 569.4 0.082 -176.9 -173.8 171.8 -172.5 0.2 2.9 34 0.318 A 602.6 0.043 -176.8 -174.8 179.3 -174.8 0.3 3.8 35 0.29 A 588.4 0.122 -177.7 -175.6 174.5 -175.6 0.3 4.4 36 0.279 A 606.3 0.071 -178.5 -176.9 169.4 -171.2 0.3 3.5 37 0.245 A 571.9 0.069 -178.4 -177 168.2 -166.8 0.2 3.7 38 0.273 A 536.6 0.167 -177.9 -177.1 -177 -173.6 0.2 3.4 39 0.284 A 531.5 0.06 -178.9 -177.7 -169.7 -170 0.2 4.2 40 0.289

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172EXP 22 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P A 560.8 0.106 -179.4 -178.4 177.4 -169.3 0.2 4.8 41 0.252 A 486.7 0.105 -179.3 -178.8 -175.4 -169.4 0.3 4.6 42 0.245 EXP 23 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P N 159.6 1 4.8 0.33 21.1 22.2 595 0.33 21.6 22.8 409 0.33 21.9 23 353 0.0 0.0 1 0.138 N 163.8 1 -2.5 0.33 19.6 20.5 381 0.33 19.8 20.9 418 0.33 20.1 21.3 394 0.0 0.0 2 0.268 N 169 1 -9.6 0.33 17.3 18.4 398 0.33 17.3 18.6 409 0.33 17.3 18.7 463 0.0 0.0 3 0.207 N 176 1 -20.1 0.33 13.8 15.1 454 0.33 14.3 15.8 368 0.33 14.4 15.8 376 0.0 0.0 4 0.3 N 182.1 1 -36.4 0.33 9 10.5 525 0.33 9.3 11.2 524 0.33 9.8 11.7 470 0.0 0.0 5 0.293 N 184.1 1 -49.1 0.33 4 5.4 435 0.33 4.3 6.4 398 0.33 4.7 6.7 413 0.0 0.0 6 0.333 N 193.3 1 -75.5 0.33 -3.6 -1.8 562 0.33 -3.8 -1.1 579 0.33 -2.8 -0.1 520 0.0 0.0 7 0.354 N 192.5 1 -88.6 0.33 -10.6 -9.1 541 0.33 -10.2 -7.8 476 0.33 -9.7 -7.2 509 0.0 0.0 8 0.312 N 194.1 1 -98.9 0.33 -17.7 -16. 5 372 0.33 -17.6 -15.2 355 0.33 17.3 -14.8 373 0.0 0.0 9 0.35 N 200.9 1 -149.6 0.33 -25.2 -24. 3 418 0.33 -25.7 -23.3 438 0.33 24.5 -22.1 382 0.0 0.0 10 0.349 N 202.8 0.076 -145.3 0.33 -32.3 31.8 365 0.33 -33 -30.8 352 0.33 33.3 -30.8 419 0.0 2.5 11 0.352 N 204.8 1 -165.8 0.33 -39.5 -39. 3 368 0.33 -40.5 -38.5 369 0.33 40.6 -38.7 375 0.0 0.0 12 0.368 N 210.8 1 -169.7 0.33 -46.8 -46. 9 389 0.33 -48.1 -46.3 388 0.33 48.5 -46.7 408 0.0 0.0 13 0.343 N 220 0.139 -169.8 0.33 -54.8 -55 440 0.33 -56.7 -54.8 456 0.33 -57.2 55.4 469 0.0 1.8 14 0.385 N 227.9 1 -169.6 0.33 -62.4 -63.1 449 0.33 -64. 9 -63.3 472 0.33 -65.6 -64 487 0.0 0.0 15 0.396 N 227.3 1 -170.5 0.33 -69.4 -70.5 439 0.33 -72. 2 -71.1 456 0.33 -73 -71.9 472 0.0 0.0 16 0.393 A 223 0.043 -170.4 0.33 -75.7 -77. 4 428 0.33 -78.6 -77.9 419 0.33 79.8 -79.2 460 0.6 2.2 17 0.363 A 221.4 0.049 -171 0.33 -81.3 -83. 6 396 0.33 -84.5 -84.2 410 0.33 85.3 -85.2 402 0.4 2.4 18 0.379 A 218.5 0.043 -171.6 0.33 -86.2 88.9 362 0.33 -89.7 -89.8 377 0.33 -91 -91.2 426 0.3 2.9 19 0.388 A 225.8 0.053 -172 0.33 -91.7 -94. 6 413 0.33 -95.1 -95.3 399 0.33 96.2 -96.7 407 0.4 2.1 20 0.395 A 228.4 0.023 -171.8 0.33 -96.3 99.6 370 0.33 -100.3 -100.7 425 0.33 -100.7 -101.5 378 0.6 4.0 21 0.393 A 229.3 0.053 -172.1 0.33 -100.6 104.3 367 0.33 -104.5 -105.3 359 0.33 -105.6 -106.5 416 0.3 2.5 22 0.371 A 234.6 0.031 -173.1 0.33 -107.7 110.8 562 0.33 -112.4 -112.5 653 0.33 -112.4 -112.7 556 0.4 3.7 23 0.393 A 242.7 0.045 -173 0.33 -110.6 -115 351 0.33 -114.7 -116.2 331 0.33 -114.4 -116 282 0.4 2.9 24 0.375 A 243 0.042 -173.6 0.33 -114 -118.4 312 0.33 -119.9 -121.1 515 0.33 -120.5 121.4 545 0.5 2.9 25 0.384 A 241.9 0.088 -173.6 0.33 -116.7 121.5 293 0.33 -121.9 -123.9 296 0.33 -122.2 -124.2 267 0.3 1.8 26 0.357 A 231.6 0.057 -174.3 0.33 -120 -124. 8 331 0.33 -125.6 -127.4 426 0.33 125.2 -127.1 320 0.4 2.3 27 0.387 A 238.2 0.057 -174.5 0.33 -122.7 127.8 308 0.33 -128.4 -130.4 382 0.33 -128.6 -130.4 386 0.4 2.2 28 0.394 A 237.2 0.063 -174.7 0.33 -125.2 130.6 294 0.33 -131 -133.2 375 0.33 -130.9 -133 308 0.3 2.2 29 0.376 A 253.1 0.045 -175.1 0.33 -127.4 132.8 249 0.33 -134.1 -136.4 463 0.33 -133.9 -135.9 374 0.4 3.0 30 0.361 A 256.9 0.091 -175.1 0.33 -128.9 134.7 214 0.33 -134.6 -137.5 174 0.33 -134.8 -137.5 196 0.3 1.8 31 0.373 A 258.8 0.086 -175.1 0.33 -130.8 136.8 266 0.33 -134.8 -137.8 63 0.33 -134.7 -137.8 42 0.4 1.4 32 0.348 A 262.9 0.086 -176 0.33 -132.7 -138. 9 266 0.33 -136.9 -139.6 279 0.33 136.5 -139.1 212 0.3 2.0 33 0.346

