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Analysis and testing of an integrated refrigeration and storage system for liquid hydrogen zero boil-off, liquefaction, ...

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 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Current state of the art in hydrogen...
 Proposed integrated refrigeration...
 Analysis of governing equation...
 Hydrogen safety
 Test system design and analysi...
 Laboratory testing and data...
 Conclusions and recommendation...
 Appendices
 References
 Biographical sketch
University of Florida Institutional Repository

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ANALYSIS AND TESTING OF AN INTEGRATED REFRIGERATION AND STORAGE SYSTEM FOR LIQUID HYDROGEN ZERO BOIL-OFF, LIQUEFACTION, AND DENSIFICATION By WILLIAM USILTON NOTARDONATO 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 William Usilton Notardonato

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To the men and women of NASA KSC and their operations contractors for their dedication and commitment in performing an often-unappreciated role of preparing and launching spacecraft.

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iv ACKNOWLEDGMENTS I have a number of people to thank fr om NASA Kennedy Space Center, including Roy Bridges, who set up the Kennedy Graduate Student Fellowship, Joe Porta, my boss, who let me take the time to do the res earch work; and a number of KSC cryogenic engineers who lent their expertise, includi ng but not limited to Robert Johnson, James Fesmire, Zoltan Nagy, Carl Exline, Diane St ees, and Maria Little field. In addition, a number of industry sources, including people at PHPK, Praxair, Sierra Lobo, Air Liquide, and NIST have contributed their expertise. I am also particularly indebted to Dr. Jong Baik of the Florida Solar Energy Center, my partner, who did the laboratory set up and much of the testing, and Dr. Glen McIntosh of CTS, for significantly contributing to the design and fabrication of the cryostat. I express my sincere gratit ude to all my committee memb ers for agreeing to take the time to help my work and review this document. Specifically, I wish to thank Dr. Peterson and Dr. Chung for all of their help and guidance while I was revising this dissertation, Dr. Chow for a number of disc ussions and projects worked between KSC and UCF, and Dr. Sullivan and Dr. Ingley for agreeing to step in late and take over for other departed members. I also would like to thank all the professo rs I had at UF for rekindling my desire for learning about adva nced engineering con cepts. Finally, and most importantly, I acknowledge and thank Dr. Sherif for his time, patience, and guidance over the past five years.

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v This work would not be possible without the support of my immediate family, and for this I am very grateful. I thank my parents Mary-Lou and Joe for all their support over the years and for stressing the value of a good education. I al so recognize Loretta Parenteau for her support and help with my fa mily during the year I was in Gainesville. Finally, and most importantly, I thank my wife Celeste for all of her patience, understanding, support, praise, motivation, and he lp over the past five years. I could not have done it without her.

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vi TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................ix LIST OF FIGURES.............................................................................................................x ABSTRACT.....................................................................................................................xi ii CHAPTER 1 CURRENT STATE OF THE ART IN HYDR OGEN LIQUEFACTION, ZERO BOIL-OFF, AND DENSIFICATION..........................................................................1 Hydrogen Liquefaction.................................................................................................2 Linde-Hampson Cycle...........................................................................................6 Pre-Cooled Linde-Hampson Cycle........................................................................8 Linde Dual Pressure Cycle..................................................................................11 Claude Cycle.......................................................................................................12 Large Scale Hydrogen Liquefaction Plants.........................................................14 Zero Boil Off..............................................................................................................15 Ground Applications...........................................................................................15 Space Applications..............................................................................................19 Hydrogen Densification..............................................................................................21 Launch Vehicle Operations........................................................................................25 Summary.....................................................................................................................27 2 PROPOSED INTEGRATED REFRIG ERATION AND STORAGE SYSTEM.......28 Integrated Refrigeration and Storage Concept...........................................................28 System Behavior.........................................................................................................31 Behavior Issues...........................................................................................................36 3 ANALYSIS OF GOVERNING EQUATIONS..........................................................40 Thermodynamic Analysis of Liquefaction Cycle.......................................................41 Cycle Description................................................................................................41 Model Development............................................................................................44 Analysis...............................................................................................................46

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vii Thermodynamic Analysis of Storage System.............................................................55 Definitions and Assumptions..............................................................................55 Conservation of Mass..........................................................................................58 Conservation of Energy.......................................................................................59 Equation of State.................................................................................................62 Operational Simplifications.................................................................................62 Closed Storage With Heat Transfer To the System (Self Pressurization)...........63 Open Storage With Heat Transf er To The System (Boil off).............................69 Closed Storage With Zero Net Heat Transfer (Zero Boil Off)............................72 Open System With Heat Transfer Out Of The System (Liquefaction)...............73 Closed Storage With Heat Transfer Out Of The System (Densification)...........76 Corrected model..................................................................................................79 Storage Fluid Analysis................................................................................................81 Conservation of Mass..........................................................................................89 Conservation of Momentum................................................................................90 Conservation of Energy.......................................................................................94 Summary..............................................................................................................95 Solution Procedure..............................................................................................96 Boundary Conditions...........................................................................................97 Dimensionless analysis......................................................................................100 4 HYDROGEN SAFETY............................................................................................105 Hydrogen Properties.................................................................................................105 Combustion Hazards.................................................................................................108 Hydrogen Embrittlement..........................................................................................111 Cryogenic Hazards....................................................................................................112 Facility Design..........................................................................................................114 Management and Operations....................................................................................117 Conclusion................................................................................................................118 5 TEST SYSTEM DESIGN AND ANALYSIS..........................................................119 Preliminary Design and Analysis.............................................................................119 Hydrogen Storage..............................................................................................120 Cryogenic Refrigerator......................................................................................120 Instrumentation and Data Acquisition...............................................................123 Fluid Distribution..............................................................................................123 Vacuum System.................................................................................................124 Safety and Leak Detection System....................................................................124 Cryostat Specification...............................................................................................125 Cryostat Detailed Design..........................................................................................125 Cryostat Construction........................................................................................127 Cryogenic Refrigeration....................................................................................129 Acceptance Testing...................................................................................................131 Support Systems.......................................................................................................131

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viii 6 LABORATORY TESTING AND DATA ANALYSIS...........................................134 Liquid Nitrogen Chilldown.......................................................................................134 LN2 Drain and Purge................................................................................................139 Hydrogen Liquefaction.............................................................................................144 Hydrogen Densification............................................................................................148 Zero Boil Off............................................................................................................155 Measurement Uncertainty Analysis..........................................................................157 7 CONCLUSIONS AND RECOMMENDATIONS...................................................161 APPENDIX A CRYOSTAT SYSTEM SPECIFICATION..............................................................165 Configuration and Performance Requirements........................................................165 Design, Fabrication, Inspecti on and Testing Requirements.....................................167 Submitta ls.................................................................................................................168 Shipment...................................................................................................................169 B HEAT LEAK CALCULATION...............................................................................171 C DENSIFICATION SAMPLE MODEL....................................................................172 D ACRONYMS AND SYMBOLS..............................................................................173 LIST OF REFERENCES.................................................................................................176 BIOGRAPHICAL SKETCH...........................................................................................181

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ix LIST OF TABLES Table page 1-1 Ideal work of liquefaction for cryogenic fluids............................................................4 1-2 Ideal work input and density for li quefaction vs. pressuri zation of hydrogen.............5 3-1 Operational scenarios.................................................................................................63

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x LIST OF FIGURES Figure page 1-1 Ideal liquefaction process T-s diagram and system schematic.....................................3 1-2 Linde Hampson schematic............................................................................................7 1-3 Linde Hampson T-s diagram........................................................................................7 1-4 Pre-cooled Linde Hampson schematic.........................................................................9 1-5 Pre-cooled Linde Hampson T-s diagram....................................................................10 1-6 Cascade cycle schematic............................................................................................10 1-7 Linde dual pressure cycle schematic..........................................................................11 1-8 Linde dual pressure cycle T-s diagram.......................................................................12 1-9 Claude cycle schematic..............................................................................................13 1-10 Claude cycle T-s diagram.........................................................................................14 1-11 Zero loss storage economic analysis........................................................................19 1-12 Saturated liquid hydrogen dens ity, enthalpy, and vapor pressure............................23 3-1 Proposed Liquefaction Cycle Schematic....................................................................42 3-2 Acceptable Intermediate Temperatur es as a Function of Helium Compression........48 3-3 Compression Work vs Intermed iate Temperature (P2=120 kPa)...............................49 3-4 Compression Work vs Intermed iate Temperature (P2=1200 kPa).............................50 3-5 Turbine Mass Flow Rates and Cycle Work................................................................51 3-6 Heat Rejection at HX3 and HX4................................................................................52 3-7 Cycle Work vs Temperature fo r a Range of Hydrogen Pressures..............................53 3-8 Cycle Work vs Hydrogen Pressure.............................................................................54

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xi 3-9 Cycle Work vs Helium Pressure.................................................................................54 3-10 Simplified system representation..............................................................................57 3-11 Self pressurization temper ature and pressure vs. time.............................................66 3-12 Self pressurization tank qual ity and phase volume vs. time.....................................67 3-13 Self pressurization rate s for variable liquid level.....................................................68 3-14 Self pressurization (model vs. data).........................................................................68 3-15 Liquid and vapor mass during boil off.....................................................................71 3-16 Boil off time dependence on pressure......................................................................71 3-17 Cryocooler performance and heat leak vs. temperature...........................................72 3-18 Comparison of predicted vs. actual liquefaction rate...............................................75 3-19 Predicted densification temperature and pressure....................................................77 3-20 Densification rates fo r variable liquid levels............................................................77 3-21 Predicted vs. actual densification rates.....................................................................78 3-22 Corrected model vs. densification data.....................................................................82 3-23 Corrected model vs. pressurization data...................................................................82 3-24 Proposed system representation................................................................................84 3-25 Predicted Free Convection Velocity........................................................................86 3-26 Predicted Free Convection Reynolds Number.........................................................87 3-27 Predicted Grashof Number.......................................................................................88 4-1 Hydrogen T-s diagram .............................................................................................107 5-1 Cryostat design detail ..............................................................................................126 5-2 Cryocooler AL330 capacity curve ...........................................................................130 5-3 Liquid hydrogen cryos tat test arrangement..............................................................133 6-1 Liquid nitrogen chilldown........................................................................................136 6-2 Hydrogen dewar overpressurization.........................................................................136

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xii 6-3 Liquid nitrogen chilldown detail..............................................................................138 6-4 Completion of chilldown..........................................................................................138 6-5 Liquid nitrogen drain and purge...............................................................................140 6-6 Tank drain and purge pressure cycles.......................................................................141 6-7 Tank drain and purge temperature profile................................................................142 6-8 Cryocooler chilldown in vacuum.............................................................................143 6-9 Hydrogen liquefaction on 6/24/04............................................................................144 6-10 Temperature transients during initial gas flow.......................................................147 6-11 Mass flow rate and pr essure during liquefaction....................................................147 6-12 Total hydrogen volume in tank...............................................................................148 6-13 Heat pipe saturation................................................................................................149 6-14 Overnight densification..........................................................................................150 6-15 System relocation warm up....................................................................................151 6-16 Continuing liquefaction..........................................................................................152 6-17 Liquid temperature and pressure saturation curve..................................................152 6-18 Ullage collapse.......................................................................................................153 6-19 Liquefaction on 6-30-04.........................................................................................154 6-20 Liquefaction on 7-1-04...........................................................................................154 6-21 Zero boil off operations..........................................................................................156 6-22 Non-dimensional thermal stratifi cation during self pressurization.........................157 6-23 ZBO operations with P and T error bars.................................................................158 6-24 Expanded section plots of P and T with error bars.................................................159 A-1 System Specification Schematic..............................................................................170

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xiii 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 ANALYSIS AND TESTING OF AN INTEGRATED REFRIGERATION AND STORAGE SYSTEM FOR LIQUID HYDROGEN ZERO BOIL-OFF, LIQUEFACTION, AND DENSIFICATION By William Usilton Notardonato December 2006 Chair: S. A. Sherif Major Department: Mechanic al and Aerospace Engineering While hydrogen was first liquefied in th e laboratory by Sir James Dewar in 1898, it was not until the beginning of the space age in the 1950s that large-scale production of liquid hydrogen was common. Since then, the methods used by NASA to produce, liquefy, store and distribute hydrogen for launc h vehicle applications have not changed. Specifically, gaseous hydrogen is produced from natural gas, liquefied in large scale plants by performing external work on the ga s and then expanding it, transported to the launch site via tanker trucks and stored in large ground tanks in the saturated state until it is loaded into the vehicle during launch c ountdown. During the pro cess, heat leak and tank pressurization create boil-off losses, and ch ill-down of the transport lines cause more product losses. Other handling issues, incl uding low liquid density, large thermal transients, leakage and safety concerns, a nd two phase flow problems have given liquid hydrogen a reputation for being a diffi cult fluid to store and control.

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xiv This dissertation proposes a novel method of liquefying and storing hydrogen by incorporating a closed -cycle helium refrigerator in to the storage tank. There are numerous advantages to this system. Localiz ed production and liquef action eliminates the need for transportation of hazardous liquid hydrogen, minimizes heat flow into the system, and reduces the number of personnel re quired at the launch site. Proper design of the refrigerator also allows for densifica tion of the liquid, incr easing the amount of propellant loaded into the flight tank. In addition, subcooling below the normal boiling point allows the liquid to store more refriger ation energy, leading to less boil off losses or eliminating boil off completely, and possible allowing for recovery of chill down losses. Subcooled propellants also pr ovide greater thermal margin before onset of evaporation and two-phase flow. Details of these perfor mance and economic benefits are provided in Chapter 2. While there are benefits, refrigerated and subcooled cryogens behave in a different manner than saturated liquids. These behavior issues must be invest igated before large-scale incorporation in future launch system s. The conservation equations have been presented, and simplification of these equati ons in a 2-dimensional transient mass and energy model has been developed. Chapter 3 presents some results of the predicted behavior. A small testbed has also been proposed, designed, and fabricated for experimental validation of this model, and initial testing has occurred to validate the proposed concepts of liquefacti on, zero boil off and densifica tion. Results of this initial round of tests are prov ided in Chapter 6.

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1 CHAPTER 1 CURRENT STATE OF THE ART IN HYDR OGEN LIQUEFACTION, ZERO BOIL-OFF, AND DENSIFICATION Hydrogen has many favorable properties that make it attractive as a secondary energy carrier. Hydrogen is very abundant. It is believed to make up 90% of the mass in the universe, and is the ninth most comm on chemical element on Earth. Combustion of hydrogen is clean, with the major com bustion products being water and heat.(1) With a higher heating value (HHV) of 142,000 J/g, hyd rogen carries more energy per unit mass than other fuels.(2) This is particularly useful for space applications as liquid hydrogen/liquid oxygen rockets have the highest specific impulse of any combination of chemical propellant currently in use.(3) For this reason, NASA and the US Air Force (USAF) have been interested in hydrogen as a propellant for space vehicles since the late 1950s. More recently, there is much interest in using hydrogen as an energy carrier in transportation applications, including automobiles, busses, and aircraft.(4-5) Use of hydrogen does have some nega tive aspects however. Hydrogen gas has very low mass density, so volumetric concer ns limit it use to small applications. Hydrogen can be stored as a gas in a solid matrix such as metal hydrides, but these systems are not mass efficient for space use. The most practical storage method for hydrogen fuels has been as a low temperat ure liquid. Hydrogen has a normal boiling point (NBP) of 20.27 K, and the dens ity at this point is 70.79 kg/m3. Its critical point has a pressure of 1315 kPa and temperature of 33.2 K, and the triple poin t has a pressure of 7.2 kPa and a temperature of 13.9 K.(6) While NASA and USAF have pioneered methods

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2 for large scale production, storage, and dist ribution of liquid hydrogen, there are issues that must still be addressed before liqui d hydrogen gains more widespread use as a practical energy carrier. H ydrogen requires large quantitie s of energy to liquefy, and since it is stored far below ambient temperat ure, heat leaks into the storage vessels creating evaporation and produc t losses. In addition, although liquid hydrogen density is 789 times greater than gaseous hydrogen, it is still a very low-density fuel and requires large, well-insulated storage vessels. These issues will be addressed in the present chapter. Hydrogen Liquefaction One factor delaying development of widesp read use of hydrogen in the economy is the difficulty of storing and distributing la rge quantities. Gase ous storage requires extremely large volumes and storage in a me tal hydride requires heavy storage tanks and addition of energy to drive the hydrogen out of the storage state. Liquid hydrogen has the potential to eliminate these concerns, but the process of liquefying hydrogen is energy intensive. Many different cycles have been proposed and used for hydrogen liquefaction, ranging from small-scale laboratory use to la rge liquefaction plants capable of producing 60 tons per day of liquid hydrogen.(7) A challenge associated with liquid production and storage is the need for development of sma llto medium-scale distributed liquefaction systems that have efficiencies of the sa me order of magnitude as the large-scale liquefaction plants. This a llows for localized production of hydrogen gas optimized for the specific location coupled with localized efficient liquefacti on for higher energy storage densities.(8) Generalized descriptions of procedures for hydrogen lique faction exist in cryogenic technology literature.(1,7,9) These methods all rely on ta king a purified gas at room