PAGE 192

173EXP 23 Region 1 Region 2 Region 3 FR G x Tsat A1 Tw,i Tw,t h1 A2 Tw,i Tw,s h2 A3 Tw,i Tw,b h3 t b t P A 266.5 0.085 -176.1 0.33 -134 -140. 3 190 0.33 -139.4 -141.9 370 0.33 139.8 -142.1 431 0.4 1.6 34 0.355 A 268.8 0.084 -176.6 0.33 -135.9 142.3 288 0.33 -140.2 -143.2 220 0.33 -139.3 -142.4 22 0.3 2.1 35 0.364 A 279 0.065 -176.4 0.33 -137.3 -143. 8 220 0.33 -142.7 -145.5 437 0.33 141.6 -144.1 285 0.4 2.4 36 0.368 A 283.2 0.082 -176.4 0.33 -138.8 145.2 213 0.33 -144.9 -147.7 463 0.33 -143.9 -146.2 343 0.4 2.0 37 0.344 A 286.6 0.063 -176.4 0.33 -139.5 146.2 142 0.33 -145.6 -148.8 269 0.33 -144.3 -147.2 131 0.4 2.7 38 0.308 A 298.8 0.044 -176.9 0.33 -141.3 147.5 201 0.33 -149.4 -152.1 756 0.33 -148.2 -150.2 535 0.4 3.7 39 0.319 A 380.8 0.053 -176.8 0.33 -142 -148.5 138 0.33 -150 -152.1 128 0.33 -155.3 157.2 1417 0.4 2.7 40 0.338 A 351.7 0.039 -177 0.33 -144.8 -149.9 147 0.33 -161 162.2 2268 0.33 -165.7 166.7 2631 0.4 3.4 41 0.318 A 414.6 0.053 -177.2 0.33 -147.3 -151. 3 64 0.33 -168.2 -170.5 4210 0.33 -166.5 -169.1 1150 0.3 2.1 42 0.357 A 457.9 0.073 -176.9 0.33 -152.8 0.33 -173.7 0.33 -172.6 0.2 2.7 43 0.353 A 465.4 0.081 -177.3 0.33 -156.4 0.33 -175 0.33 -172.4 0.4 2.1 44 0.34 A 472.6 0.048 -177.7 0.33 -160.8 0.33 -176.9 0.33 -174.6 0.4 3.4 45 0.344 A 510.2 0.132 -177.8 0.33 -166.1 0.33 -176.1 0.33 -173.3 0.2 1.6 46 0.328 A 475 0.075 -177.8 0.33 -171.6 0.33 175.5 0.33 -173.6 0.3 2.6 47 0.323 A 487 0.085 -178.2 0.33 -174.6 0.33 175.5 0.33 -172.3 0.3 2.4 48 0.332 A 485.8 0.038 -178.4 0.33 -175.4 0.33 -172.3 0.33 -170.2 0.5 3.7 49 0.338 A 422.8 0.043 -178.4 0.33 -175.8 0.33 -173.9 0.33 -171.1 0.6 3.3 50 0.324 A 449.5 0.059 -179 0.33 -176.3 0.33 -174 0.33 -171.5 0.4 3.0 51 0.317 A 440.7 0.117 -179.1 0.33 -176.5 0.33 -175.9 0.33 -172.8 0.2 1.9 52 0.337 A 417 0.049 -179.3 0.33 -176.8 0.33 175.4 0.33 -172.8 0.4 3.3 53 0.293 A 415.3 0.088 -179.6 0.33 -177.2 0.33 -176.1 0.33 -173.2 0.3 2.3 54 0.292 A 425.3 0.06 -179.5 0.33 -177.4 0.33 -172.6 0.33 -171.8 0.4 3.0 55 0.314 A 404.7 0.09 -179.4 0.33 -176.8 0.33 -177.5 0.33 -176.2 0.4 2.0 56 0.289 A 461.3 0.054 -179.8 0.33 -177.6 0.33 -175.1 0.33 -171.4 0.4 2.9 57 0.283 A 403.1 0.058 -180.2 0.33 -177.9 0.33 -176.8 0.33 -173.4 0.3 3.2 58 0.327 A 332.1 0.054 -179.9 0.33 -177.8 0.33 -173.6 0.33 -173.6 0.4 3.3 59 0.315 A 355.1 0.061 -180 0.33 -178.5 0.33 172.3 0.33 -171.6 0.3 3.3 60 0.248 A 362.1 0.08 -180.6 0.33 -178 0.33 173.1 0.33 -174.9 0.4 2.4 61 0.287 A 387.5 0.053 -180.1 0.33 -178.6 0.33 -164.5 0.33 -166.7 0.3 3.5 62 0.312

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177 35. Collier, J. G., 1981, Forced Convective Boiling, in Two-Phase Flow and Heat Transfer in the Power and Process Industries, A. E. Bergles, J. G. Collier, J. M. Delhaye, G. F. Hewitt, and F. Maying er. Eds., McGraw-Hill, Hemisphere, New York, USA. 36. Gungor, K. E., and Winterton, R. H. S ., 1986, “A General Correlation for Flow Boiling in Tubes and Annuli,” Internationa l Journal of Heat and Mass Transfer, Vol. 29, No. 3, pp. 351-358. 37. Cooper, M. G., 1984, “Saturation Nucleate Pool Boiling. A Simple Correlation,” 1st U.K. National Conference on Heat Transfer, Vol. 2, pp. 785-793. 38. Klausner, J. F., Chao, B. T., and Soo, S. L., 1990, “An Improved Method for Simultaneous Determination of Frictional Pressure Drop and Vapor Volume Fraction in Vertical Flow Boiling,” Experi mental Thermal and Fluid Science, Vol. 3, pp. 404-415. 39. Mller-Steinhagen, H., and Jamialahmadi, M., 1995, “Subcooled Flow Boiling Heat Transfer to Mixtures and Soluti ons,” Proceedings of Convective Flow Boiling, Alberta, Canada, April 30-May 5, pp. 277-283. 40. Petukhov, B. S., and Popov, V. N., 1963, “Theoretical Calculation of Heat Exchanger in Turbulent Flow in Tubes of an Incompressible Fluid with Variable Physical Properties,” High Te mperature, Vol. 1, pp. 69–83. 41. Filonenko, G. K., 1954, “Hydrau lic Resistance in Pipes,” Te ploenergetica, Vol. 1, pp. 69-83. 42. Gorenflo, D., 1984, Behltersieden, VDI-Wrmeatlas, Sect. Ha (4th ed.) VDIVerlag, Dsseldorf, Germany. 43. Steiner, D., and Taborek J., 1992, “Flow Bo iling Heat Transfer in Vertical Tubes Correlated by an Asymptotic Model,” Heat Transfer Engineering, Vol. 13, pp. 4369. 44. Shah, M. M., 1976, “A New Correlation for Heat Transfer During Boiling Flow Through Pipes,” ASHRAE Transactions Vol. 82, part 2, pp. 66-86. 45. Shah, M. M., 1982, “Chart Correlation fo r Saturated Boiling Heat Transfer: Equations and Further Study,” ASHRAE Tr ansactions, Vol. 88, part 1, pp. 185196. 46. Kandlikar, S. G., 1990, “A General Corre lation for Saturated Two-Phase Flow Boiling Heat-Transfer Inside Horizontal and Vertical Tubes,” Journal of Heat Transfer, Vol. 112, pp. 219-228. 47. Kutateladze, S., S., 1961, “Boiling Heat Tr ansfer,” Internationa l Journal of Heat and Mass Transfer, Vol. 4, pp. 31-45.