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3 temperature and cooling it to the extremely low temperature of 20.3 K, the normal boiling point of hydrogen. In order to compare th ese systems, the thermodynamically ideal process first must be identified. The optimum cycle from the thermodynamic perspective is the Carnot Cycle, which consists of tw o reversible isothermal processes and two reversible adiabatic processes. This cycle w ould be the ideal refrig eration cycle, however, the liquefaction process is not a closed cycle but an open cycle where mass is continuously liquefied at the cold end a nd must be re-supplied at the warm end. Therefore the ideal liquefaction process can be taken as the first two steps of the Carnot cycle, namely a reversible isothermal compre ssion of the gas to a suitably high pressure, followed by an isentropic expansion where the gas completely condenses in the expander. Refer to Figure 1-1 for details on th is process depicted on a T-s diagram.(9) However, the high pressure required for complete liquefaction of hydrogen, 105 bar, makes this process technically not feasible. The minimum work required for this ideal liquefier can be determined and used as a benchmark for comparison with real processes. T s 1 2 f p=const COMPRESSOR EXPANDER LIQUID RESERVOIRfm fm cW eW rQ 12 f f Figure 1-1 Ideal liquefa ction process T-s diagram and system schematic

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4 The First Law of Thermodynamics for stea dy flow with one inlet and one outlet, neglecting kinetic and potential energy change between the initial and final state, can be written as ) (1 3h h m W Q 1-1 From the Second Law of Thermodynamics for an ideal reversible process, an entropy balance on the heat ex change process gives ds T m Q or ) (1 2 1s s T m Q 1-2 Combining equations 1-1 and 1-2 and knowing s2 is equal to s3 we find the minimum work required for liquefaction can be expressed as ) ( ) (3 1 3 1 1h h s s T m W 1-3 From equation 1-3 we find the minimum work required to liquefy a gas (assuming the initial and final pressure are e qual) depends on the initial stat e of the gas and the type of gas to be liquefied. Some common cryogenic fl uids are listed in Table 1-1 along with their NBP and their ideal work of liquefaction. Note that hydrogen requires the highest work input for liquefaction, more than even liquid helium, which has the lowest NBP of any fluid. Table 1-1 Ideal work of li quefaction for cryogenic fluids Gas Normal Boiling Point (K)Ideal Liquefaction Work (J/g) Helium 3 3.19 8178 Helium 4 4.21 6819 Hydrogen 20.27 12,019 Neon 27.09 1335 Nitrogen 77.36 768 Argon 87.28 479 Oxygen 90.18 636 Methane 111.7 1091

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5 As an interesting side note regardi ng hydrogen storage for automotive use, US manufacturers tend to favor high-pressure hydrogen gas st orage over liquid storage, which differs from some European auto manuf acturers. Storage pressures range from the present 5000-psi systems to proposed 10000-psi systems.(10) Reasons cited for this preference include longer storage times, since there is no boil as with liquid systems, less systems complexity, and less energy input requi red. The advantages to liquid storage are greater energy density and hence greater range and inherent purity of liquid hydrogen as opposed to gas.(9,11,12) Table 1-2 shows the relative energy costs associated with ideal liquefaction systems as compared to id eal gas compression systems for 5000 and 10000 psi. Ideal isothermal compression is given by the equation ) ln(1 o o oP P V P W 1-4 although this is not attainable in real life. A more realistic pro cess is the adiabatic compression process, expressed as } 1 ) {( ) 1 (1 1 o o oP P V P W 1-5 This table also shows the density of the product. From this table it is apparent that there is still significant energy cost associat ed with high-pressure gas storage. Table 1-2 Ideal work input and density fo r liquefaction vs. pressurization of hydrogen Ideal Work Input Density kJ/kg kg/m3 Liquid 12019 70.8 10000 psi fluid 8603 38.7 5000 psi fluid 7468 22.9

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6 Now that a baseline liquefaction work require ment for ideal systems has been identified, actual liquefaction processes can be compar ed. A parameter called the Figure of Merit (FOM) is defined as ideal work required divi ded by the actual work required, and varies between 0 and 1. Linde-Hampson Cycle The most simple liquefaction system is the Linde-Hampson system, which uses a Joule Thomson (J-T) valve for isenthalpic expansion of the gas. The basic LindeHampson system is unacceptable for use in hydrogen systems because of that isenthalpic expansion, since the J-T coefficient for hydr ogen at ambient temperature is negative. This means the expansion of hydrogen gas at ambient temperature will create a heating effect. It is not until the hydrogen gas reaches 205 K, its maximum inversion temperature that the J-T coefficient becomes positive and refrigeration may occur upon expansion. However, the Linde Hampson cycle will be discussed here because many of the same principles are used in other cycles. A simple schematic of the Linde-Ham pson cycle is shown in Figure 1-2(9), and the cycle state points are represented in the T-s diagram shown in Figure 1-3(9). First, the gas is compressed isothermally from a low pressure P1 to a high pressure P2. The highpressure warm gas stream then passes th rough an isobaric heat exchanger (HX), being cooled from the cold low-pressure gas stre am. Next, the gas undergoes an isenthalpic expansion back to the original low pressure though a flow restricti on, and enters the twophase region. Here, some fraction of the proce ss stream is withdrawn as a liquid, and the remaining vapor is used to c ool the high-pressure gas stream before being re-compressed

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7 for another round though the cycle. Make-up gas, equal in mass to the liquid withdrawn, is added prior to the compression step. COMPRESSOR LIQUID RESERVOIRfm fm cW rQ 12 f g 3 4 JT VALVE HEAT EXCHANGERm fm m Make up gas Figure 1-2 Linde Hampson schematic T s 1 2 3 4 f g h=const P=const Figure 1-3 Linde Hampson T-s diagram

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8 A control volume energy balance for the heat exchanger, expansion valve, and liquid tank, using the same assu mptions as before, allows one to solve for the liquid yield. f fh h h h m m y 1 2 1 1-6 Applying a similar energy balance to th e compressor gives the work per unit mass liquefied to be )] ( ) ( )[ (2 1 2 1 1 2 1 1h h s s T h h h h m Wf f 1-7 This is an ideal analysis that does not take into account imperfect heat exchange, pressure drops in the system, heat leak into the system, and assumes isothermal compression. Nevertheless, this analysis will give a liq uid yield of about 7% for liquid nitrogen systems, and has a typical LN2 FOM of 0.115. Pre-Cooled Linde-Hampson Cycle The basic Linde-Hampson cycle can be us ed as a hydrogen liquefier if the highpressure gas stream is cooled below the JT inversion temperature prior to undergoing expansion in the valve. This system, refe rred to as the pre-cool ed Linde-Hampson, is shown schematically in Figure 1-4(9) and the cycle state points are shown in Figure 1-5.(9) A secondary refrigerant, most commonly liquid nitrogen in either an open or closed cycle, is used to decrease the temperature of the gas prior to ente ring the recuperative heat exchanger. Again using an energy balance for the control volume including the two heat exchangers, expansion valve and receiver tank, a relation for th e liquid yield can be found to be ) ( ) (1 1 2 1 f c a r fh h h h m m h h h h y 1-8

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9 and the ideal work requirement pe r mass of gas liquefied becomes )] ( ) ( ) ( [ 12 1 2 1 1 a b r fh h m m h h s s T y m W 1-9 The final term represents the additional work required by the refrigerant compressor. There are added complexities with this type of system, and careful design is required to find the optimum refrigerant flow rate. Typical ly this type of system will raise the FOM for a nitrogen liquefier to a value of 0.168. Variations on the pre-cooled Linde-Hampson include the Cascade cycle, where the refrigeran t is pre-cooled by another cycle, which in turn could be pre-cooled by another cycle. A simple schematic of a cascade system is shown in Figure 1-6.(9) COMPRESSOR LIQUID RESERVOIRfm 1 cW rQ JT VALVE HEAT EXCHANGERm fm m Make up gasfm HEAT EXCHANGER2 cW 1 2 3 4 5 f g 6 a b c dREFRIGERANT LOOP Figure 1-4 Pre-cooled Li nde Hampson schematic

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10 T s 1 2 3 4 5 f g 6 Refrigerant BP h=const P=const Figure 1-5 Pre-cooled Li nde Hampson T-s diagram AMMONIA ETHYLENE METHANE NITROGEN Figure 1-6 Cascade cycle schematic

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11 Linde Dual Pressure Cycle Another modification to the basic Linde-Ham pson cycle is to add an intermediate pressure compression to the system, so not all the gas is compressed to the final pressure. This reduces the total work requirement somewhat and allows some of the heat to be removed from the gas at a higher temperature, making the process more efficient in terms of work required per unit mass liquefied. A schematic of the dual pressure cycle is shown in Figure 1-7(9) and the T-s diagram is shown in Figure 1-8.(9) The liquid yield is found to be ) ( ) (1 2 1 1 3 1 f i fh h h h m m h h h h y 1-10 And the ideal work per mass liquefied is )] ( ) ( { ) ( ) ( [ 12 1 2 1 1 2 1 2 1 1h h s s T m m h h s s T y m Wi f 1-11 HIGH PRESSURE COMPRESSOR LIQUID RESERVOIR1 cW 2 rQ JT VALVE HEAT EXCHANGERm i fm m m Make up gasfm LOW PRESSURE COMPRESSOR1 rQ 2 cW fm JT VALVEim 1 2 3 4 5 8 2 6 7 f g Figure 1-7 Linde dual pre ssure cycle schematic

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12 T s 1 2 3 4 6 f g 7 5 8P=const H=const Figure 1-8 Linde dual pre ssure cycle T-s diagram Claude Cycle Another typical cryogenic liquefaction cycle, commonly used in hydrogen liquefiers, is the Claude cycle. This syst em is shown schematically in Figure 1-9(9) and the state points are shown in Figure 1-10.(9) The major difference between this and other cycles discussed so far is the first stage of expansion is done through a work-extracting turbine. This expansion is typically appr oximated as isentropic, and this allows the hydrogen to be cooled more effi ciently than isenthalpic expans ion, and cooling will occur no matter what the initial temperature. The refrigeration produced in the first stage expander is used to pre-cool the remained of the gas, so heat can be removed more efficiently at a higher temper ature. A second stage J-T e xpansion is used for final

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13 liquefaction, for simplicity sinc e turbines typically cannot tole rate large liquid flow. An additional benefit of large scale Claude sy stems is the work produced in the turbine expander is used to help compress the gas, reducing the total work required. Liquid yield can be approximated as ) ( ) (1 3 1 2 1 f e e fh h h h m m h h h h y 1-12 And the ideal work per unit mass liquefied is )] ( ) ( ) ( [ 13 2 1 2 1 1 e e fh h m m h h s s T y m W 1-13 There are many variations of the Claude cy cle in use, not just for liquefaction of hydrogen but in many cases refrigeration of he lium as well. This cycle can be combined in many ways with dual-pressure systems and pr e-cooled systems. In some cases work is recovered in the outlet of the turbine but in others with work is dissipated in a braking system. COMPRESSOR LIQUID RESERVOIRcW rQ JT VALVE HEAT EXCHANGERm fm m Make up gasfm HEAT EXCHANGER HEAT EXCHANGERfm EXPANDEReW em 1 2 3 4 5 6 g f 7 8 9 3 e Figure 1-9 Claude cycle schematic

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14 T s 1 2 3 4 7 5 6 f g e 8 9P=const H=const S=const Figure 1-10 Claude cycle T-s diagram Large Scale Hydrogen Liquefaction Plants Several large-scale hydrogen liquefaction pl ants are in operation around the world and supply the majority of liquid hydrogen currently consumed. Details of the exact cycles used are considered proprietary but in general the plants use variations on the Claude cycle with a dual pressure system, and include several stages of isentropic turbine expansions before the final J-T expansion step for liquefaction.(1,7,13) These plants have been designed and optimized for the speci fic conditions of the local economy, and compromises between capital co sts (typically the number of stages of turbine expansion and heat exchanger effectiveness) and operati ng costs (electrical input and maintenance) have been analyzed for economic efficiency. Generally, plants in the US also include a

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15 liquid nitrogen pre-cooling stage while this practice has not been favored in Europe as much. Surveys of existing large scale liquef action plants as well as thermodynamic analysis has found that these sy stems typically operate at effi ciencies approaching 40% of the Carnot ideal cycle.(14) This calculates that the total work required per mass of gas liquefied is typically around 30,000 kJ/kg. O bviously this is significant since this is approximately 22% of the HHV of the hydrogen. Another factor to consider is the ortho-para conversion, and the energy associated with this exothermic reaction. Details of the ortho to para hydrogen conversion are given in Chapter 4. The optimum method of removing the heat of conversion is to use a catalyst to speed up the conversion proce ss and remove the heat at the highest temperature possible. Current plants perfor m the catalyst step and heat removal in a number of discrete temperatur e points, but prototypes have been built and tested that perform conversion and heat rem oval in a continuous process. Zero Boil Off Ground Applications One common feature of liquid hydrogen sy stems, indeed of cryogenic systems in general, is the fact that they are neve r in thermodynamic equilibrium with their surroundings. Heat transfer from the ambi ent temperature to the cryogenic storage temperature will always occur, no matter how good the thermal insulation systems are. If the liquid is subcooled, the heat leak increases the sensible heat of the liquid, and if the liquid is saturated the heat leak is absorbed by the latent heat of vaporization and boil off occurs. This boil off increases the vapor pressure in the tank until the maximum operating pressure is reached, and product lo sses occur as the excess vapor is vented

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16 through the pressure relief syst em. As a side note, although the term boil off is in general use in the cryogenic industry to describe this product loss, heat le aks into the tank are typically so small that no nucleate boiling is actually occurring. A more accurate term would be surface evaporation. Due to the cost of producing hydrogen from natural gas feedstock, liquefying it at a central plant, and then shipping it to th e final destination, it appears economically attractive to ensure that boil off losses are minimized or perhaps even eliminated. NASA has been investigating zero boil off (ZBO) systems for many years at the Kennedy Space Center (KSC). Martin Marietta proposed a hydrogen reliquefier for the LC-39 complex in 1977 that would remove the heat that le aked into the tank by compressing the cold vapor at the top of the tank and then expandi ng it isenthalpically to obtain cooling in a modified basic Linde-Hampson system.(15) The compressors would operate at ambient temperature, with the compressor inlet stream cooling the compressor outlet stream, after the heat of compression was removed at am bient temperature. The compressor and coldbox were to be installed at the top of the LH2 tank at LC-39. Review of the thermodynamics and economics of the system indicated the approach was feasible, however the idea was never implemented b ecause NASA management was concerned the work at the pads would impact the upcomi ng maiden launch of the Space Shuttle. In 1991, Ergenics Inc. proposed a system that would capture boil off losses in a metal hydride bed.(16) The captured gas would then be compressed in a hydride compressor, pre-cooled with liquid nitrogen, and expanded in a J-T expansion system. The analysis done indicated the system could be sized to capture not just the normal boil-off of the hydrogen tank, but also losses during tanker offload operations, from chill down of the

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17 transfer lines as well as losses from tanker venting. This approach required the development of a large metal hydride storage system as well as a 2-ton per day liquefier that would only operate a few weeks per year. This proposal was reje cted partly for the reason of complexity of a transient refrigera tion system operating in batch processes, and concerns over reliability in such a design. At this same time, a Phase II SBIR contract was awarded to Hydrogen Consultants Inc. to prove the concept of a metal hydride compressor design that could r un a J-T refrigeration system.(17) This system was sized to provide just enough refrigeration to overcome the steady heat leak into the tank, and the concerns over thermal transients was eliminated since the system was designed to operate continuously, using dual regenerative hydrid e beds. The program did produce working hardware, but there were technical issues with the J-T expansion device freezing and sticking during operation. In addition, the m easured efficiency of the system was just 8.5% Carnot, poor by comparison with other cryo genic refrigerators. In all three cases discussed above, the hydrogen was allowed to vaporize, and then work was performed on the vapor to compress it prior to expansion and reliquefaction. Despite the lack of success in creating a zero boil off system at KSC in the past, there are still sound economic advantages to recapturing hydrogen lo sses from boil off. In the case of liquid hydrogen at Kennedy Space Center a quick analysis shows the potential payoff for such a system.(18) Assume KSC pays a rough cost of $5.40 per kg of LH2 (not a true cost). This includes the cost to produce the hydrogen from the natural gas, cost to chill the hydrogen from its ambi ent temperature to a saturated vapor, cost to liquefy the vapor, the cost to ship the hydroge n to KSC in the tanker (plus losses in the transfer process), the cost to offload it to the KSC storage vessel, and profit for the

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18 vendor. Now, after all the energy and effort th at went into that pr ocess, every 20 J of heat that leaks into the storag e vessel creates a lo ss of 1 gram of product. From an energy ratio standpoint, the equation is ss transferlo shipping fg K K production H fgE E h m h m E h m Ratio * *21 3002 1-14 It is difficult to estimate all the energy put into the entire process, especially the production process, but 88% of the enth alpy removed from the hydrogen during the liquefaction process occurs between ambient te mperature and the saturated vapor state. However, when the liquid boils off and vents fr om the tank, this stored refrigeration is vented to atmosphere. This heat leak can be intercepted without creating boil off losses and the only energy cost to the system is the energy that goes into refrigeration. Assuming a refrigeration temperature of 20 K, an efficiency of 35% Carnot, and an electrical energy cost of $0.09 per kW-hr, a ZBO system equates to buying hydrogen for $0.50 per kg. There would be capital costs to be amortized over the life of the system, and these are not included in this simple analysis. Any additional operations (manpower) cost associated with this refrigeration will be offset by operational reductions in tanker offloads. There are safety benefits from th e elimination of tank venting as well as reducing the number of transient operations. Some estimates of the economic savings associated with ZBO ground systems are shown in Figure 1-11. There are a variety of cases analyzed, from current Shuttle launch operations to projected Crew Launch Vehicl e and Heavy Launch Vehicle launch rates. The options include only recove ry of boil off in the pad tanks, recovery of boil off and tanker losses, and finally recovery of boil off, tanker losses, and chill down losses. This figure shows the estimated payback time for the system is between 2 and 6 years.