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178 48. Liu, Z., and Winterton, R. H. S., 1991, “A General Correlation for Saturated and Subcooled Flow Boiling in Tubes and A nnuli, Based on a Nucleate Pool Boiling Equation,” International Jour nal of Heat and Mass Transfer, Vol. 34, No. 11, pp. 2759-2766. 49. Thome, J., R., 2005, “Update on Advances in Flow Pattern Based Two-Phase Heat Transfer Models,” Experimental Thermal and Fluid Science, Vol. 29, pp. 341-349. 50. Rouhani, Z., and Axelsson, E., 1970, “Calcu lation of Volume Void Fraction in the Subcooled and Quality Region,” Internationa l Journal of Heat and Mass Transfer, Vol. 13, pp. 383-393. 51. Kattan, N., Thome, J. R. and Favrat, D., 1998, “Flow Boiling in Horizontal Tubes: Part 3 – Development of a New Heat Tr ansfer Model Based on Flow Pattern,” Journal of Heat Transfer, Vol. 120, pp. 156-165. 52. Zurcher, O., Thome, J. R., and Favrat D., 2000, “An Onset of Nucleate Boiling Criterion for Horizontal Flow Boiling,” Inte rnational Journal of Thermal Science, Vol. 39, No. 9, pp. 909-918. 53. Greco, A., Vanolia, G. P., 2005, “Flow Boili ng Heat Transfer with HFC Mixtures in a Smooth Horizontal Tube. Part II: Assessment of Predictive Methods,” Experimental Thermal and Fluid Science, Vol. 29, pp. 199-208. 54. Zhang, W., Hibiki, T., and Mishima, K ., 2004, “Correlation for Flow Boiling Heat Transfer in Mini-Channels,” International Journal of H eat and Mass Transfer, Vol. 47, pp. 5749-5763. 55. Qu, W., and Mudawar, I., 2003, “Flow Boili ng Heat Transfer in Two-Phase MicroChannel Heat Sinks – I. Experimental I nvestigation and Assessment of Correlation Methods,” International J ournal of Heat and Mass Transfer, Vol. 46, pp. 27552771. 56. Velat, C. J., 2004, “Experiments in Cr yogenic Two Phase Flow,” M.S. Thesis, University of Florida. 57. White, F. M., 1986, Fluid Mechanics, McGraw-Hill, New York, USA. 58. Carey, V., 1992, Liquid-Vapor Phase-Cha nge Phenomena, Taylor and Francis Press, New York, USA. 59. Zuber, N., and Findlay, J. A., 1965, “Ave rage Volumetric Concentration in TwoPhase Flow Systems,” Journal of H eat Transfer, Vol. 87C, pp. 453-468. 60. Klausner, J. K., 1989, “The influence of Gravity on Pressure Drop and Heat Transfer in Flow Boiling,” Ph.D. Thesis University of Illinois at UrbanaChampaign.

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179 61. zi ik, M. N., 1993, Heat Conduction (2nd ed.), Wiley-Interscience, New York, USA. 62. Hirsch, C., 1990, Numerical Computation of Internal and External Flow, Vol. 1, Fundamental of Numerical Discretization, Wiley, Indianapolis, Indiana, USA. 63. Van Dresar, N. T., and Sieg warth, J. D., 2001, “Near-hor izontal, two-phase flow patterns of nitrogen and hydrogen at low mass and heat flux,” Technical Report NASA/TP-2001-210380, National Aeronautic s and Space Administration, Glenn Research Center, Cleveland, Ohio. 64. Milne-Thomson, L. M. 1960. Theoretical Hydrodynamics. The Macmillan Co., New York. 65. Kordyban, E. S., and Ranov, T. 1970, “Mechanism of slug formation in horizontal two-phase flow,” Journal of Basic Engineering, Vol. 92, pp. 857-864. 66. Wallis, G. B., and Dodson, J. E. 1973, “The onset of slugging in horizontal stratified air-water flow,” International Journal of Multiphase Flow, Vol. 1, pp. 173-193. 67. Lin, P. Y., and Hanratty, T. J. 1986, “Predi ction of the initiation of slugs with linear stability theory,” International Journal of Multiphase Flow, Vol. 12, pp. 79-98.

PAGE 199

180 BIOGRAPHICAL SKETCH Jelliffe Kevin Jackson was the second of four children born to Victor and Eva Jackson on the southern most Caribbean isla nd of Trinidad. He received his BSc in mechanical engineering with First Class Honor s from The University of the West Indies, St. Augustine, Trinidad, in Ma y of 2000. He received a Fulbright Fellowship which gave him the opportunity to earn his MSc in aeros pace engineering from the University of Florida in May 2003. His is currently working toward his PhD in mechanical engineering under the guidance of Professor Jame s Klausner at the University of Florida.