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19 0 5 10 15 20 25 30 35 0246810 Time (years)Total cost ($M) HLV ZBO HLV boiloff CLV ZBO CLV boiloff HLV breakeven point CLV breakeven point 2004 fixed hydrogen price 2004 labor rates Figure 1-11 Zero loss storage economic analysis Space Applications In addition to developing ZBO system s for large-scale ground use, NASA has actively worked on developing a ZBO system fo r in space cryogenic storage. In this instance, the primary concern of product lo ss is magnified by the penalties imposed by the rocket equation. The cryogen in this case, fuel and oxidizer for a future propulsion stage, is considered payload for the launch vehicle and is subjected to the same small payload mass fraction as other payloads. As an example, consider an in space cryogenic depot situated in low Earth orbit (LEO). For every kilogram of product delivered, 6.5 kilograms of propellant are required for the la unch vehicle to deliver it to LEO. The ratio becomes 12.9 to 1 for a depot at the L1 poi nt, and 22 to 1 for hydrogen delivered to the surface of Mars.(19) Thus product loss from heat le ak can make the use of cryogenic propellants prohibitive for many missions, unl ess zero boil off systems are developed. Lockheed Missiles and Space first proposed the use of cryogenic refrigerators for long-term space missions in 1971(20), and the USAF investigated similar concepts in

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20 1982(21). At the time, cryocooler developmen t was not at the required level of development in terms of low mass and flight quality reliability to warrant inclusion in systems at that time. Advances in fli ght quality cryocoolers in the 1980’s and 1990’s, especially using Stirling and pulse tube cycles, have made their use more attractive. Analysis of proposed hydrogen storage systems as feedstock for In Situ Resource Utilization (ISRU) systems for Mars explorati on determined that ZBO made sense if the mission duration lasted longer than 45 days.(22) That is, less mass was added by the incorporation of a cryocooler and its associated power gene ration and heat rejections systems than was lost by boil off and the a ssociated increase in tank size if the mission lasted longer than 45 days. Partially due to this analysis, NASA funded a series of experiments to determine the optimum integration methods of cryocoolers in microgravity cryogenic storage systems. Initial testing at NASA Glenn Research Center (GRC) in 1999 was a proof of concept demonstration using an existing off the shelf cryocooler and a condensing heat exchanger in the vapor space of the tank. Test results were positive, showing constant or negative hydrogen vapor pre ssure slopes over the duration of 77 hours, but this configuration was not represen tative of actual space conditio ns, as there are no gravity forces that would separate the liquid and vapor phases.(23) Two phase flow handling in zero-g is the key technology that must be dem onstrated. A more representative flight like test, performed at NASA Marshall Space Flight Ce nter in 2001, used a circulatory system with a hydrogen pump drawing liquid from a liquid acquisition device and flowing it through a heat exchanger coupled with a cryoc ooler cold head. Th e cooled liquid then exited out a spray bar vent tube designed to provide destratification independent of ullage

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21 and liquid positions in zero-g. The bulk hydr ogen was maintained in the saturated liquid state, and refrigeration energy provided was ex actly balanced by heat leak into the tank. Again, this cryocooler was not a flight quality unit but a commercial unit purchased off the shelf.(24) Testing ZBO concepts with a flight like cooler was accomplished in 2003 at NASA GRC. This test was performed with liquid nitrogen and a Northrop Grumman High Efficiency Cryocooler developed fo r the USAF. A submerged mixer pump was included to provide forced liquid nitrogen fl ow across a heat exchange surface, which was coupled to the cryocooler by a heat pipe and a flexible conductive link. Unfortunately, degradation in the system in sulation performance ove r time led to larger than expected heat leak, and true ZBO conditions were never achieved. However, important information regarding integration of flight like cryo coolers with storage vessels was proven.(25) In all the above cases, ZBO systems were proposed and tested that depended on the incorporation of a closed cycle refrigeration sy stem to remove heat that had leaked into the tank. NASA Ames Research Center ha s proposed and performed a first order efficiency analysis on a system that uses the vapor from boil off as the working fluid in a refrigeration cycle.(26) This analysis shows it is advantag eous from an efficiency point to directly perform work on the fluid to be mainta ined, primarily due to the fact that there is no temperature difference required to promote heat exchange at the low temperature end of the system. This concept, similar to ground based studies mentioned earlier, has not been proven in a test environment. Hydrogen Densification One performance enhancement under consider ation for the next generation of space launch vehicles is densification of the cr yogenic propellants. Propellant densification

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22 refers to cooling the cryogens below th eir normal boiling point. Decreasing the temperature of liquid hydrogen from 20.3 K to 15 K increases the density from 70.8 kg/m3 to 76.0 kg/m3, an improvement of 7. 3%. This density increase has a corresponding decrease in vehicle propellant tank volume and mass, reducing the overall dry mass of the vehicle. In addition to re duction in tank sizes, propellant densification has other performance benefits. Liquid hydroge n has a vapor pressure of 13 kPa at 15K, compared to 101 kPa at the normal boiling point. Lower vapor pressures mean lower tank operating pressures while still meeting the engine inlet net positive suction pressure required to prevent cavitation. This lower tank pressure can result in thinner tank walls, further reducing dry mass. Higher propellant density also results in smaller engine turbomachinery for a given mass flow rate, or increased safety ma rgins by reducing the rotational speed on exis ting sized turbopumps. Finally, su bcooled propellants can provide greater cooling power to the engine nozzl es and combustion chambers due to the increased enthalpy gain prior to boil off, possibly making cooling passages smaller or minimizing chill down losses. All of the a bove reductions in vehicle dry mass have a cascading effect on the rest of the vehicle subsystems, resulting in mass reductions in airframes and aerodynamic surfaces, orbital maneuvering systems, thermal protection systems, landing gears and other systems. Studies by NASA contract ors have estimated that propellant densification can result in th e reduction of Gross Li ft Off Weight by 12% to 20%, depending on the vehicle design and number of stages.(27) Figure 1-12 plots liquid hydrogen density, enth alpy, and vapor pressure as a function of temperature between the critical point and triple point.(6)

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23 0 50 100 150 200 250 300 350 1318232833 TemperaturePressure (psia) Enthalpy (J/g0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Density (g/cm3) P (psia) h (J/g) rho (g/cm3) Figure 1-12 Saturated liquid hydrogen dens ity, enthalpy, and vapor pressure Because of the advantages that densified propellants offer, NASA and the Department of Defense have been interested in their potential use for many years. The National Bureau of Standards performed de nsified propellant property studies in the 1960’s, usually producing the necessary refrigeration by evaporative cooling. Evaporative cooling refers to the technique of vacuum pumping the ullage space in a LH2 tank to reduce the vapor pressure, leading to ev aporation of some of the liquid. The heat of vaporization needed for this evaporation is provided by the remain ing liquid, creating a cooling effect. Union Carbide analytically investigated several slush hydrogen production techniques in the same timeframe. During the 1970’s, Martin Marietta studied the concept of using a 50% slush LH2 mix with tr iple point oxygen in a si ngle stage to orbit launch vehicle. Using slush hydrogen has in creased benefits over subcooled liquids, primarily due to a density increase of almost 16% over normal boiling point hydrogen, and one of the recommendations from the report was to concentrate on hydrogen slush development only.(28) At this point, propellant densifi cation was considered an immature

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24 technology and NBP liquids were chosen as th e propellants on the Space Shuttle. Further slush hydrogen work was accomplished during the National Aerospace Plane program in the late 1980’s, with batch production of slush hydrogen being accomplished in 2000liter quantities by the freeze-thaw method of evaporative cooling at NASA Glenn Research Center.(29) Operational and handling issues associated with pressurization, transfer, mixing and sloshing, and instru mentation was investigated. Although slush hydrogen offers significant performance benefi ts over subcooled liqui ds, technical issues with its use (including filtering, mixing to ensure homogeneous states, and mass gauging) has led NASA to primarily consider subcooled liquids above the triple point in most current studies. More recently, NASA and aerospace contr actors have considered using subcooled hydrogen on a modified Shuttle system, the X-33, and other 2nd Generation Reusable Launch Vehicles (RLV). Many of the funded pr ograms in this area have concentrated on development of a densification production system. NASA GRC and Lockheed Martin have developed and tested subscale liquid hydrogen and liquid oxygen densification units based on the evaporative cooling method.(30) The largest hydrogen unit was capable of cooling 3.6 kg/sec of NBP hydrogen to 15 K, and the oxygen unit cools 13.6 kg/sec of NBP LOX to 66.6 K. In addition to pr oduction testing, tanking tests of the X-33 structural test article tank were comple ted. Tank loading procedures, including recirculation of warm propellants, were test ed using subcooled LH2. However, safety and operational concerns with using subatmospheric boiling bath heat exchangers and cold compressors led NASA to solicit alte rnate technologies to producing subcooled propellants for the 2nd Gen RLV program. Re frigeration cycles that were chosen for

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25 further development included orifice pulse tu be refrigerators, a mixed gas J-T cycle refrigerators, and a packed column cooli ng tower design based on evaporation of liquid into a non-condensable gas. A ll three technologies were chos en based on the promise of simplicity and reliability of operation once development issues had been addressed.(31) After two years of development, these pr ojects were not extended when the 2nd Gen RLV program transitioned into the Next Generation Launch Vehicle program and densified hydrogen fell out of favor comp ared to RP-1. However, operability assessments by NASA KSC during this program led to questions regarding the manner in which densified propellants would be implemented at the launch site.(32) This operability assessment is the basis of the proposed inte grated refrigeration and storage system discussed in this dissertation. Other prope llant studies have shown the mass savings associated with using densified oxygen and meth ane for ascent vehicles on the surface of Mars, coupled with an ISRU production facility.(33) Launch Vehicle Operations NASA has developed techniques for se rvicing spacecraft and launch vehicle cryogenic propulsion systems since the late 1950’s. Techniques have evolved as hardware and software capability has deve loped, and each current program has some vehicle and pad specific systems and operations required. However, the basic approach remains similar, and servicing capabilities (i n terms of quality of propellant loaded) are nearly identical. These systems, or derivativ es of them, are capable of meeting the needs of an in space cryogenic depot, provided this depot uses propellant at or above the normal boiling point, and free venting of boil off in space is permitted. Conditioning of propellants via advanced ground storage systems has the potential to minimize cost and safety risks, while maximizing launch performance.

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26 The current method of large-scale cryogenic storage and distribution is very similar across all programs at Kennedy Space Center an d Cape Canaveral Air Station. Cryogens (Liquid Hydrogen and Liquid Oxygen) are produ ced off site, delivered via tanker trucks, and transferred to ground storage tanks days or weeks prior to launch. Cryogens in the tanks are stored as a saturated liquid, and boil off gas is not recovered. During launch countdown, as late as possible into the count, the cryogens ar e transferred to the flight tank, and in the event of a launch scrub, are drained back into the ground storage tanks. Details on how this is accomplished vary across programs. Hydrogen for the Space Shuttle Program is purchased from Air Products New Orleans plant and delivered via 13000-gallon ro ad tankers. Periodic sampling of tankers is done to ensure the propellant meets purity specifications. Waves of up to five tankers can be offloaded at a time, and two waves can be done in a day. Prior to offload, transfer lines are purged with gaseous helium and sa mpled. The tank is vented and valves are opened to start chill down. Product losses from tank venting and tran sfer line chill down are free vented at the top of the pad storage ta nk. After offload is complete, transfer lines are purged of hydrogen. The pad storage tank holds 850,000 gallons of liquid, with 10% ullage on top. The tank has a vacuum jacket and perlite bulk fill insulation. The crosscountry lines 10” ID, 1500 feet long and are vacuum jacketed (VJ) with multi-layer insulation (MLI). The storage tank is pressu rized using vaporizer heat exchangers. Prior to launch, the tank must be fille d to 700,000 gallons, which is enough for three launch attempts. Loading of the STS ex ternal tank (ET) begins at T-6 hours on the countdown clock. Purges to the various disconn ect cavities is initia ted and transfer line blanket pressure is vented. The ET vent valv e is opened, chill down line valve is opened,

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27 and chill down of cross-country lines begins Then the storage tank is self-pressurized, and slow fill (1000 gpm) to the lower ET liqui d level sensors is completed. The main transfer valve is then opened and fast fill to 98% initiated, with flow rate of 8500 gpm. When the ET ullage pressure rate reaches a limit, LH2 topping at 775 gpm is initiated until the upper liquid level sensor reads 100% we t. Then the replenish valve controls the flow to maintain 100%, usually less than 300 gpm. At T-1:57 minutes, replenish mode terminates. Overall, 383,400 gallons is lo aded into the ET, with 48,000 gallons lost during chill down and 40,000 gallons lost during replenish. These vapor losses are burned in a flare stack. If the launch is scr ubbed, drainback procedur es are initiated. Summary The state of the art in ground processing of cryogenic propella nts is considered mature, and KSC operators have over 50 years of experience in this type of operations. There are performance enhancements that can be made. Of these, local production and liquefaction of hydrogen offers benefits of eliminating tanker operations, and zero boil off storage can eliminate wasteful produc t losses. Hydrogen densification has performance benefits for the flight vehicl e. NASA has invested significant funds to investigate these systems over the past 30+ years, but has never fielded an actual operating system. There are many reasons for this, but the most powerful of these has always been a lack of confidence that the benefits would outweigh the operational impacts, and conservative forces in mana gement were unwilling to try something different. This work is an attempt to change some of these positions.

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28 CHAPTER 2 PROPOSED INTEGRATED REFRIGERATION AND STORAGE SYSTEM The current state of the art in hydrogen liquefaction, storage and distribution for space launch systems has successfully served it s intended purpose for the past 50 years. However, there are possible improvements th at can be made that will make liquid hydrogen use more economical, reliable, and safe than current systems. This chapter will describe the basic concept of such a sy stem, will explain the significance of the development, and will qualit atively describe the thermodynamic behavior of the system. Later chapters will detail designs of an experimental system built to test these concepts, and data analysis of initial liquefaction, zero boil off and densification tests will be presented. Integrated Refrigeration and Storage Concept The optimum design of a liquid hydrogen stor age and distribution system is highly dependent on the intended use of the product. For example, most industrial uses of liquid hydrogen are in a continuous or semi-continuous process, such as a steady flow of hydrogen to hydrogenate oils in the production of margarine or cooking oils or steady flow of hydrogen in an anhydrous ammonia plan t. In these cases, hydrogen is liquefied only because of the transportation issues asso ciated with supplying large quantities of gaseous hydrogen make the process impractical The hydrogen is ultimately used as a gaseous product, although much of the cooling power is re cuperated elsewhere in the process. Most of the time, there is not a large quantity of liquid transfer lines, the hydrogen is vaporized immediatel y downstream of the storage tank. In these cases, large

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29 scale use of a continuous flow of gaseous hydrogen from a liquid storage system, heat leak into the tank that creates boil off is not considered an issue, there are not many issues associated with chill down and two phase flow in the supply lines, and there is no reason to increase the density of the liquid in the storage tank. Current state of the art in hydrogen storage and distribution is acceptable for these applications. The typical usage scenario for a liqui d hydrogen system in support of the space program is very different than that in indus try. The hydrogen is used in a batch process, often with many months in between launches. During this time heat leak into the tank leads to significant produc t losses, in fact only 65% of the hydrogen delivered to Kennedy Space Center is ever actually launched aboard the Space Shuttle.(34) Another major difference is the hydrogen is required to be a liquid at the use point as opposed to a gas as in most major industrial operations. Not only is the hydrogen required to be a liquid, there are strict limits on the state of that liquid that are dictated by the design of the tank and the engine start box. For the Space Shuttle main engines, temperature measurements on the turbopump exit and reci rculation lines as well as power limits on the recirculation pump (to detect cavitation) ensure there is liq uid flowing through the engine passages prior to start.(35) In this manner, the usage requirements between industry and aerospace vary greatly, and current state of the art, while acceptable, is not optimized for space use. These usage re quirements are even more strict when considering liquid hydrogen produced In Situ on the Moon or Mars. Therefore, liquid hydrogen systems designed to minimize or elimin ate heat leak and boil off, operate in a number of batch processes with large therma l transients, and stil l deliver good quality

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30 liquid when required at a use point many hundreds of meters away, are required for the next generation of space launch systems. What is truly needed is a novel appro ach to ground processing of cryogenic propellants, as opposed to incremental impr ovements in existing philosophies. The new philosophy should conform to the KISS princi ple, by minimizing operations, especially ones that cause thermal transients or require opening the system to outside contamination. This new philosophy should take advantage of advances in cryoge nic engineering over the past 20 years including efficient and reliab le refrigeration systems, health monitoring of vital components, and advanced insulation systems. Most important, the system should offer economic and energy efficiency by mini mizing boil off and chill down losses as well as venting of high cost purge gasses like helium. One possible appr oach to this issue is to integrate a closed cycl e helium refrigeration system into the ground storage tank. This integrated refrigeration system would o ffer the advantage of exercising more control of the propellant thermodynamic state while st ill in ground storage. Such an advanced system could serve as a liquefier, a zero boil off storage system, and possibly a propellant densification system. Properly designed, this could provide cost, safety, reliability, and performance benefits over curr ent state of the art. This work proposes to integrate a cry ogenic refrigerator into a liquid hydrogen dewar. Advantages to this proposal are numerous First, the refrigerator can be used to remove the heat that leaks into the vessel from the ambient environment, so there is no pressure rise and associated boil off from the heat leak. This has obvious economic savings, however, there are safety benefits as well since the tank is not venting gaseous hydrogen most of the time. Second, if the refrig erator is sized properl y, it can serve as a