Permanent Link: http://ufdc.ufl.edu/UFE0014782/00001

Material Information

Title: Cryogenic Two-Phase Flow during Chilldown: Flow Transition and Nucleate Boiling Heat Transfer
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0014782:00001

Permanent Link: http://ufdc.ufl.edu/UFE0014782/00001

Material Information

Title: Cryogenic Two-Phase Flow during Chilldown: Flow Transition and Nucleate Boiling Heat Transfer
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
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CRYOGENIC TWO-PHASE 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 NAG3-270. 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 Wood-Jackson, for her unwavering support and

patience throughout the course of this endeavor. She has provided the much needed

encouragement in times when self-doubt 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

2-1 Empirical constants for the Kandlikar correlation. ...............................................25

4-1 Influence of grid resolution on the computed outer wall temperature ...................52

5-1 Sample data points for cryogenic chilldown. SW denotes stratified-wavy flow; I
denotes intermittent flow; A denotes annular flow ...............................................70

5-3 Summary of measured average nucleate flow boiling heat transfer coefficients
using inverse m ethod for regions. ........................................ ........................ 81
















LIST OF FIGURES


Figure pge

2-1 Schematic representation of flow regimes observed in horizontal two-phase
flo w .......................................................................... ............ 7

2-2 The Baker flow regim e m ap ............................................................. ............... 10

2-3 The Taitel and Dukler flow regime map. ..................................... ............... 13

2-4 The Steiner flow regim e map. ...... ......................................................................14

2-5 The Wojtan et al. flow regime map ........................... .......... ............... 15

2-6 Flow structures used to evaluate stratified flow liquid film thickness and
stratifi ed angle. .........................................................................28

2-7 Flow structures used to evaluate (a) annular flow liquid film thickness, (b)
annular flow liquid film thickness and partial-dry out angle .................................29

3-1 Schematic of chilldown experimental facility................... ................ ............... 31

3-2 Schematic of the flange assembly. ............. .............. ..........................33

3-3 Calibration plot of the actual velocity versus the ideal velocity (Velat [56]). .........36

3-4 Thermocouple arrangement on the steel transfer line prior to the visual test
se ctio n ...................................... .................................. ................ 3 7

3-5 Thermocouple placement for heat transfer test section................ ... ..... ...... 38

4-1 Model used for the stratified, wavy and intermittent flow volume fraction
c o m p u tatio n ..............................................................................................................4 4

4-2 Diagram of the model used for the annular flow volume fraction computation......44

4-3 Flow chart for transient heat transfer coefficient extraction. ..................................45

4-4 Coordinate system for heat conduction through the pipe wall.............................47

4-5 Calibration for determining the outer pipe surface heat transfer coefficient. ..........48









4-6 Assumed variation of heat transfer coefficient on the inside surface of the pipe. ...50

4-7 Computation of a parabolic varying heat transfer coefficient using the inverse
m eth o d ........................................................................... 5 5

4-8 Comparison of heat transfer coefficient computed using the inverse procedure
and the Dittus-Boelter correlation for single-phase nitrogen gas flow. ..................56

5-1 Quenching front that marks transition for film boiling to nucleate boiling .............57

5-2 Temperature profile during chilldown for low mass flux experiment ...................58

5-3 Temperature profile during chilldown for moderate mass flux experiment. ...........59

5-4 Transient mass flux for low mass flux experiment. ............................................59

5-5 Transient mass flux for moderate mass flux experiment. ......................................60

5-6 Transient vapor volume for low mass flux experiment............. .................60

5-7 Transient vapor volume fraction for moderate mass flux experiment ...................61

5-8 Transient vapor quality for low mass flux experiment. ........................................61

5-9 Transient vapor quality for moderate mass flux experiment.............................. 62

5-10 Transient inlet pressure profile for low mass flux experiment ..............................63

5-11 Transient inlet pressure profile for moderate mass flux experiment ..................63

5-12 Comparison of Van Dresar and Siegwarth data with the Baker map.....................67

5-13 Comparison of Van Dresar and Siegwarth data with the Taitel and Dukler map....67

5-14 Comparison of Van Dresar and Siegwarth data with the Wojtan et al. map...........68

5-15 Comparison of current chilldown data with the Baker map................................69

5-16 Comparison of current chilldown data with the Taitel and Dukler map ................69

5-17 Comparison of current chilldown data with the Wojtan et al. map........................71

5-18 Liquid-vapor 2-D channel flow configuration. .............................. ............... .72

5-19 Comparison of current chilldown data with the modified Taitel and Dukler map. .75

5-20 Heat transfer coefficients for each region in the film boiling regime of the low
m ass flux experim ent. ..................................................................... ...................77









5-21 Heat transfer coefficients for each region in the film boiling regime of the
moderate mass flux experiment...................................... ................. ......... 77

5-22 Average two-phase heat transfer coefficient variation with time...........................79

5-23 Comparison of predicted and measured average nucleate flow boiling heat
transfer coefficients using Gungor and Winterton correlation ..............................83

5-24 Comparison of predicted and measured average nucleate flow boiling heat
transfer coefficients using Kandlikar correlation. .............. ................................... 83

5-25 Comparison of predicted and measured average nucleate flow boiling heat
transfer coefficients using Miller-Steinhagen correlation .......................................84

5-26 Comparison of predicted and measured average nucleate flow boiling heat
transfer coefficients using W ojtan et al correlation. .............................................. 84

5-27 Method for assigning the heat transfer coefficient on the inside surface of the
pipe. ...................... ...................................... 85

5-28 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................87

5-29 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................87

5-30 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version .......................88

5-31 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version .......................88

5-32 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................89

5-33 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................89

5-34 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................90

5-35 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................90

5-36 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................91

5-37 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................91









5-38 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................92

5-39 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................92

5-40 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................93

5-41 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................93

5-42 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................94

5-43 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................94

5-44 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................95

5-45 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................95

5-46 Comparison of the predicted and measured temperatures using both the Miller-
Steinhagen and Jamialahmadi correlation and the modified version.....................96

5-47 Comparison of predicted and measured average nucleate flow boiling heat
transfer coefficients using modified MUller-Steinhagen correlation.....................97















NOMENCLATURE

A cross-sectional area (m2)

a constant in the Mtiller-Steinhagen 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 Zuber-Findlay 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 (Pa-s)

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 single-phase

21! denotes two-phase 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 single-phase 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 TWO-PHASE 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, non-cryogenic 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 stratified-wavy 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 Miiller-Steinhagen 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 non-cryogenic propellants [1] and the storage systems for these cryogenic

propellants are lighter than those required for their non-cryogenic 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 "cool-down". 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 [5-7] on the cool-down 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, non-cryogenic 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 two-phase 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 under-predicted 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 two-phase 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 re-wetting phenomenon

encountered in the nuclear industry when re-establishing 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 [10-12]. Chan and

Banerjee [13-15] used a two-fluid numerical model to investigate the re-wetting 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 non-cryogenic 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 two-phase 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 two-phase flow is more complex than single-phase flows.

Apart from the inertia, viscous, and pressure forces experienced in single-phase flow,

two-phase 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 two-phase 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 two-phase flow regimes that are

typically encountered for horizontal flow are illustrated in Fig. 2-1.




















. ...... ..ct n


Bubbly Flow



Plug/Intermittent Flow



SIg/I ntermittel Flow


Wavy Flow



Stratilied Flow



Annular Flow


Figure 2-1. Schematic representation of flow regimes observed in horizontal two-phase
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 plug-type 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 liquid-vapor interface becomes

unstable (due to Helmholtz instability), resulting in stratified-wavy flow. At high liquid

flow rates the amplitude of the waves may grow until the crest spans the cross-section 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 two-phase 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 air-water and

steam-water 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 two-phase flow with fluids other than air-water and

steam-water, 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 non-dimensional 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

0.2--1

0.1-- 0.5

6-6
0.05 --40.2


0.02--0.1 -

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 2-2. 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 cross-sectional 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
Annular-Dispersed
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 10-3

10- 10-2 10-' 100 10' 102 10 104
Xtt

Figure 2-3. 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


0-34 0 51


10.1





Fr al





101
10 ,


Figure 2-4. 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/m2-s) regime based on observations made

with R-22. 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
Stratified-wavy
50 Slug & Stratified-Wavy

0 Stratified-smogth
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x


Figure 2-5. 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 co-current water-air 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 two-phase frictional

pressure drop. The two-phase heat transfer coefficient is represented by h2, hl,t is the

single-phase 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 two-phase 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

two-phase 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 single-phase 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 two-phase 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 single-phase 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 two-phase 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 two-phase 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

single-phase liquid heat transfer coefficient is evaluated using the well-known 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 T-at( ] 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 two-phase 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+1.15x10-6E2 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 1-2Fr) (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 Mtller-Steinhagen 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 two-phase 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 0-6m.

One of the most popular enhancement models is the Shah correlation, which was

first developed in graphical form [44] and was later re-established in equation form [45].

Shah proposed that the two-phase heat transfer coefficient might be determined as

follows,

h2 = 'Phl. (2.35)









The liquid convective heat transfer coefficient, h,, is evaluated using the Dittus-Boelter

[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>lx10-4 (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 =C-lx 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 post-dryout 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 two-phase heat transfer coefficient is predicted as follows,

h2 = ( CCoC2 (25FrN)c + CBo4 Fk, I. (2.43)

h, is evaluated using the Dittus-Boelter [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 fluid-surface combination effect. The values

of these coefficients may be determined from Table 2-1 below.









Table 2-1. 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 two-phase 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 Dittus-Boelter [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 Dittus-Boelter 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 1-x 1.18(1-x) go- )T2g
a= (1+0.12(1-x)) -+ +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 2-6. Flow structures used to evaluate stratified flow liquid film thickness and
stratified angle.


















dry-0 ,,s-tr.tilrNd

(a) (b) (c)

Figure 2-7. Flow structures used to evaluate (a) annular flow liquid film thickness, (b)
annular flow liquid film thickness and partial-dry out angle, and (c) stratified
liquid film with partial dry-out angle.