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31 local liquefaction system. This minimizes operations cost since fewer personnel are required for tanker offload operations. There are less purge and sampling operations as well since there are no tanker s upply lines to inert. An adde d benefit is elimination of tanker offload losses from venting the tankers and chilling down the transfer lines. Again, there are safety and reliability benefits due to minimization of transient operations and venting operations. A third advantage of the integrated refrigeration and storage is the ability to control the state of the propellant. Currently liquid hydrogen is created and stored as a saturated liquid, although some degree of subcooling is possible with pressurization of the liquid. This proposal allows for both subcooling for an extended period of time as well as densification of the liquid below the normal boiling point. This is a fundamental change in the way liquid hydrog en is stored. Currently, there is no true thermodynamic equilibrium in a cryogenic system as there is always some degree of heat leak between the ambient temperature and the liquid temperature. This proposal mechanically removes this heat leak, so the cryogen can be stored in a manner similar to thermodynamic equilibrium. System Behavior By integrating a cryogenic refrigerator into a storage vessel, thermodynamic control of the cryogenic propellants can be ach ieved. The control of the system will be based on the ability to change the enthalpy of the stored liquid, and depends on the design of the system. Specifically the difference between the amount of heat removed at the storage temperature by the refrigeration sy stem compared to the energy entering the system from either heat leak into the system from the warm surroundings or energy entering the system from a mass input will dete rmine the rate of change of the stored enthalpy. Mathematically this is expressed as

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32 h m Q Q t h mHL ref 2-1 There are three possible types of behaviors associated with such a system. If the first term on the right is less than the other tw o, there will be a net positive flow of energy into the system. This leads to a temperature increase, or if the fluid is saturated, an evaporation of some of the liq uid combined with a pressure increase. Eventually the pressure will increase to the limit on the ta nk relief valve, and tank venting will lead to product loss. This type of system is what is currently used at KSC. A second type of system beha vior is to balance the en ergy entering the tank with the refrigeration produced, so there is no net energy input in to the system. This quasi steady state behavior is char acterized by constant system pressure and temperatures, despite the fact that the system is not truly in thermal equilibrium with the surroundings. NASA has been studying similar systems recently for the application of long term zero boil-off storage for space missions. Most of th ese studies are for closed systems with no mass input, but some proposals have sized the refrigerator to allo w for liquefaction of some small amount of incoming propellant from an ISRU reactor. The third type of behavior is exhibited when the refrigerator removes more energy from the system than enters via either mass input or heat leak. This results in a decrease in system pressure and temperature and a corresponding condensation of some of the ullage gas. Assuming a homogeneous system, the state will follow saturated liquid line to the triple point and then eventually the liquid completely freezes and the path follows the sublimation curve. For systems of intere st to spaceport propellant servicing, the solid phase most probably will be a voided and refrigeration will be controlled to keep the state above the triple point. In a ddition, to avoid contaminati on the system pressure would

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33 probably need to be kept above atmos pheric pressure by using a non-condensable pressurization gas such as helium. Combined with the fundamental change in behavior of the integrated refrigeration and storage system as described above, ther e are a number of operational enhancements to be considered. First and foremost, the system can be developed to be a zero loss storage system. Better than a zero boil off sy stem, a true zero loss system would never have any product loss, including during chill do wn and transfer operations. While this idealized case will probably never be fully achieved, capture and recovery of 50% of current chill down losses during countdown will have substantial savings. This implies to less venting and flaring operat ions at the launch pad, wh ich is a potential safety improvement, and requires a smaller storage ve ssel with less capital costs and heat leak than the current alternative. Another ambitious goal would be elimination of boil off from heat leak into the flight ta nk during loading operations. This would lead to a “storable” form of cryogenic propellant, which has grea t benefits from an ope rational standpoint. Storable cryogens will have extended countdow n hold times, and can be useful as a rapid response type of launch vehicle. Since flight tanks are gene rally insulated with foam, the heat leak is an order of magnitude higher th an what is found in the ground supply tank. This necessitates a refrigeration system with highe r capacity, but this is a benefit in itself. Larger capacities imply greater efficiencies and the added capacity can be used as a liquefaction system when not in launch countdo wn. If liquefaction capab ility is built in to the storage system, there is no need for tanker delivery of liquid, and the only supply connection can be a pure gaseous hydrogen input at the top of the tank. This leads to less ground support equipment (GSE), no tanker ports and transfer lines, less hazardous

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34 operations, less thermal transients, and less potential for contamination from line connections. Finally, when the refrigerati on system is not performing zero boil off or liquefaction operations, the capacity can be us ed to densify and subcool the propellant. Densification has advantages for launch vehicl e performance, as will be discussed in later sections, however, even if launch vehicles use NBP propellants ther e are advantages in densifying and subcooling on the ground. De nsified, subcooled propellant acts as a source of stored refrigeration energy that can be used as a thermal mass in liquefaction and zero boil off applications, may allow fo r faster chill down times, and are easier to transfer due to greater density and less tendency to exhibit tw o phase flow and cavitation. These three new operational capabilities, ZBO or zero loss, liquefaction, and densification/subcooling, will be discussed in greater detail below. The added capability will come at some cost, mainly capital improvement of the pads by adding a cryogenic refrigeration system. This capital cost will be offset by savings in procurement by adding ZBO and lique faction capability. If properly designed, there should be little added operations required as a result and should be offset by operational savings resulting from elimination of tanker operations. Close cycle helium refrigerators using the reverse turbo-Brayton cycle are current state of the art, and need no advanced development to be modified for this application. These systems are in use at many large-scale magnetic labs and particle acce lerators and are proven to be efficient and reliable. Many components are also in use at open cycle lique faction plants around the world. Helium screw compressors are at ambient temperatures and are oil lubricated. The only cold moving parts are the turbines and at hydrogen temper ature ranges these do not require expansion of helium into the tw o-phase region. The turbines are also

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35 mounted outside the cold box and can be re placed LRU style with no interruption in service. The refrigerators are designed with modern controls systems are self-regulating to provide optimum operation at a range of output conditions.(36) In a full scale Spaceport system, the refrig eration system may be sized to remove the heat leak in the flight tank. Flight tanks generally use Spray on Foam Insulation, so overall heat leak may be on the order of 200 kW When the flight ta nk is not loaded, the refrigerator will be oversized. This excess capacity can either be turned down or the system can be used as a hydrogen liquefie r. On site liquefaction has operational advantages. There are safety benefits, si nce there is no trans portation across public highways, no transfers of cryogenic liquids from tankers to storage tanks, and less hazardous venting. Cost savings will occur due to less operations and transportation, especially if the hydrogen produc tion facility can be sized to provide economy of scale for many sites. The entire spaceport can c onsist of one centraliz ed hydrogen production facility supplying a number of modular, self-contained lique faction and storage sites at each pad thru pipelines not unlike the natural gas lines in common use. There is possible synergy with the future hydrogen economy and the need for localized hydrogen production and storage, and the system serves as a prototype of a fu ture Lunar or Mars propellant production and storage facility. The proposed testbed will have the capabil ity to deliver hydrogen gas to the liquid system. After pressure reduction, the gas will be metered thru a mass flow controller. The regulated gas stream can be delivered in three possible ports. First, the gas can be added to the ullage space on top of the liquid, conde nsing at the liquid/vapo r interface. Second, the gas can bubble up thru the bo ttom of the tank, with the b ubbles exchanging heat with

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36 the subcooled liquid. Finally, the gas can exch ange heat directly with a condensing heat exchanger line at the cold h ead. For all three methods, the liquefaction rate must be measured. To increase efficiency of the lique faction process, the gas may be pre-cooled with a liquid nitrogen HX or an intermediate stage of helium refrigeration, so the high temperature enthalpy changes can be remove d with less expensive refrigeration. In addition, pre-cooling allows the addition of an ortho to para conversion catalyst to be added. This will help remove some of the heat of conversion before the hydrogen enters the dewar. Behavior Issues The proposed novel operational system w ill behave different than the NBP counterpart and there will be a learning curve associated with their use. Research into operational behavior must be addressed. The t opics to be explored include pressurization and venting of stored subcooled liquids, in tegrated refrigeration systems controls to provide optimum performance dur ing different operational phas es of densification, zero boil-off and liquefaction, determination of heat and mass transfer coefficients, and methods of handling stratification layers. A dvanced instrumentation should be developed to accurately determine the state of the propellant quality The vapor pressure of liquid hydrogen st ored at 14 K is onl y 7 kPa. Having a subatmospheric pressure inside the dewar may create safety concerns since any leak path in the tank will draw in outsi de air, which will immediatel y freeze. While the inner tank must be designed to hold a vacuum, that shoul d not be the normal mode of operation. Another issue is the tendency of the tank pressure to decrease as heat is removed from the tank, as opposed to normal heat leak into a tank causing a pressure increase. The tank will operate at two pressure settings, normal (extended) operation with a small positive

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37 pressure differential, and tran sfer operations pressure with a higher positiv e pressure to overcome line resistance and elevation changes. Normal operational pressure will be approxi mately set at 140 kPa. The inside of the tank will not be in thermodynamic equilibr ium, as the cold liquid will continuously condense the vapor at the top of the tank. To maintain positive pre ssure, three different sources of ullage pressure may be considered First, gaseous helium, non condensable at 14 K, will be used. Testing will be performed to determine the rate of pressurization of the system using various flow rates of gaseous helium. This will depend on the heat transfer rate between the li quid/vapor interface and the convection heat transfer in the gaseous helium. Techniques to prevent the collapse of the ullage pressure will be investigated, including b ubbling the helium up through th e liquid hydrogen to increase heat exchange rate and pre-cool the helium. The other option for pressurization gas is hydrogen. Liquid hydrogen from th e tank will be directed to a vaporizer consisting of a heat exchange coil, is olation valve, and pressurization regulator. The dynamics of the system heat exchange rates will be recorded, in an attempt to balance the rate of heat transfer between the liquid/vapor interface and the vaporizer and atmosphere. Again, gaseous hydrogen will also be bubbled up through the liquid, although this is not advantageous since the amount of heat entering the tank will increase using this method. Finally, a bottle of room temp erature hydrogen will be used as a pressurization source. This gas will liquefy at the interface, so a continuous source of gas must be used to prevent ullage collapse. This pressuri zation method will be discussed more when hydrogen liquefaction is considered.

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38 During operations that require transfer of liquid from one tank to another, tank pressure will need to be in creased to overcome friction a nd elevation head losses. All three pressurization sources disc ussed above will also be eval uated for their suitability for this purpose. In this case, the ullage space in the tank will be increasing as the tank liquid level is decreasing, so the mass flow rate re quired will be greater than just tank pressure maintenance. This mass flow rate must equa l the rate required to fill the extra volume plus the rate required to make up the contrac tion as the gas cools dow n. Depressurization without venting the tank will be achieved by te rminating the flow rate of pressurization into the tank while maintaini ng the cooling of the hydrogen. However, this approximation depends on perfect heat exch ange between the cryocooler and the hydrogen, and it assumes th ere are no temperature gradients in the liquid (lumped capacitance method). In reality, the overall heat transfer coefficient of the free hydrogen convection must be determined. The tank will be instrumented to allow for monitoring of the temperature gradients in the liquid, so the total thermal energy in the system can be calculated. Knowing the performance capabilities of the cryocooler as a function of temperature, the rate of heat transfer from the liquid to the cold heat exchanger can be calculated, and the heat tr ansfer coefficient can be determined. The cold head of the cryocooler will be designed to allow for a variety of heat exchangers to be used. The initial cold heat exchanger will be bundled of OHFC copper extending downward from the cold head. Future desi gns will include horizo ntal and vertical surfaces with a variety of extended fins. The vertical position of the heat exchanger will be variable by removing or replacing the he at pipe in the system. One enhancement under consideration will be the addition of a mi xing or stirring device in the tank. This

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39 could help the rate of heat transfer in tw o ways; ensuring a uniform temperature in the tank, and creating a forced convect ion current across the cold HX.

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40 CHAPTER 3 ANALYSIS OF GOVERNING EQUATIONS In Chapter 2, the concept of the integrat ed refrigeration and storage system was discussed, and the behavior of the system was addressed from a qualitative standpoint. This chapter will look at the thermodynamic behavior from a quantitative perspective. First, a thermodynamic model of the proposed li quefaction cycle will be developed. This model will integrate the closed cycle helium refrigerator into the hydrogen input stream. Details on the system operating characteristics will be presented, and a range of acceptable intermediate cycle temperatures will be found. Optimizing the cycle parameters, namely the hydrogen and helium compression ratios and the intermediate temperature, to minimize the total work i nput will be completed. Next, a simplified model of the storage system will be made using a two-dimensional transient mass and energy balance approach, starting with the in tegral form of the conservation equations. This model will then look at specific operati onal situations and predict system behavior. Where applicable, this behavior will be comp ared to experimental data obtained in Chapter 6. Corrective changes to this model will be proposed to more accurately predict the system behavior. These changes incor porate correction factors accounting for the variable liquid level in the system as well as non-isothe rmal temperature profiles in the ullage space that lead to variations in the system heat leak. Finally, since the bulk fluid mass and energy balance approach still falls shor t of a true physical m odel of the system, the full conservation equations will then be presented in differential form based on an analysis of expected flow and heat tran sfer regimes. Initial conditions and boundary

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41 values will be presented to fully pose the pr oblem. This problem formulation is an important first step in the ge neration of a full solution, as CFD experts may not have the requisite experience in understa nding the behavior of the sy stem to be modeled. These conservation equations will then be converted to dimensionless form, using the initial system energy and heat leak rate as dimensiona l constants. This will provide insight into the system behavior from the perspective of how much heat is entering the system with respect to how much energy was initially in the system. Thermodynamic Analysis of Liquefaction Cycle Cycle Description A novel cycle for hydrogen liquefaction is pres ented in this section. This cycle takes advantage of the required helium refrig eration cycle needed for maintaining the hydrogen in the controlled storage state and uses excess refrigeration capacity to precool the incoming hydrogen stream as well as remove the latent heat of vaporization of any saturated hydrogen vapors downs tream of the expansion valve. A schematic of this proposed cycle is show in Figure 3.1. Pure hydrogen from a production plant enters the cycle at point 1 and is compressed to pressure P2 by a hydrogen compressor. HX3 removes the heat of compression and sends the ambient temperat ure, high-pressure hydrogen gas to the recuperative heat exchanger HX3. In HX3, a cold helium refrigeration system removes heat from the hydrogen and cools it down to the intermediate temperature T4. Then, the cold compressed hydrogen is expanded thr ough a Joule-Thompson valve to the storage pressure P5. At this point, depending on the storage pressure P5 and the unexpanded hydrogen state (T4, P4) the hydrogen is either a cold vapor or a two-phase flow. The integrated heat exchanger HX4 inside the storage tank removes the remainder of the heat

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42 to convert the hydrogen to 100% liquid that can be stored or drai ned from the tank at location 6. Hydrogen Compressor Helium Compressor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 WhydTurbine Turbine JT Valve HX3 HX1 HX2 HX4 LH2 Figure 3-1 Proposed Lique faction Cycle Schematic The closed cycle helium refrigerator in this model is a two-stage Brayton cycle with external heat loads at HX3 and HX4 The helium is compressed from the low pressure to an undefined high pressure P8. Heat of compression, as well as external heat loads, is removed in HX2. The helium flow is split downstream of this heat exchanger, and some mass flow (14m ) is split off to be expanded th rough the first (high temperature) turbine. The remainder of the flow (10m ) is pre-cooled in HX3 and then expanded in the

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43 second (low temperature) turbin e to a temperature required to remove the leftover heat of the hydrogen vapors in the tank for that par ticular mass flow rate. Both expansion turbines operate at the same pressure inlets and outlets and it is not a dual pressure cycle. The two turbine flow streams recombine immediately downstream of HX3 and flow together to pre-cool the high pressure helium stream and incoming hydrogen stream. Some of the unique features that differe ntiate this cycle from other hydrogen liquefaction cycles are now di scussed. Note how the hydrogen input stream is not a continuous cycle with cold vapors returni ng to the hydrogen compressor. The hydrogen flow is in one direction only, from the co mpressor to the tank, and the ultimate liquid yield is 100%. This is due to the presence of HX4, which removes the remaining heat of vaporization from hydrogen downstream of the JT valve. In fact, in some cases the JT expansion may not even be needed and no cooling of hydrogen comes internally from expansion. The final pressure of the JT expa nsion is not fixed, but variable depending on the mass flow rate of the hydrogen and the am ount of cooling provided by the helium refrigerator at HX4. In some cases this ma y be subatmospheric pressure if the desired storage state is densified hydrogen. The recuperative heat exchanger HX3 is a ke y component in this cycle. It is a counterflow heat exchanger w ith two warm inlet streams and one cold inlet stream. There is a net heat load on the helium cycle that is determined by the hydrogen mass flow rate multiplied by the enthalpy difference between state 3 and state 4. The final hydrogen temperature T4 prior to expansion is a vari able to be optimized in the model. This optimization is done in a later section with HX3 assumed to be a perfect heat exchanger with no pressure drop. The advantages to using HX3 to precool the hydrogen are

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44 obvious. The greater the amount of energy removed from the input stream at high temperatures, the more efficient the cycle efficiency will be. This is the purpose for many of the LN2 pre-cooled systems in us e today, except this cycle does not use consumable nitrogen as a pre-cooling source but relies on closed cycle helium refrigeration instead. An additional feature is the incorporation of an ortho-para catalyst in the inner passages of the hydrogen stream, wh ich allows for the heat of conversion to be removed continuously at every temperatur e in the most effici ent manner possible. The depiction of the compression step is shown for simplicity only and in most cases multiple stages of compression will be used with interstage cooling. The helium compressor is most probably an oil flooded screw compressor, and extra equipment will be needed downstream of the compressor to remove oil and other contaminants prior to flowing into the coldbox. These compressors are used successfully in large-scale helium liquefiers at major particle acc elerator facilities. The hydr ogen can be compressed either by a mechanical compressor or as a high pressure output of a hydrogen production system, such as a steam methane reformer or an electrolysis unit. If the hydrogen is already compressed by the production system, this will save energy by taking advantage of the prior compression, and in these cases the work input for compression of hydrogen will not be factored into the liquefaction work input. In some cases the hydrogen may not even be compressed, if the JT expansion pr ocess is not needed. This is the situation presented in the Chapter 6 experimentati on section, with room temperature hydrogen being cooled and liquefied entirely by the heat exchanger in the storage tank. Model Development A thermodynamic model based on the cons ervation of mass and conservation of energy principles has been developed to predict cycle behavior and optimize the

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45 operating conditions. The model uses P1, T1, P7, T7, and hydm as input parameters. The heat exchanger delta pressure and temperature can be specified as well, but in most cases the heat exchange process was approximated as perfect. In the model, an isentropic compression in one stage is used, but multiple stages and intercooling more closely approximates an isothermal compression stag e and would reduce the overall work input. An isentropic expansion efficiency of 80% is used for the calculations for both the compressors and expansion turbines. The desire d liquefaction storage temperature is also required as an input, and has a great effect on the outcome. The compression ratios of the hydrogen and helium streams are variables to be optimized. Work required for compression is calc ulated, then the heat exchange required to reject the heat of comp ression is performed prior to flowing through the recuperative heat exchanger. Knowing the desired storage pressure and the heat exchanger pressure drops, the system pressures are known at all points in the cycle. The high temperature turbine exit pressure is set by the low-pre ssure requirements of the compressor, and a dual pressure system is not approximated. The unknown parameters at the recuperative heat exchanger are the outlet temperatures (T4, T11, and T16) and the required helium mass flow rates through both the high temp erature and low temperature turbines. Assuming an intermediate hydrogen temperat ure at T4, the other heat exchanger temperatures can be calculated. The helium mass flow rates are then computed using the energy balance on the tee and th e energy balance across the whole heat exchanger by the relations 16 15 13 16 16 15 15 13 13) ( h m m h m h m h m 3-1 ) ( ) ( ) (7 16 16 10 11 10 3 4 3h h m h h m h h m 3-2

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46 From there, an isenthalpic expansion is ca lculated across the JT valve to the desired storage pressure. The heat required to fully liquefy the JT product st ream is calculated, and that determines the sizing of the helium at heat exchanger 4. If the hydrogen is not saturated at the exit of the JT valve (a condi tion that can occur if T4 is not low enough or P2 is not high enough), then the helium in HX4 must remove the remaining sensible heat prior to hydrogen liquefaction. The low temper ature expansion turbin e pressure ratio is already determined by the cycle parameters, so the turbine exit temperature is known. The required mass flow rate is calculated using an energy balance across HX4. The model optimizes the cycle in terms of minimu m mass flow rate required for the desired cooling in HX3 and HX4. Severa l constraints are placed on the optimization subroutine. A minimum temperature at the outlet of the low temperature turbine is set at 14K to eliminate the potential for freezing hydrogen in the vessel. The mass flow rates for all points on the helium cycle must be positive or zero. The low-pressure helium stream into the recuperator is constrained to be lower than the hydrogen exit intermediate temperature and the high-pressure helium exit temperature. Analysis From the development of the model, it b ecomes apparent the independent variables to be used in the optimization process ar e the hydrogen compression pressure P2, the intermediate temperature downstream of the recuperative heat exchanger T4, and the helium compression pressure P8. The combined work of the hydrogen and helium compressors are the dependent variables to be minimized. This process can be repeated for a range of inlet conditions and final st orage pressures for hydrogen, variations in compressor and turbine efficiencies, and ineffici encies in the recuperative heat exchange process.

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47 For a given pair of hydrogen and helium high pressures, there is a range of intermediate temperatures that can be used to give a satisfactory solution to the equations 3-1 and 3-2. The family of curves shown in Figure 3.2 displays this relation. For this figure, the hydrogen cycle was assumed to have no hydrogen compression and the stream is isobaric at 120 kPa. This means no is enthalpic cooling of the hydrogen and the liquefaction is completely performed by the heat exchange with the helium in HX3 and HX4. Using a range of different helium pr essures (ranging from 360 kPa to 7200 kPa), the temperatures that give a non-trivial so lution are plotted. If the intermediate temperature is colder than the left hand cu rve in the figure, the system will not work because the high temperature turbine will be limited to the temperatures it can achieve, and T16 will not be less than T4. Similarl y, using T4 higher than the right hand curve requires a greater amount of cooling has to be performed at the low temperature turbine, and the turbine exit temperature decreases. In order to get the required cooling inside the storage tank, the mass flow rate increases. The recuperative heat exchanger becomes unbalanced and eventually the required mass flow rate through the high temperature turbine becomes zero. Notice the range of temperatures increase as the helium compression ratio increases, which allows for greater cycle flexibility during operation. Similar behavior was observed in the cy cle when the hydrogen was compressed and expanded in the JT valve. The dependence of the cycle feasibility on a small range of acceptable intermediate temperatures places many constraints on the actual system, and care must be taken to ensure the cycle does not operate outside these limits. It is also shown later that the overall work increases as the intermediate temperature increases, so operating on the left hand side of the curve is desired.

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48 0 1000 2000 3000 4000 5000 6000 7000 8000 20253035404550 T4 (K)P8 (kPa)P2 = 120 kPa P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXT Figure 3-2 Acceptable Intermediate Temper atures as a Function of Helium Compression The figure above gives no information on the work input requirements, only operating conditions that are acceptable for the cycle at those temperatures and pressures. Since the cost of liquefa ction is directly related to the energy input rate, regards for the dependence of work input on the system opera ting points should be considered. Below, Figure 3-3 plots the work input for liquef action of 1 gram per second of gaseous hydrogen against the interm ediate cycle temperature, for a range of compression ratios in the helium cycle. All other cycle parameters are constant and define d below. No work input was done on the incoming hydrogen gas st ream and all cooling was done through a heat exchange process in HX3 and HX4. Noti ce there is a range of acceptable solutions for certain intermediate temperatures, and poi nts past the endpoints of the isobaric lines do not have solutions that converge in the model. For a given helium compression ratio, the work input is reduced as the intermediate temperature is decreased. This dependence is more pronounced as the helium compression is reduced, as small increases in T4 lead

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49 too much larger increases in work input. In addition, the required work actually increases for these smaller pressure ratios, due to the increase in required mass flow rate. Subsequent analysis therefor e concentrates on helium compre ssion ratios of 10 or greater. 75000 85000 95000 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000 205000 253035404550 T4 (K)Work (W) 1200 2400 3600 4800 6000 7200 840 600 360P2 = 120 kPa P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXTP8 (kPa) Figure 3-3 Compression Work vs Inte rmediate Temperature (P2=120 kPa) Figure 3.4 shows a similar plot of work vs T4 for a cycle that has some compression work in the hydrogen side. The hydrogen compression ratio is 10, and some isenthalpic cooling is occurring at the JT valve. Note the lower helium compression ratios are not included in the figure. The plots look very similar to the case where there is no hydrogen compression (Figure 3-3), but there are some slight differences in values of total work. These differences will be explored a little later in Figure 3.8, when the work is plotted as a function of the hydrogen comp ression ratio. Again, for the low helium pressures, there is a steep increase in work for very small increases in intermediate temperature, and these cycles should be avoided if possible. The higher helium compression cycles also exhibit greatl y increased work input requirements.

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50 P2 = 1200 kPa P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXTP8 (kPa) Figure 3-4 Compression Work vs Inte rmediate Temperature (P2=1200 kPa) Meanwhile, it is informative to look at some of the cycle parameters in this case to see how the cycle functions. Figure 3-5 plots the required helium mass flow rate through each turbine as a function of intermediate te mperature for a cycle with both the hydrogen and helium compression ratios set at 10 to 1. Note how the overall mass flow rate increases as the intermediate temperature increases, and the high temperature turbine flow rate decreases from approximately 10% of the flow at the lower T4 to zero at the upper end of the T4 curve. The secondary y-axis plots the work input for both the hydrogen and helium. The hydrogen work is constant since the compression ratio and mass flow rate are fixed. The helium work i nput increases due to the increase in requires mass flow rate, even though th e compression ratio is fixed. Another way to evaluate the efficiency of each cycle is to look at the heat rejected by the hydrogen in each heat exchanger. Figur e 3-6 shows the heat rejection in HX3 and HX4 for a range of intermediate temperatures and helium compression ratios, with the

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51 0 5 10 15 20 25 30 35 40 45 50 33.53434.53535.53636.53737.538 T4 (K)Mass flow rate (g/s)0 20000 40000 60000 80000 100000 120000 140000Work (W) T1 flow T2 flow Hydrogen work Helium workP2 = 1200 kPa P8 = 1200 kPa P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXT Figure 3-5 Turbine Mass Flow Rates and Cycle Work hydrogen pressure fixed at 1200 kPa. The upper curve shows the majority of the heat being rejected in HX3, which is the higher temperature heat exchange. However, for warmer intermediate temperatures, the amount of heat rejected is decreased in HX3 and increased in HX4. This fact does not change with increases in helium cycle pressure, as is evidenced by the different P8 curves plot ting on top of each other. Another way of looking at this plot is to thi nk the cycle that rejects the gr eatest amount of heat at the highest temperatures will be the most efficien t, and the work curves plotted in Figures 33 and 3-4 provide more evidence of this. In the preceeding paragraphs, it is demonstrated that the optimum intermediate temperature to have in the cy cle is the lowest temperature allowed for the given hydrogen and helium pressures. The next step is de termining the work required as a function of hydrogen pressure. The total amount of hydrogen work is much less than the helium

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52 0 500 1000 1500 2000 2500 3000 3500 4000 4500 303234363840424446 T4 (K)Q (W) HX3 (P8=1200) HX4 (P8=1200) HX3 (P8=2400) HX4 (P8=2400) HX3 (P8=3600) HX4 (P8=3600)P2 = 1200 kPa P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXT Figure 3-6 Heat Reje ction at HX3 and HX4 work due to the flowrates involve, but an ove rall advantage can occur if some level of cooling can be achieved by hydroge n expansion. Again, work input may not matter if the work is from the hydrogen production process. Figure 3-7 shows the work required as a function of T4 for a range of hydrogen pre ssures. The helium cycle is working at a pressure of 2400 kPa. There is little movement in the curves for the pressure ratios less than 10 to 1, then gradually the curve shifts to the higher temperature areas. Then the curves start clustering again above P2=3000 and no further advantage can be gained by higher compression. Choosing the lowest temperature point in the curves in Figure 3-7 obtains a plot of lowest allowed work input for each speci fic helium compression ra tio as a function of hydrogen pressure. Figure 3-8 shows there is an initial small spike in compression work, followed by a decrease to a local minimum, followed by a gradual increase as systems reach very high hydrogen pressures. This shows there exists an optimum hydrogen

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53 70000 80000 90000 100000 110000 120000 130000 140000 150000 160000 34363840424446 T4 (K)Work (W) 120 240 360 480 1200 2400 4800 6000 7200P2 (kPa) P8 = 2400 kPa P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXT Figure 3-7 Cycle Work vs Temperatur e for a Range of Hydrogen Pressures pressure, for each helium pressure and intermediate temperature, for which the liquefaction cycle operates at maximum thermodynamic efficiency. This hydrogen pressure occurs at 2400 kPa. Similarly, Figur e 3-9 shows the cycle work for a range of helium pressure ratios. It is evident ther e exists a helium pressure that leads to a minimization of work for each set of hydrogen pr essures, and this pressure is below 1200 kPa. This figure also show s the curve with a hydrogen pr essure of 2400 kPa provides the lowest work total. Based on the above analysis, it is conc luded that the proposed combined hydrogen and helium liquefaction cycle is feasible, and a range of operating conditions exist. There is a minimum and a maximum intermediate te mperature that can be used downstream of the recuperative heat exchanger. Temperatures higher than this range will not work due to HX3 becoming unbalanced as the mass flow rate through the high temperature turbine

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54 goes to zero. Temperatures lower than the acceptable range will not work due to the high temperature turbine not being able to provide a low e nough temperature to 70000 75000 80000 85000 90000 95000 010002000300040005000600070008000 Hydrogen pressure (kPa)Work (W) 2400 1200 3600P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXTP8 (kPa) Figure 3-8 Cycle Work vs Hydrogen Pressure 70000 75000 80000 85000 90000 95000 05001000150020002500300035004000 Helium pressure (kPa)Work (W) 120 480 1200 2400 4800P7 = 120 kPa P5 = 101 kPa80 0 c80 0 t10 HXPkPa0 HXTP2 (kPa) Figure 3-9 Cycle Work vs Helium Pressure

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55 ensure T16 is less than T4. The most effi cient intermediate temperature to use for a given set of hydrogen and helium pressures is the lowest temperature possible. This maximized the amount of heat rejected at hi gher temperatures. The analysis in this section also shows the func tional relationship between hydrogen and helium pressures and work. It is shown the most efficient cycl e will operate with th e hydrogen pressure at 2400 kPa, and a helium pressure at 1200 kPa. The efficiency of the liquefaction system is 17%, which is respectable for a small scale LH 2 system with only 1 intermediate stage. Thermodynamic Analysis of Storage System An effort will now be made to model the thermodynamic behavior of the liquid hydrogen in the storage tank for a variety of operating conditions. In many practical applications, simplifications to the full conservation equations can be made to provide great insight into the physica l characteristics of a system without sacrificing too much accuracy. Such simplifications allow for clos ed form analytical solutions that do not require sophisticated numerical techniques to solve. This section will focus on applying these simplifications over a control volume to obtain general expressions for the mass and energy balance of the system. These control volume mass and energy balances will then be tailored for the specific operational constraints found during the zero boil off, liquefaction, and densification processes, and these specific expressions will be compared to results of the experimental testing discussed in Chapter 6. Definitions and Assumptions The control volume to be analyzed is pr esented in Figure 3-10. A cylindrical double walled tank of volume 150 liters, with a di ameter of 50.8 cm and length of 74 cm, is initially partially full of liquid hydrogen in the saturated condition. The temperature of the tank is well below the ambient temperature a nd there is a flow of heat into the tank

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56 from the surroundings through the insulation into the system. This heat transfer can be assumed to be of two forms, the radiation heat transfer from the outer vessel to the inner vessel, and conduction heat tran sfer down the length of the n eck of the vessel and other solid supports. In addition, there is a cold he at exchanger integrated into the vessel that can remove heat from the liquid. There are three ports connecting th e inner vessel to the surroundings. The liquid fill and withdraw port is present to allow for the flow of the hydrogen from the storage vessel to the use point, in this case the flight tank of a rocket. The vent port is designed to vent vapor from the top of the tank to the ambient pressure surroundings, either in a controlled vent or as an emergency relief when the system pressure reaches the maximum operating pressu re. The gas supply port is necessary to allow for pressurization of the fluid as well as to introduce hydroge n gas for liquefaction operations. The inner tank hol ds only hydrogen in gaseous or liquid form. The system thus defined constitutes an open, transient, homogeneous, multiphase system with heat and work interactions. Despite the apparent complexity of the system as defined above, numerous simplifications can be made to allow for fairly accurate analysis. First, it can be assumed that the time constant associated with de fining an equilibrium st ate between the liquid and vapor phases is much less than the tim e constant associated with any system interactions with the surroundings. This assumption is vali d as long as the heat transfer into or out of the system is low, as it typically is in well insulated cryogenic vessels, or the mass flow rate into and out of the system is small compared to the total system mass.(37) This defines the system as being in thermodynamic equilibrium with respect to the liquid and vapor phases, and requires the liquid and vapor phases to have equal

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57 LH2 GH2 HX MLI Q QREF RAD QCONM P T M r z M P Tvp vp vp gsp gsp gsp fg lfwU M P Tlfw lfw lfw Gas Supply Port (gsp) Vent Port (vp) Liquid Fill and Withdrawl (lfw) Temp=f(t)=T Press=f(t)=P Mass=f(t)=Mg g gVolume=f(t)=VgVolume=f(t)=V Mass=f(t)=M Temp=f(t)=T Press=f(t)=Pl l l l Figure 3-10 Simplified system representation temperature and pressure. It is important to keep in mind that the definition of thermodynamic equilibrium does not imply there is no time dependence in the system, and in this case the model is a still a transient system. A second assumption is the liquid and vapor phase have a defined, impenetrable boundary. It is assumed there are no bubbles in the liquid and no mist in the vapor. This allows for modeling the system as a combin ation of two separate single-phase control

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58 volumes, with heat and mass transfer between them at the liquid to vapor interface. The overall volume of these control volumes will vary with time, depending on the level of evaporation or condensation at the interface as well as the temperature and pressure of the liquid and vapor. Next, assumptions about the properties of the fluids must be made. The fluid velocities are considered small. Effects of heat addition or removal and mass addition or removal are considered over the entire cont rol volume instantaneously, and there are no boundary layer effects. The fluid can therefor e be assumed inviscid. Since interactions with the surroundings are assumed to act instantaneously, the fluid properties are assumed to be constant with respect to spatial dimensions in the control volume. Conservation of Mass The general form of the conservation of mass equation for a fixed control volume can be expressed in integral form as(38) S d V V d tS v 3-3 For the system described in Figure 310, with uniform, one-dimensional flow across one inlet and two outlet locations, the conservation of mass reduces to vp vp vp lfw lfw lfw gsp gsp gsp vA u A u A u V d t 3-4 While the total control volume is fixed, there are actually two volumes of interest inside the tank that are variable, the tota l liquid volume and the total gas volume. Breaking these up into separate volumes, and assuming the density is constant in that particular volume, the conservation of mass equation becomes

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59 vp vp vp lfw lfw lfw gsp gsp gsp g g l lA u A u A u V t V t 3-5 For this model, it is assumed that the thermodynamic state and the total mass flow rate of the gas entering the gas supply port is known. The density of the vapor venting out of the tank is assumed to be equal to the dens ity of the vapor in the ullage, and the density of the liquid leaving the tank out the liquid withdraw port is assumed to be equal to the density of the bulk liquid in the control volum e. Using the assumption that the system can be treated as a bulk fluid, the mass addi tion is immediately dist ributed over the entire control volume and the effects of the fluid veloci ty at the inlets are outlets are neglected. Breaking up the system into two control vol umes at the liquid to vapor interface the following expressions for the cons ervation of mass are obtained t m m m V Vfg vp gsp g g g g ) (1 1 2 2 3-6 t m m V Vfg lfw l l l l ) (1 1 2 2 3-7 Conservation of Energy The general form of the conservation of energy equation for a fixed control volume, assuming inviscid flow and neglecting gravitational poten tial energy and assuming there are no internal reactions that are exothermic or endothermic, can be expressed in integral form as(38) Sv vdV V F S d V P dV q ) ( 3-8 S d V V u dV V u tv S ) 2 ( )] 2 ( [2 2

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60 where the first term is the rate of heat adde d to the fluid inside the control volume from the surroundings,(38) the second term is the rate of work done on the fluid by surface (pressure) forces, the third term is the rate of wo rk done on the control volume by body forces, the fourth term is the time rate of change of energy inside the control volume due to transient effects, and the fifth term is th e net rate of flow of energy across the control surface. Breaking down the first term, q is defined as the rate of heat added per unit mass. Physically accurate modeling of this heat transfer would acco unt for the heat flux across a narrow thermal boundary layer near the surface of the tank, however this control volume model assumes bulk fluid properties and no bounda ry layer effects. Furthermore, the nature of the integrated refrigeration and storage system includes two heat transfer mechanisms, the heat leak into the tank from the ambient surroundings as well as the heat removed from the system from the refrigerator Integrating the firs t term over the entire volume therefore gives the following simplified expression for heat transfer to the system as REF HL vQ Q dV q 3-9 Body forces, namely the gravitational effect s required for natura l convection, are an important physical effect that must be taken into account to accurate ly predict the heat transfer rates across the system boundaries. However, for this simple control volume mass and energy balance where bul k fluid properties a nd inviscid flow are assumed, the work done by body forces can be neglected, and the third term in Equation 3-8 can be dropped.