In order to better model the physical process that occurs in two-phase 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],

2o-T,,h,
qo =2c (2.57)
rcntPghg

in which r,, is the critical nucleation radius, and is assigned the value 0.38x10-6 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 micro-channels 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. 3-1 below.


Collection Tank


--1 CCD

Vented to environment


Nitrogen
Supply Tanks


FdP1


rnB


Heat Element
Ball Valve
Temperature
Pressure
Differential
Pre-nure
Venturi
Heat
Exchanger
Heat Transfer
Section


Figure 3-1. Schematic of chilldown experimental facility.

Liquid nitrogen was selected as the working fluid for this investigation since it is

chemically inert, colorless, odorless, non-corrosive, 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 high-pressure 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 Joule-Thompson 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 304-stainless steel section (I.D.

12.7 mm, O.D. 15.9 mm, approximate thermal conductivity 16.3 W/m-C and specific

heat 0.46 kJ/kg-C), which is fitted with a series of external type E (Chromel-Constantan)

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 (Charge-Coupled 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 leak-free operation, see Fig. 3-2.

Hex Nut Teflon O-ring




...... ...... .... ::::::...... ............ .. .... Test
Sectio
.... *:* .... .......

S. .....Teflo
nGor

Goretex Gasket


Figure 3-2. 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 leak-free operation, see Fig. 3-2.

Static Pressure Transducers

Two Validyne P2-200V 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% full-scale 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 1-kilowatt 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 3-3. 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 10-7)uea -(5*10-5)* 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 1/16-inch type E (Chromel-

Constantan) thermocouple probes from Omega Engineering. These probes were placed

through precision-drilled 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 (Chromel-Constantan) thermocouples were placed

along the top and bottom of the 304-stainless steel tube prior to the test section, see Fig.

3-4.

Temp3 Temp2 Tempi






.... TestSection
32 mmr
-* -






Temp 6 Temp 5 Temp 4

Figure 3-4. 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. 3-5. 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 0.25-inch 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 3-5. 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 analog-to-digital board









was a Measurement Computing PCIM-DAS 1602/16 with 8 channels and 16 bit

resolution and was connected to two Measurement Computing CIO-EXP32 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 analog-to-digital 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 low-pass filter having a 7 Hz filtered cutoff. Open

thermocouple detect, and a reference to ground through a 100 k-ohm resistor are also

provided. The analog-to-digital 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

DT-3145 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 shell-side 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(1-x) 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 non-uniform 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 1-Co+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

two-phase 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 two-phase 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 two-phase 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. 4-2. 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 4-1. Model used for the stratified, wavy and intermittent flow volume fraction
computation.


Figure 4-2. 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 least-square 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. 4-3 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 4-3. Flow chart for transient heat transfer coefficient extraction.









Computing the Temperature Field in the Pipe Wall

The unsteady 3-D form of the heat conduction equation in cylindrical coordinates,

see Fig. 4-4, 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 non-dimensionalized 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 4-4. Coordinate system for heat conduction through the pipe wall.

pipe insulation must be determined. This is accomplished through a steady-state

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. 4-5. 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.

4-5. However, the measured heat transfer coefficient, 4.38 W/m2-K, 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 Linear-fit

4 40

30

20

10


0 2 4 6 8 10 12
AT (K)


Figure 4-5. Calibration for determining the outer pipe surface heat transfer coefficient.

which is non-dimensionalized 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,(T-l, (4.13)
ar

which is then non-dimensionalized to give,

_~ = h,,d d h,,t h,jl (
k-k 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 two-phase 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 4-6. 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
a-a (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 single-phase 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 4-1.

Table 4-1. 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 4-1 we see that the refinement of 60x32 or better gives an error of less

than 4 x 10-3%. 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. 4-7 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 single-phase 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 single-phase 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 4-7. 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. 4-8 (the time step size used in this test is 0.1 sec; all other


parameters are as specified previously). In Fig. 4-8 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. 4-9. 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 single-phase heat transfer coefficient with the Dittus-


Beoelter correlation for flowing nitrogen gas is shown in Fig. 4-10 (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/m2-s.

Figure 4-11 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 4-8. Computation of a parabolic varying heat transfer coefficient using the inverse
method.


0004


00031


0002


0001
" oool
E

0



S-0 001


-0 002


-0 003


-0 004


Time (sec.)


Figure 4-9. 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 4-8.