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61 Assuming the fluid velocities are negligible, the effect of kinetic energy of the fluid can be neglected. Again assuming bulk fluid properties, the density and internal energy of the fluid are constant in the control volume and can be taken out of the volume integral in the fourth term. After integrating over th e control volume, the transient term the right hand side becomes vmu t dV V u t)] 2 ( [2 3-10 The two surface integrals can be evaluated to gether. This integral is evaluated only over the inlet and outlet locations since S d V equals zero at all other locations. Assuming bulk fluid proper ties, the evaluation of these integrals yields SSS d V u S d V P 3-11 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1) ( ) ( ) (A V u P A V u P A V u P Rearranging Equations 3-9, 3-10, and 3-11, substituting in the definitions for mass flow rate and enthalpy, break ing up this expression for separate control volumes in the liquid and vapor space, and in tegrating over time reduces the general conservation of energy equation to(39,40)) t h m t h m t h m h v h vg fg vp vp gsp gsp g g g g g g 1 1 1 2 2 2 3-12 t h m t h m Q Q h v h vg fg lfw lfw REF HL l l l l l l 1 1 1 2 2 2 3-13 where the mass flow rate between the liqui d and vapor phases is found by assuming all heat leak into the tank enters the liquid control volume a nd creates an equivalent amount of boil off to the vapor control volume. Th e heat leak term is the summation of the individual heat transfer components of conduction dow n the solid supports and

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62 convection and radiation thru th e MLI. The selection of the vapor enthalpy as the amount of energy leaving the liquid cont rol volume is somewhat arbitrary, and reflects the true control volume boundary as being drawn macr oscopically in the vapor space above the liquid level. Equation of State At these low temperatures, the ideal gas m odel cannot be assumed. To relate the thermodynamic properties of pressure, temper ature, and specific volume, the National Institute of Standards and Technology (N IST) Thermophysical Properties Database RefProp was used. This database incor porates the Modified Benedict-Webb-Rubin (MBWR) equation of state for hydrogen, usi ng eight empirical constants derived from testing at the NIST laboratory.(41) Once the state of the fluid is determined, Maxwell’s relations can be used to find th e other thermodynamic variables. Operational Simplifications Although the above equations can be used fo r analysis of operations with multiple simultaneous mass influx and outflows, such sc enarios are rare. In the vast majority of operations, there will be mass in flux or outflow thr ough only one of the ports at a time, if any at all. The operations can be classified depending on whether the system is open or closed to mass transfer from the surroundings, and the directio n of heat transfer in the system. Table 3-1 shows the different opera ting characteristics of the system. If the refrigerator is operating and greater the capacity is greater than the heat leak, the heat transfer is out of the system, and if the refrig eration capacity is less than the heat leak the net heat transfer is into the system. This leads to the following simplifications of the conservation equations, depending on the operational scenario.

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63 Table 3-1 Operational scenarios HEAT IN ADIABATICHEAT OUT MASS IN Gas Pressurization Liquefaction CLOSED Self Pressurization ZBO Densification MASS OUT Boil Off or Transfer Liquid Transfer Liquid Transfer Closed Storage With Heat Transfer To the System (Self Pressurization) Current storage systems often have periods of time where they are vented and then closed from the surroundings. During these periods, the valves remain closed and the heat leak into the tank creates an evaporation of liquid that causes a pressurization of the system. The pressure will rise until the ma ximum operating pressure is reached and the relief valve opens. During this time, the mass inside the entire tank is constant, but the relative amounts of liquid mass and vapor mass will change. The conservation of mass equations for the vapor and liqui d space can be expressed as t m V Vfg g g g g 1 1 2 2 3-14 t m V Vfg l l l l 1 1 2 2 3-15 During this period it is assumed the refrigerat or is off and the only heat transfer in the model is the heat leak. The conservation of energy equations for the vapor and liquid space can be written as t h m h V h Vg fg g g g g g g 1 1 1 2 2 2 3-16 t h m Q h V h Vg fg HL l l l l l l 1 1 1 2 2 2 3-17 The above equations have seven unknowns (fg l l l g g gm and h V h V_ , , ,2 2 2 2 2 2 ). The initial temperature and pr essure in the tank are known gi ving the rest of the initial

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64 thermodynamic state variables, and the heat leak is assumed known by either design data on the insulation system effectiveness or by experimentation. However the liquid and vapor volume are related by the following expression, g l systemV V V 3-18 and the mass flow between the liquid and vapor depends on the heat transfer by fg fg HLh m Q 3-19 Combing equations 3-14 thru 3-19 with the equation of state, the system of seven equations and seven unknowns can then be solved. A Microsoft Excel based program has been wr itten to model this behavior. First, the heat leak into the system is estimated for the given initial conditions. This heat leak model includes the effects of radiation and convection thru the multi layer insulation as well as the effect of conduc tion down the solid wall of th e neck and various interface tubing. The radiation and convection acro ss the tank surface area follows the modified Lockheed correlation for multi layer insulation.(42) This takes into account the number of layers of insulation, the density of the laye rs, and the boundary conditions of temperature. This also assumes a vacuum in the annulus of less than 10-3 Torr. The conduction heat leak down the length of the neck or tube can be found by the Fourier equation, except the thermal conductivity will not be constant ove r that wide range of temperatures. The thermal conductivity can be integrated over a range of temperatures if the governing equation is known, and the th ermal conductivity integral has been calculated for a range of materials and temperatures by McMordie.(43) These relations are then added into the model to create an estimate for heat leak into the tank as a function of geometry and thermal boundary conditions. For this m odel, it is assumed the upper boundary

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65 temperature is constant at 300K, while the lower boundary temperatur e is variable and equal to the fluid temperature at that instant. Once the heat leak is know n, the total interactions with the surroundings are known since this is a closed system. Next, the initial temperature, pressure, and mass are set, and the rest of the initial conditions are determined Then, the equation of state is used to find the liquid and vapor densities. Then the tota l volume of liquid and gas are found using the conservation of mass and the volume relation expressed in Equation 3-18. The liquid and vapor specific enthalpies ar e found using the RefProp progr am, and the total liquid and vapor enthalpy is then computed. At this point all stat e properties of th e liquid and vapor phases are known for the initia l condition. The total amount of energy transferred into the system is then calculated by multiplying the heat leak rate by the chosen timestep. Ideally, knowing the new enthalpy in the tank, RefProp should be able to calculate the new pressure since the specific enthalpy a nd the density of the system are known. Unfortunately, there are some thermodynamic st ates for certain fluids where convergence of the enthalpy/density specifications cannot be met by the RefProp program, and this proved to be the case in this situation. An alternate procedure was developed, where a new pressure is assumed, then new liquid and vapor enthalpies and total quality are calculated, and the total system enthalpy is compared to the previous timestep plus the known heat leak. The Excel add in Solver was used to eliminate the differences in these system enthalpies by varying the pressure, and a new system pressure was determined. This model was used to predict system pressure and temperature increases over a period of time for a liquid hydrogen system with a known h eat leak. Figure 3-11 shows

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66 the temperature and pressure for a 150-liter hydrogen dewar initially filled with liquid hydrogen at the 50% mark. Notice th e system temperature rate 50 100 150 200 250 300 350 400 450 0240480720960 Time (min)Pressure 20 21 22 23 24 25 26 27 28 29 30Temperature P (kPa) T (K) V=50% (5412 g) Q=f(T) Figure 3-11 Self pressurization te mperature and pressure vs. time of increase begins to fall while the pressurizat ion rate of increase gets larger as time progresses. As the time continues, the syst em temperature increases so the heat of vaporization decreases, and more of the heat leak is contribu ting to latent heating of the hydrogen as opposed to sensible heating. Although liquid hydrogen is bei ng converted into a vapor, the overall liquid level continues to rise over time. Figure 3-12 s hows the system quality and the liquid and vapor volumes respectively. Notice the fraction of the vapor in the system increases in a similar manner to the pressure, again this is due to the decrea se in the heat of vaporization. But due to a decrease in dens ity in the warmer liquid, the overall liquid volume is increasing. The corresponding decrea se in vapor volume al so plays a role in the pressurization rate increas e, although the vapor density is also increasing. This increase in liquid volume is critical to the desi gn of dewars especially when they are near

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67 68000 70000 72000 74000 76000 78000 80000 82000 02004006008001000 Time (min)Volume (cm3) 0.00 0.02 0.04 0.06 0.08 0.10Quality Liquid Volume Vapor Volume Quality P1=101 kPa T1=20.2 K Figure 3-12 Self pressurization ta nk quality and phase volume vs. time their 100% full level, since further increas es in temperature will lead to thermal expansion of the incompressible liquid, a nd a rapid overpressurization may occur. A comparison of system pressurization ra tes is shown in Figure 3-13 for three different liquid levels. It seems intuitive that the system that is most full will pressurize more quickly since there is less vapor space to fill. However, this proves not to be the case. This is explained by the fact that th e greater the liquid quant ity in the tank, the more of the heat leak is absorbed by sens ible heat of the liquid and less goes to vaporization. For example, the liquid absorbed 97% of the heat leak into the system as sensible energy for the tank that was 75% full, but only 78% of the heat leak for the 25% full case. Figure 3-14 shows the behavior of the syst em as predicted by the model compared to the experimental data. The data is from a zero boil off test conducted overnight with the cryocooler turned off, after liquefaction operations introduced 1.25 kg of hydrogen into the tank. The initial pressure was measur ed at 33 kPa. As is evident in the graph,

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68 0 50 100 150 200 250 300 350 400 450 0200400600800100012001400 Time (min)Pressure (kPa) 25% full 50% full 75% full T1=20.3 K Q=f(T) Figure 3-13 Self pressurization rates for variable liquid level 0 50 100 150 200 250 300 0150300450 Time (min)Pressure (kPa) Model Experiment T1=17.6 K Liquid volume =16 L Figure 3-14 Self pressurization (model vs. data) the predicted system pressurization rate is within 15% of the actual test data. This discrepancy is explained by the assumptions th at the tank is modeled as an isothermal system, with the temperature at the top of the tank being equal to the temperature at the bottom (liquid temperature). The heat leak estim ate assumes the tank is nearly full, so it

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69 gives the heat leak rate for tanks in this condition. In this instance, 1.25 kg of hydrogen only had a liquid level of 16 liters, and ther e was a large temperature gradient down the length of the tank, reducing the heat leak co mpared to the model prediction. Corrections to this model will be made in later sec tions to account for variable liquid levels. Open Storage With Heat Transf er To The System (Boil off) There may be periods of time when the heat leak into the tank created a pressure rise that causes the tank relief valve to open, creating a boil off loss. During these times, it is assumed the system is closed to gaseous mass input or from liquid mass output. Typically during boil off situa tions, the tank pressure will remain constant, at the set pressure of the relief valve. Some system s with no backpressure vent directly to atmospheric pressure. This implies the liquid temperature inside the tank will also remain constant, at the saturation temperature co rresponding to the tank pressure, and so the liquid density is also constant Likewise, the vapor temperature and density can assume to be constant, although there will be some small increase in density as the liquid boil off creates a forced convection current that c ools the upper part of the vapor volume. The conservation of mass equations then reduce to t m m V Vfg vp g g g ) ( ) (1 2 3-20 t m V Vfg l l l ) (1 2 3-21 and the conservation of energy equations reduce to t h m t h m V V hg fg vp vp g g g g ) (1 2 3-22 t h m Q V V hg fg HL l l l l ) (1 2 3-23

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70 The above equations have four unknowns and can be solved easily. Note the equation of state is not necessary since the stat e of the fluid is assumed constant with the isobaric venting process. A Microsoft Excel spreadsheet has been de veloped to model this boil off process. Initial conditions and system cons traints are first determined. For this exampl e, the initial system mass must be input, and the relief va lve set pressure is determined. Using these parameters with the system volume, the in itial temperature, li quid and vapor mass, density and volumes, and heat of vaporization are calculated. The system heat leak is calculated for this tank temperature. Then, th e mass of the liquid boil off is calculated, and the new liquid mass and volumes are found. Next, the new vapor volume is calculated and using the consta nt vapor density, a new vapor mass is found. Knowing the initial and final vapor and liquid masses, the mass of the vent loss is calculated. This mass will always be slightly less than the ma ss of the liquid boil off, since some boil off vapor must fill in the additional volume lost by the liquid. Figure 3-15 shows the values of liquid and vapor mass in a 150 liter dewar filled halfway with liquid hydrogen at atmospheric pressure. Notice the liquid mass drops at an approximately linear rate, since the heat l eak is a function of the constant liquid temperature. The vapor mass increases sligh tly over the boil off process. Figure 3-16 compares the time it takes to completely evaporate a given volume of liquid depending on the boil off pressure. Hydrogen storage lo sses occur more quickly when the vapor pressure is elevated, mainly due to the decrea se in heat of vaporization, but also partly due to the greater mass fraction of hydrogen that is in the vapor phase initially.

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71 Figure 3-15 Liquid and va por mass during boil off 0 1000 2000 3000 4000 5000 01020304050607080 Time (hr)Liquid Mass (g) P=1 atm P = 3 atm P = 5 atm P = 0.05 atm Liquid Volume = 75 L Figure 3-16 Boil off time dependence on pressure The simplification made that the liquid and va por temperature and pr essure were uniform throughout the volume makes this boil off model less precise, in actuality there will be temperature gradients in the ullage space and down the tank walls that will decrease the total heat transfer to the liquid as the liqui d volume drops. There is no experimental data 0 1000 2000 3000 4000 5000 01020304050607080 Time (hr)Mass (g) Liquid Vapor P1=101 kPa T1=20.3 K

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72 in this work to compare this model to, since no boil off occurr ed during the liquid hydrogen experimentation portion discussed in Chapter 6. Closed Storage With Zero Net Heat Transfer (Zero Boil Off) The ZBO operation is a closed storage system with refrigeration provided to remove heat leak into the tank. The state of the fluid will depend on the capacity of the refrigeration system. There exists a point on the refrigerator capacity vs. temperature curve where the capacity is exactly equal to the heat leak into the tank. As such the system can be modeled as steady state and th e conservation equations can be reduced to 1 2g gV V 3-24 1 2l lV V 3-25 REF HLQ Q 3-26 As given by Cryomech, the AL330 performance cu rve is plotted with the heat leak vs. temperature curve below in Figure 3-17. Afte r curve fitting the performance curve, 0 25 50 75 100 1015202530 Temperature (K)Heat Transfer Rate (W) Predicted Heat Leak(59)Predicted Cryocooler Performance(63) ZBO Data Points Figure 3-17 Cryocooler performance and heat leak vs. temperature

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73 the equations can be set equa l to each other and solved for the intersection, which is 16.25 K. This system temperature can be c onsidered analogous to a cryocooler no-load temperature. The results of this closed sy stem energy balance derived in this section agrees very well with the experimentation va lue of no load system temperature, ranging from 16.42 K to 16.85 K, obtaine d during several densification tests. These data points are plotted on the cryocooler curve and are labeled below Open System With Heat Transfer Ou t Of The System (Liquefaction) During liquefaction operations it is prefer able there is no mass outflow from the tank, so there is always an increase in ove rall system mass. The refrigeration system must be operating (except when stored refr igeration energy in a subcooled liquid can temporarily liquefy a small quant ity of gas) to remove the enthalpy flowing into the gas supply port. The conservation equati ons can be simplified as follows; t m m V Vfg gsp g g g g ) (1 1 2 2 3-27 t m V Vfg l l l l 1 1 2 2 3-28 t h m t h m h V h Vg fg gsp gsp g g g g g g 1 1 1 2 2 2 3-29 t h m Q Q h V h Vg fg REF HL l l l l l l 1 1 1 2 2 2 3-30 At first it is tempting to consider the lique faction model to be equivalent to the boil off model as they both are open systems with net heat exchange, but instead of heat transfer into the tank and mass transfer out of the tank, the liquefaction system operates in the opposite direction. However this is not accurate, as there are additional simplifications in the boil off model imposed by the relief valve, namely that the pressure in the tank is constant. Depending on the gas supply port mass flow rate and the net amount of refrigeration, the tank pressure may increase, decrease, or remain constant. But

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74 during operations where the ullage pressure is increasing, gas is entering the tank at a faster rate than the cryocooler capability to remove its energy, and a non-saturated vapor condition occurs. This phenomenon is not described accurately by this model, which assumes thermodynamic equilibrium betw een the liquid and vapor phases. The model has been modified to accept these conditions and predict the system liquefaction rate to maintain thermal equilibr ium for a given set of initial conditions. The net heat transfer out of the system from the combination of heat leak and cryogenic refrigeration is then calculated for that given temperature condition. To maintain equilibrium this must match the increase in system enthalpy from the gas supply port. Knowing the conditions of the inlet stream and the final liquid state, the change in enthalpy required for liquefaction is calculate d. The appropriate mass and vapor volumes are then found. Figure 3-18 shows predicted liquefaction rates for a range of storage states. This chart shows the liquefaction rate increases as expected, when the storage pressure is higher. This is due to the saturation temperature corresponding to this pressure being higher, which has three effect s. First, the cryocooler operates more efficiently at higher temperatures and there is greater cooling power available. Second, the amount of enthalpy required to be removed from the incoming gas is less. Finally, the net heat transfer from the surroundings is slightly less since there is a smaller thermal gradient. Figure 3-18 also shows the e xperimental data for three periods where the mass flow rate was constant and sufficient to maintain a constant pressure in the tank. This comparison shows a general correlation in the shape of the profile, but the results vary by as much as +/28%. The discrepancies be tween the predicted vs. actual liquefaction

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75 rates can be partially explai ned by the experiment not taki ng into account the heat of conversion between ortho and para hydrogen. The model assumes equilibrium hydrogen but there is a finite time required to ch ange the normal hydrogen to equilibrium hydrogen. Other factors include the actual experiment was no t an isothermal system and there were temperature stratifications that the model did not include An additional cause of the discrepancy is the uncertainty in th e measurements, since the exact state of the incoming gas was not known and there was no experimental method to control the 0 1 2 3 4 5 6 7 8 9 10 6080100120140160 Pressure (kPa)Flowrate (slm) model experiment 1 experiment 2 experiment 3 Figure 3-18 Comparison of predicte d vs. actual liquefaction rate pressure and mass flow rate. In these cases it can be seen that while the pressure and mass flow rate was relatively constant, there were variations in the measurements that implied the system was not truly in thermodynamic equilibrium. These uncertainties are plotted as x and y error bars in the individual liquefac tion experiment data points. In some cases, variations in the “c onstant” mass flow rate were as high as 8.7%, and pressure fluctuations were up to 2.2%. Clearly, more da ta needs to be collect ed, and with better control and fidelity.

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76 Closed Storage With Heat Transfer Out Of The System (Densification) A closed system with heat transfer out of the system by refrigeration is similar to the closed self-pressurization case with th e exception the pressure and temperature will decrease until the system reaches steady stat e and the refrigeration capacity balances out the heat leak into the tank. In the meantime, the mass of the liquid and vapor will change as some vapor is condensed out of the ullage space. The conserva tion equations can be written as t m V Vfg g g g g 1 1 2 2 3-31 t m V Vfg l l l l 1 1 2 2 3-32 t h m h V h Vg fg g g g g g g 1 1 1 2 2 2 3-33 t h m Q Q h V h Vg fg REF HL l l l l l l 1 1 1 2 2 2 3-34 Again this is a system of seven unkno wns and seven equations (including the volume relation, the mass transfer between th e vapor and liquid relation, and the equation of state), and can be solved in a similar ma nner. The same Excel program was used to estimate densification rates as the self pre ssurization rates, with the exception that the heat transfer rate previously given by the heat leak estimation is now the difference between the heat leak and the refrigeration capacity of the cryocooler at the system temperature. Results of this model are shown below. Figure 3-19 shows the temperatur e and pressure of the system with a tank initially 50% full of LH2 at the normal boiling point. The pressure and temperature decrease more rapidly at first since the cryocooler is producing more re frigeration at higher temperatures. Eventually the pressure and temperature reach the steady state condition

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77 0 20 40 60 80 100 120 02468 Time (hr)Pressure (kPa)15 17 19 21 23 25Temperature (K) Pressure Temperature Liquid Volume = 75 L Figure 3-19 Predicted densifica tion temperature and pressure defined by the zero boil off model. Figure 320 demonstrated the predicted densification times for three different initial liquid levels ranging from 25% to 75% full. As expected the smaller the mass in the tank, the less time it takes for densification. Some launch Figure 3-20 Densification rates for variable liquid levels 15 16 17 18 19 20 21 024681012 Time (hr)Temperature (K) 25% 50% 75% P1=101 kPa T1=20.3K Volume

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78 scenarios may depend on on-board densification, and predictive models will need to be developed to estimate countdown hold times for densification Figure 3-21 compares temperature data obt ained during experimentation with the simplified model. Note the predicted densification time profiles vary widely; this is explained by two factors. First, non-equi librium processes are occurring in the tank where the ullage space is developing signi ficant temperature stratifications. Some cryocooler capacity must be used to chill this vapor back to the saturated state. Refer to Figure 6-14 on page 149 for details on the thermal profiles in the tank during this densification process. Second, similar to the pressurization m odel, heat transfer processes are modeled using a uniform temperature in the tank and the heat leak and cryocooler performance will vary in those conditions. 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 00.511.522.5 Time (hr)Temperature (K) Model Data P1=180 kPa ML=0.98 kg Figure 3-21 Predicted vs. actual densification rates Based on the above discussions, it appear s the model has two major components of error. First, the isothermal model is not en tirely accurate as therma l stratification in the tank will cause variations in heat leak. Second, there are nonequilibrium processes

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79 happening during many operational scenarios, esp ecially when the liquid and vapor states are not fully saturated. An attempt to create a correction factor fo r these two situations will be made in the following section. Corrected model Variations in the predicted heat leak w ill occur since the model used assumes an isothermal tank and the physical system has te mperature stratificati ons inside the vapor region. These stratifications will cause warmer temperatures at the top of the tank, minimizing the temperature gradient and reducing heat leak from the outside. A correction to the isothermal model develope d above will be proposed to account for this variation. The correction factor will consist of two components. Fi rst, an adjustment must be made to account for variations in the tank liquid level. The modified Lockheed Martin correlation for MLI performance depe nds on the tank being at 100% full and at a constant temperature. Actual tanks will have a temperature gradient up the vertical walls of the tank between the liquid level and the top of the tank. This means the delta T between the hot and cold temperatures will be less than 100% for a portion of the tank, especially any warm supports and tubes that connect to the top of the tank. Boil off testing at KSC has shown heat leak is a pproximately a linear re lationship with liquid level, so the first component of the heat leak correction will be of this form. The second component of the correction f actor must take into account transient effects associated with the generation or destru ction of thermal strati fication layers inside the system. This correction will be applied during operational models when the state of the liquid and vapor in the tank is changi ng. For the cases above, this includes pressurization and densification operations. During boil off venting, steady state zero boil off, and steady liquefaction the thermodynamic variables exhibit no time

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80 dependence, since there is no net heat transfer to or from th e fluid at these times. During the steady boil off or liquefaction the enthalpy flow into or out of the tank cancels the heat leak or refrigeration, and during zero boil off the refrige rator is balanced by the heat leak. During the pressurization case, a net heat leak into the system creates a temperature change is the fluid, while dur ing densification the net refrig eration power has the opposite effect. Looking at an energy balance in the system during this transient operation shows a general relationship for the heat leak into the tank and a te mperature change according to the relation T k t h 3-35 Integrating this equation with respect to tim e gives a function for heat leak that is dependent on the time and the initial volume. To determine exact true function of this relationship, this differentia l equation can be solved. The boundary conditions for this case would be a variable temperature at z=0 (liquid level), variable temperature along the walls of the tank and a variable temperature at the top of the tank. This would also need to be modeled with a variable thermal c onductivity and specific heat, and enthalpy would need to be expressed in terms of the temperatur e and pressure in the ta nk. This exercise is beyond the scope of this simplified model correc tion. To determine a general form of this correction term, it is useful to examine the prof iles of ullage temperatures in Figure 6-22. Data taken during self pressuri zation tests that show thermal stratifications in the liquid level give an indication a logarithmic relati onship of heat leak with respect to time. Adding a time dependent logarithmic correction in combination with the linear dependence on liquid level gives a corre cted heat leak of the form

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81 ) ( * ) ) ( (t D Ln C B A Q Q A QCON LM corrected 3-36 where A is the heat leak in the tank as the liquid level approaches zero, QLM is the predicted heat leak from the MLI correlation, QCON is estimated conduction heat leak, B is the liquid level (%), and C and D are c onstants used to fit the model data to the experimental curve. The corrected model (model B) shown below uses the following values; A=5, B=10% (based on conditions used in experi ment), C=0.019, and D= 10,500. Figures 322 and 3-23 below show the results of this co rrected model for the de nsification and selfpressurization processes as compared to the experimental data. An additional day of data was added to each figure, and this data is compared to the model as well. The added pressurization data has the same initial conditions as the first, and the curves plot on top of each other very neatly. The added densif ication data was from testing several days after the previous data curve, and the initia l mass and temperature change. In this case, the corrected model was run again and the curve is plotted against the data. In both the pressurization operation and the densification operation, the co rrected model is a better prediction tool than the original isothermal m odel. However, in order to get a true model of the system behavior the full conservation equations must be discretized and solved numerically. Storage Fluid Analysis In order to more accurately model the be havior of the hydrogen in the system, the full conservation of mass, momentum and ener gy equations must be considered. The system described by Figure 3-24 is an unstea dy, open system that will be approximated in

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82 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 00.511.522.5 Time (hr)Temperature (K) model A (6-25) data (6-25) model B(6-25)) data (7-16) model B(7-16) P1=78 kPa Mass=1.22kgP1=180 kPa Mass=0.98 kg Figure 3-22 Corrected mode l vs. densification data 0 50 100 150 200 250 300 0150300450 Time (min)Pressure (kPa) model A (7-15) data (7-15) model B(7-15) data (7-16) T1=17.6 K Mass=1.22 kg Figure 3-23 Corrected mode l vs. pressurization data three-dimensional space using cylindrical coor dinates. Due to symmetry about the axis, dependence in the direction can be neglected. Gravit ational effects must be taken into account. The overall system boundary is set as th e inside wall of the inner tank, defined as r=R. The upper height of the tank is at the coordinate z=Z. Th ere are three modes of

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83 heat exchange between the system and the surroundings, radiation on the outer surfaces through the MLI, conduction dow n the length of any pipe or tube support between the inner and outer vessel, and refrigeration by th e cold heat exchanger of the cryocooler. There is mass transfer in and out of the tank from the gas supply line and the vent line. The velocity profiles at the tank inlet and outlet will depend on the geometry, and for now a fully developed laminar flow profile driven by the pressure gradient can be assumed at the interface. There is a longitudinal and radial velocity component in both the liquid and vapor space. The liquid velocity is driven by the free convection currents at the heat exchange surfaces, with a circulat ion pattern of warm updrafts along the walls and a cold downdraft in the center at the cold HX. This differs from conventional cryogenic dewars that only have the warm upwa rd velocity with a la yer of warm fluid at the top of the liquid. Therefore the liquid velocity will have a superimposed freestream velocity from the circulation currents as well as the free convection velocity. One important result of a full numeric analysis is to determine whether this freestream velocity will drive the heat tr ansfer coefficient higher than otherwise, and hence increase the amount of heat transfer from the surrounding s. If so, anti convection baffles may be added. The vapor velocity will be driven by warm convection currents as well as the velocity in and out of the supply and vent line. The thermodynamic state of the liquid and gas is variable, dependent on both time and location inside the tank. The total mass of the liquid and vapor will depend on the initia l conditions as well as mass flow into and out of the tank and evaporation or condensat ion at the liquid to vapor interface. The liquid to vapor interface is assumed to be a free liquid surface, with homogenous phases above and below, and the location of the inte rface in the z directi on and the profile will

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84 LH2 GH2 HX MLI QTemp=f(r,z,t) Press=f(r,z,t) Press=f(r,z,t) Temp=f(r,z,t) Mass=f(t) Mass=f(t) VELOCITY BOUNDARY LAYER TEMPERATURE FREE CONVECTION CURRENTS QREF RAD QCON M U P T M r z FREE CONVECTION CURRENTS M P Tvp vp vp gsp gsp gsp fg gspUvp lfwU M P Tlfw lfw lfw Liquid Fill and Withdrawl Gas Supply Port Vent Port Volume=f(t) h Figure 3-24 Proposed sy stem representation vary. This location will be denoted as z=h. More details on this interface will be given when the boundary conditions are discussed. To understand the fluid behavior in order to model it, a consideration of the flow regime must be taken into account. While th e exact flow velocity is unknown, order of magnitude estimates can be made to find a re presentative Reynolds number. A potential

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85 and kinetic energy balance of the flui d gives a velocity of the magnitude(44) 2 1} { gL V 3-37 The velocity depends on the char acteristic length of the system and the relative change in density, which depends on the temperature grad ient. An energy balance between the heat leak thru the insulation compared to the h eat transfer to the liq uid allows for a rough calculation of the temperature difference betw een the wall and the bulk fluid. Using the heat transfer coefficient found in Chapter 6, fo r steady state conditions this delta T will be between .01 and .04 K. This estimate co mpares well to the experimental data found during boil off tests conducted w ith liquid nitrogen at KSC.(45) During some transient operations this temperature gradient will be gr eater. Varying the length scale of the heat transfer and the delta T, the liquid vertical velocity ranges between 2.5 and 35 cm/sec. The vapor velocities are slightly higher. The dependency of th e characteristic velocity as a function of temperature difference is show n in Figure 3-25. The liquid velocities are plotted for cooling of the hydrogen by the cold heat exchanger, while the vapor velocities are for the warming of the vapor by the tank wa lls. The length scale is 35 cm, which is approximately with the tank half full. At firs t, this free convective velocity seems very high, but an examination of the fluid propert ies shows this is feasible. The volumetric coefficient of thermal expansion, ,for liquid hydrogen at 20 K is 0.0164 K-1. This is two orders of magnitude higher than of water, which is 2.15 x 10-4 K-1 Similarly, the bulk coefficient of gaseous hydrogen is 17 tim es greater than that of steam. Small temperature differences in hydrogen systems cause large displacements and hence, high velocities.

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86 0 10 20 30 40 50 60 70 80 90 00.511.522.53 Delta T (K)Velocity (cm/s) Liquid Vapor P1=101 kPa T1=20.3 K L=35 cm Figure 3-25 Predicted Free Convection Velocity Using the density and viscosity of both triple point and NBP liquid hydrogen, a range of estimates for Re can be computed. The characteristic length used is the height of the liquid and for the figure below is set at 50% full. Figure 3-26 plots this estimate of Reynolds number for a range of temperature grad ients. From this figure, it appears the Reynolds numbers may be quite high at time s, like when the temperature gradients are higher during transient operations. After the sy stem has had time to approach steady state conditions, the delta T will be less and the liquid and vapor Reynolds number will approach 8x104 and 4x104, respectively. In this case the flow inertia is more moderate, and viscous forces play a gr eater factor in the flow. However the Reynolds number is still high enough that the flow can be modeled with a viscous boundary layer and an inviscid core. This premise will be revisited in a few sections when an order of magnitude analysis on the conservation of momentum equation is addressed.

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87 0.0E+00 3.0E+05 6.0E+05 00.511.522.53 Delta T (K)Re Liquid Vapor P1=101 kPa T1=20.3 K L=35 cm Figure 3-26 Predicted Free Convection Reynolds Number Perhaps a better representation of the flow regime is gi ven by the Grashof number. This non-dimensional number is defined as 2 2 3Re ) (x xx T T g Gr 3-38 And is a measure of the free convective buoyancy effects vs. the viscous effects. Again, this value will depend on the exact conditions but a representative value at 20K for the liquid and vapor space for a range of temperat ure gradients has been plotted in Figure 329. Again, during transient operations with high er gradients, the flow is more turbulent, but normal operations with smaller delta T the flow regime is laminar, especially in the vapor region. The high value of the bulk co efficient accounts for the high Gr. Typically the transition to turbulen t flow occurs around Gr=109.

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88 0.0E+00 1.5E+11 3.0E+11 00.511.522.53 Delta T (K)Gr Liquid Vapor P1=101 kPa T1=20.3 K L=35 cm Figure 3-27 Predicte d Grashof Number The above analysis is a rough scaling analysis of the type of flow regime expected to occur, and is useful for later analytical so lutions based on heat tr ansfer correlations. However, to truly model the system behavi or, an exact numerical solution to the full Navier Stokes equations is requ ired. Fortunately the availability of modern fast computer processing makes this endeavor more feasible than in the past. The following section derives the equations that must be solved. The following conservation equations will be considered in differential form. There are numerous texts that derive the full conservation equations starting from an infinitesimal, fixed control volume,(46-49) and this effort will not be repeated here. The full two dimensional conservation equations fo r unsteady flow of a Newtonian fluid in cylindrical are stated below, followed by a ddition of some simplifying assumptions. The variations in the direction are neglected due to symmetry about the axis.