) 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/m2-s


Dittus-Boelter correlation
100 a o Inverse model



0 ------------
0 5 10 15 20 25 30 35

Time (sec)



Figure 4-10. Comparison of heat transfer coefficient computed using the inverse
procedure and the Dittus-Boelter correlation for single-phase 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 4-11. 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 in-coming 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 5-1. 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. 5-2 gives the temperature profile for a low mass

flux experiment, 75 kg/m2s (the actual mass flux data is shown in Fig. 5-4); 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. 5-5). By examining Figs. 5-2 and 5-3 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 5-2. 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
-o-Temp 1 (Top)
--Temp 2 (Left)
0.00 -'- Temp 3 (Bottom)

Temp 4 (Right)

3-5 VStratifie d/ Wavy
S-50.00


a- Slug Plug
E -100.00
I-


-150.00



-200.00
0 20 40 60 80 100 1:
Time (sec)


Figure 5-3. 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 5-4. 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 5-5. 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 5-6. 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 5-7. 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 5-8. 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 5-9. 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. 5-10, 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. 5-11.

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 non-uniform 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


5-10. Transient inlet pressure profile for low mass flux experiment.


0 20 40 60 80 100
Time (sec)


Figure 5-11. 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. 2-1. Experiments are carried out for mass fluxes that

range from 66 to 625 kg/m2-s; 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. 5-4 and 5-5. At low to moderate mass fluxes (usually below 350

kg/m2-s), a stratified-wavy 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. 5-2 and









5-3. 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 stratified-wavy regime to the intermittent regime. Once the pipe wall

temperature reaches the saturation temperature of the nitrogen, the flow transitions to

single-phase liquid flow. At higher mass fluxes (usually above 350 kg/m2-s), the initial

mist flow structure transitions into annular flow following the passage of the film boiling

front. The later flow transitions include intermittent and single-phase liquid flow.

The mass flux, shown in Figs. 5-4 and 5-5, and vapor volume fraction profiles,

shown in Figs. 5-6 and 5-7, 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. 5-8 and

5-9.

Performance of Current Flow Regime Maps

Modem phenomenological two-phase 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 quasi-steady two-phase 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 (97-346

kg/m2s) steady two-phase 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. 5-12, 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. 5-13 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. 5-14.

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 5-1 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. 5-15. It is observed

that the intermittent data are predicted reasonably well, but neither the annular nor the

stratified-wavy predictions give satisfactory agreement with the data. Fig. 5-16 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. 5-17. While the stratified-wavy and the








67



I l I I I I l I I I I


20- 100


2- 10


0.2-hi


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 5-12. Comparison of Van Dresar and Siegwarth data with the Baker map.


101


Annular


Bubbly


0

o__7


x = intermittent
O = annular
10 + = stratified-wavy


Kx 10-3


10-3
10-2


x Intermittent

xxx


Stratified-wavy




Stratified-smooth



100
Xtt


Figure 5-13. 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 + = stratified-wavy
150 -


1oo:000 0 (O0 0
Stratified-wavy
50 Slug & Stratified-Wavy

Stratified-smo9th
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x

Figure 5-14. 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/m2-s;

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 Kelvin-Helmholtz stability criterion

for wave propagation (Milne-Thompson [64]). Kordyban and Ranov [65] and Wallis and

Dobson [66] also utilized the Kelvin-Helmholtz 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 5-15. Comparison of current chilldown data with the Baker map.


101


Annular Bubbly


Intermittent


x = intermittent
10 0 = annular
+ = stratified-wavy


Stratified-wavy

Kx 10-3



Stratified-smooth


S100


Figure 5-16. 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 5-1. Sample data points for cryogenic chilldown.
flow; I denotes intermittent flow; A denotes
Saturation
Mass Flux Temperature
kg/m2-s 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 stratified-wavy
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 + = stratified-wavy
+++ + +

100 +

Slug & Stratified-Wavy Stratified-wavy
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 5-17. 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 2-D 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








2-D planar configuration within a confined channel, with both fluids moving. The

configuration is illustrated in Fig. 5-18.

Y,

pgg Pg Ug
c


Ix

81
p1


U,


Figure 5-18. Liquid-vapor 2-D channel flow configuration.

As determined by Milne-Thompson 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 Kelvin-Helmholtz 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

stratified-wavy 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= 4.516-2 072 (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. 5-19. 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
+ = stratified-wavy

Stratified-wavy

102
10 Kx 10-3

Stratified-smooth

10-3
10-2 10-1 100 101 102
Xtt


Figure 5-19. 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 5-20 and 5-21 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.5-20 and 5-21 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. 5-20 to 5-21 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 5-20. 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 5-21. 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], Miller-Steinhagen 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 two-phase heat transfer coefficient, k, is computed

as


k2 htop ) hsde (- bottom. (5.9)

Fig. 5-22 illustrates the variation of the average two-phase 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 two-phase 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 5-3. 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 two-phase heat

transfer in each region are tabulated. It is observed that the influence of region 1 on the










average two-phase 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 5-22. Average two-phase 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 stratified-wavy









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

stratified-wavy 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 stratified-wavy 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 5-3 is the only one we are aware of.

In Table 5-3, 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.