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89 Conservation of Mass The Conservation of Mass can be expr essed in differential form as 0 ) ( ) ( 1 z rv z v r r r t 3-39 where the first term is the rate of change of mass inside the element and the next two terms are the net mass flow into or out of the element from the r and z directions respectively. This equation is applicable for all fluids and assumes the density is variable. Typically for cryogeni c applications, a large range of temperatures does not allow for system analysis using constant propert ies. In this case, liquid densities can vary 18.8% between the triple point and 25 K, and vapor densities vary 460% between the NBP and the ambient temperature. Therefor e this system will not be modeled with a constant density as the density will vary with respect to time, dependent on the temperature and pressure variations. Temperat ure gradients will be present in the radial direction driven by heat flux from the wall a nd convection currents a nd the axial direction due to buoyancy effects. The local velocity field will be driven primarily by natural convection, although during periods of filling or draining the tank the local velocity will be driven by pressure gradients. It is an ticipated the velocity will be dependent on both spatial coordinates inside the system. R earranging the equation to do an order of magnitude analysis gives z v z v r v r v r v tz z r r r 3-40 In order for this equation to be valid, the right hand side must be the same order of magnitude as the left hand side, so the LHS order of magnitude is relevant. For this enclosed system, the order of magnitude of the radial veloci ty must be the same as the

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90 axial velocity (order of V), and knowing the ge ometry of the tank determines the order of magnitude of the radial and axial directions are the same (order of L). Breaking down the equation and dividing by V/L, the order of magnitude of the terms on the RHS become ) ( ) ( ) ( ) ( ) ( O O O O O 3-41 For the vapor region, a re view of thermodynamic vari ables as a function of temperature shows the order of magnitude of the density change is the same as for the total density. For the liquid region, the de nsity changes are an order of magnitude less than the total density, and for a simple model with less accuracy required, the r and z terms could be neglected. However, if an accuracy greater than 90% is desired, these terms must be included. Assuming boundary layer scaling (Vr<
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91 ))} ( 3 1 ( 2 { )} ( { 1 ) ( z v r v r v z v z z v r v r r r z P g z v v r v v t vz r r z r z z z z z r z 3-44 where the first term on the left hand side is the time rate of change of momentum inside the fluid element and the next two terms are the momentum flow into the element from the r and z directions. The right hand side of the equation is the summation of forces on the element, with the first term being the gravitational force (other body forces such as electromagnetic are neglected ), the second term is the pressure acting on the normal surface, and the third and fourth term s are the viscous dissipation forces. At this point it is tempting to simplify this equation by assuming constant fluid properties, reducing the viscous term s to a much simpler expression of V2. In many cases this could be a poor assumption, si nce the liquid hydrogen viscosity is highly temperature dependent. Indeed, the viscosit y of liquid hydrogen w ill vary 67% between the normal boiling point and the triple point. Changes in the fluid properties will occur over time, as the temperature of the fluid in creases or decreases de pending on the level of heat flow into or out of the tank. The vapor density and viscosity exhibit similar dependency on temperature. This depende ncy is known from thermodynamic relations and experimental data, and the function ) ( T P f can be numerically differentiated in the solution procedure. The pr evious section discussing th e conservation of mass also determined the system couldn’t be assumed to have constant density. Another common assumption, the Boussinesq approximation, cannot be used since density changes are important in all terms and the viscosity variat ions are of the same order of magnitude as the density variations. The fact that the de nsity and viscosity are variable makes these

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92 Navier Stokes equations much more compli cated, and requires a solution to the energy equation that is coupled to the momentum equation. An order of magnitude analysis, similar to the one done for the conservation of mass, will help validate the assumption that th e viscosity cannot be considered constant. Again assuming O( r)~O(z)~L and O(vz)~O(vr)~V, the order of magnitudes of the viscous terms in the LHS can be expressed as 2 2 2 2} { 1 L V L V L L V L V L L V L L V L V L L L V L L V L V L L L From this it is apparent that all the visc ous terms in this equation are of the order 2L V or 2L V. Looking at the thermodynamic and tran sport properties of hydrogen vapor, the between the NBP at ambient is 7.68 sec Pa while the actual viscosity is 1.07 sec Pa Similarly, =12 sec Pa and =13.3 sec Pa for liquid hydrogen between the NBP and 14 K. This means O( )~O( ) and the assumption of constant viscosity cannot be used to simplify the momentum equation. Another simplification that is frequen tly taken into account are boundary layer approximations, where an order of magnitude analysis of different terms in the conservation equations reveals some terms th at are so small they can be considered negligible in that thin regi on. The thickness of a boundary layer in free convection flows can be scaled(50) on the order of 4 1 4 1 2) P r Pr 952 0 ( 93 3 xGr x 3-45 The predicted Grashof number for liquid hydr ogen was previously plotted in Figure 3-29 for a range of conditions. From this pl ot it is apparent the Grashof number is

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93 between the order of Gr =109 and 1011., depending on the temperature difference between the wall and the bulk fluid. The liquid Prandtl number at the NBP is 1.22 while the vapor Prandtl number is 0.77, implying the relativ e magnitude of the viscous and thermal boundary layers are of the same order. A quick estimate shows th at the scale of the boundary layer thickness is x 022 two orders of magnitude less than the length scale of the system. Knowing the boundary layer approximations are acceptable for the thin viscous region near the tank surfaces, the conservation of momentum equations for this region can be expressed as 0 r P 3-46 ) ( ) ( z v z z P g z v v r v v t vz z z z z r z 3-47 Now that viscous effects are accounted fo r in the thin boundary layer region, an order of magnitude analysis should be done to determine if viscosity is important in the rest of the flow. The balance of forces in the momentum equation shows the inertial forces scale on the order of L V FI 2~, the pressure forces scale to L P FP~ and the viscous forces scale to 2~L V FV. Knowing estimates for the characteristic length, velocity, kinematic viscosity and density, an order of magnitude analysis can be performed. This results in the approxim ation, in the freestream outside the boundary layer, that the O(Fv)<
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94 r P z v v r v v t vr z r r r ) ( 3-48 z P g z v v r v v t vz z z z r z ) ( 3-49 Conservation of Energy The first Law of thermodynamics applied to a differential fluid element can written as 2 2 2 2 2) ( 3 1 ) ( 2 1 ) ( ) ( ) {( 2 ) ( z v r v r v r v z v z v r v r v z T k z r T r k r T k r z P v r P v t P z h v r h v t hz r r z r z r r z r z r 3-50 where the first term on the left hand side repr esents the rate of change of energy in the element over time, and the next two terms are th e convective flow of energy into or out of the element. The first three terms on the ri ght hand side is the work done on the system by the pressure forces, and the next three term s is the rate of heat transferred into the system through the control surface via conductio n. The final terms on the right hand side are the rate of energy di ssipation via viscosity. Previous analysis has shown that the visc ous terms cannot be neglected, or even simplified by assuming constant viscosity, in the boundary layer region. However, an order of magnitude analysis can reduce the complexity of the equation in the boundary layer. Knowing vr<
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95 In many applications, if Fourier’s la w is assumed, and the thermal conductivity is assumed to be constant, the heat transfer term can be reduced to T k2 However, like the density and viscosity, the thermal conductiv ity is too dependent on temperature to be assumed constant. There is no way to simplify this term, but if the nature of the thermal conductivity dependence is known, it can be numerically differentiated. This equation adds another thermodynami c variable, namely the enthalpy, to the list of unknowns. However, enthalpy can be expressed as a function of the other thermodynamic variables in a number of ways. Most often, the ideal gas approximation is used, but obviously that cannot work in th is instance. However, for all substances, enthalpy can be expressed as dP T dT c dhp) 1 ( 3-52 Outside the boundary layer, inviscid flow can be assumed, based on the same assumptions discussed above for the moment um equations. However, the boundary layer approximations cannot be used. In this cas e, the conservation of energy reduces to z T k z r T r k r T k r z P v r P v t P z h v r h v t hz r z r ) ( 3-53 Summary The preceeding section presented the conservation equations for unsteady, viscous, compressible flow with variable transport properties for cylindrical coordinates in the r and z direction. The flow is considered ax isymmetric and there is no dependence in the angular direction. It has b een shown through order of magni tude analysis of individual terms and scaling of competing forces that this system can be modeled as a whole by considering four separate regions. First, th e liquid and vapor regions must be considered separately. Then, in each of these regions, there is a thin boundary layer where viscous

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96 dissipation must be considered but many te rms will be negligible due to the normal boundary layer approximations. Inside this bou ndary layer region, for both the liquid and vapor flow, the following equations must be solved; Conservation of Mass – Eqn 3-41 Conservation of Momentum in r direction – Enq. 3-46 Conservation of Momentum in z direction – Enq. 3-47 Conservation of Energy – Eqn. 3-51 Outside the thin boundary layer, the flow can be modeled as inviscid. No boundary layer approximations are used. The following equations apply in this region; Conservation of Mass – Eqn 3-40 Conservation of Momentum in r direction – Enq. 3-48 Conservation of Momentum in z direction – Enq. 3-49 Conservation of Energy – Eqn. 3-53 Solution Procedure In general the above four conservatio n equations contain 6 unknowns in each region (z rv v h T P , , ). This is assuming the transport properties (thermal conductivity, viscosity) are known from experimental data as a function of temperature and pressure. Two additional re lations are needed to solve this system of equations. First, the equation of state can be used to relate the thermodynamic variables P, T, and The ideal gas equation of st ate will not be accurate in this region. NIST has developed a hydrogen thermodyna mic property datatbase using the Modified BenedictWebb-Rubin (MBWR) equation of state for hydrogen, and this can be used for the current analysis. Indeed, in the first part of this chapter, this NIST database is used to

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97 help close the system of simplified equati ons. A second thermodyna mic relation relating the enthalpy of a fluid to the temperature and sp ecific heat can also be used, but care must be taken to incorporate variati ons in the specific heat as a f unction of temperature. This relation was presented by equation 3-52 when the conservation of energy was discussed. More specific, this system is described by a set of six partial differential equations. This system of equations must be solved si multaneously. Variations in fluid properties are significant and the continuity and mome ntum equations are c oupled to the energy equation. In addition, these coupled equations probably need to be solved separately but simultaneously over liquid and vapor regions in the system. The overall geometry of these spaces are time dependent as we ll since the liquid le vel and boundary layer thickness will change as mass is added to the system and the temperature of the system will change. The appropriate boundary conditions between these fluid regions must then be equalized. The transport properties will vary over time and with respect to location, and the assumption that these properties are variable will add to the complexity of the conservation equations discussed above. Ho wever, these properties are assumed only dependent on temperature and the nature of this dependence is known. Therefore, a function relating this dependence must be f ound and input into the solution procedure, and the derivatives can easily be calculated. Boundary Conditions First, since the storage system to be anal yzed is unsteady, there must be initial conditions prescribed for all th e variables at all locations inside the system. These initial conditions will depend on the flow situation to be analyzed. Most likely, there will be an initial liquid level required, and the liquid will be assumed to be at a saturated condition

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98 with no mass flow in or out of the tank. The initial pressure will be constant in the vapor space, and will have a hydrostatic distribut ion in the liquid space. The initial temperature, density and enthalpy will be constant in the vapor space and will vary slightly with pressure in the liquid. All velocities will be assumed zero for an initial condition. The initial conditions can be expressed mathematically as Vapor region P(r,z,0)=Psat T(r,z,0)=Tsat vz(r,z,0)=0 vr(r,z,0)=0 Liquid region P(r,z,0)=Psat+ g(h-z) T(r,z,0)=Tsat vz(r,z,0)=0 vr(r,z,0)=0 Boundary conditions must be prescribed for the four independent variables P, T, vr, and vz. The density and enthalpy initial and boundary conditions can be calculated knowing the pressure and temperature at that location. For both the liquid and vapor boundary conditions, fluid velocity components will be assumed zero at the tank wall. This no-slip boundary condition will apply around the entire geometry, with the exception of the gas supply and vent ports, where a complete profile for the velocity, temperature and pressure distribution will ha ve to be assumed. Against the wall the thermal boundary condition is given from a cal culated heat flux through the insulation. The pressure boundary condition ca n be specified by considering the fluid at the liquid to vapor interface. There will be a thin layer of liquid at the top of the tank that will be at the saturated condition, and he re there is only one independe nt thermodynamic variable. The boundary pressure in the liquid below the interface will be equal to this saturation pressure plus the hydrostatic head pressure The pressure around the boundary in the vapor space is assumed to be constant. The most complicated boundary condition in this system is at the liquid to vapor interface(37). At this infinitesimal interface, the total velocity, shear stress and

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99 temperature must be continuous across the su rface. The normal and tangential velocities must match, and can be expressed in terms of the interface motion. The temperatures also match. Pressure equilibrium is satisfied by factoring in the surface tension forces. Heat flux is equal across the interface, although the temperature gradient will differ due to different thermal conductivity. The boundary co nditions are expressed mathematically as Vapor boundary layer P( ,z,t)=P P(r,h,t)=Pliq T( ,z,t)= T r T (R,z,t)= Q”/k z T (r,Z,t)= Q”/k kgas z T (r,h,t)= kliq z T vz(R,z,t)=0 vz( ,z,t)= zv vz(r,0,t)=0 vz(r,h,t)=vzliquid vr(R,z,t)=0 vr( ,z,t)=v r vr(r,0,t)=0 vr(r,h,t)=0 Vapor free stream P( ,z,t)=BLP P(r,h,t)=Pliq T( ,z,t)= BLT r T (0,z,t)= 0 z T (r,Z,t)= Q”/k kgas z T (r,h,t)= kliq z T r vz (0,z,t)=0 vz(r,Z,t)=0 vr(0,z,t)=0 vr(r,Z,t)=0 The liquid boundary layer and freestream bound ary conditions are similar. Using the conservation equations shown above combined with the initial conditions and boundary conditions expressed in this sec tion, the solution to the fluid behavior in this system can be modeled numerically. This would be a difficult modeling exercise, well beyond the scope of this dissertation, which is intended to focus on thermodynamic issues of this system.

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100 Dimensionless analysis The overall usefulness of these governing equations can be made greater if the equations are presented in non-dimensional fo rm. This result can be obtained when the variables in the equations are changed by dividing them by a c onstant reference property. The choice of reference constant s is arbitrary, but should ha ve some physical significance to the system being analyzed. The followi ng non-dimensional vari ables are proposed for this system. L r r L z z 0 *V V Vr r 0 *V V Vz z 0 0 *P P P 0 *h h h 0 *T T T 0 *t t t 0 0 *k k k The dimensional length constant L is taken to be the length of the diagonal of the R-Z right triangle. This gives a measure of the size of the system without having to use the both the tank radius and tank height as di mensional constants, and takes into account a variety of aspect ratios. The choice for dimensional constants for all the thermodynamic variables is just the in itial value of the vari able, most probably the saturated conditions at the normal boiling point. Similarly, the ther mal conductivity and visc osity constants are also the initial values. The choice of dimensional time constant is unique to this analysis and is taken to be the amount of heat re quired to vaporize the total amount of liquid inside the system divided by the rate of heat transfer to the system. This is simply the time required to vaporize the contents of the vessel. The dimensional velocity constant V0 then is defined as the system lengt h divided by this time constant.

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101 Plugging the new variables into the cons ervation of mass in the boundary layer yields * 0 0 * 0 0 * 0 0 * 0 0 * 0 0z v L V z v L V r v L V r v L V t tz z r r 3-54 Substituting the relation 0 0V L t leaves the equation of mass conservation unchanged when converting to dimensionless variables. Th is is expected and is a general result for all conservation of mass equations. The fina l dimensionless equations for the boundary layer region and the inviscid region are expressed below. * * * * * * *z v z v r v r v tz z r r 3-55 * * * * * * * * *z v z v r v r v r v tz z r r r 3-56 Using the same dimensional constants as above, and rearranging terms, the conservation of momentum can be derived in dimensionless terms. The equation for the boundary layer region expressed by equations 3-46 and 3-47 can be rewritten as 0* r P 3-57 * * 2 0 0 0 * 2 0 2 0 0 2 0 * * * * *) ( ) ( ) ( ) ( z v z L t z P L t P L g t z v v r v v t vz z z z z r z 3-58 For the inviscid core region, the non-dimens ional momentum equations can be simplified to * 2 0 2 0 0) ( ) (r P L t P z v v r v v t vr z r r r 3-59 * 2 0 2 0 0 2 0 * * * * *) ( ) ( ) ( z P L t P L g t z v v r v v t vz z z z r z 3-60

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102 There are three dimensionle ss parameters contained in the above equations, shown in parenthesis on the right ha nd side of equation 3-58. Th ese dimensionless parameters show the relative strength of the buoyancy, pres sure, and viscous forces with respect to the inertial forces, but in a different manner than the classi c dimensionless equations. The choice of dimensionless constants emphasi zes the relation of the latent heat of vaporization in the system to the rate of heat leak as a dimensional time constant. For small time constants, the heat leak is very high with respect to the latent heat, and the liquid boils off more rapidly. This implies the heat transf er to the liquid is greater, leading to higher convection velocities. This makes th e dimensionless parameters smaller, and the viscous, buoyancy, and pressu re forces are respect ively lesser than the inertial forces. Large time constants imply a well-insulated system with small heat leak and smaller convection velocities. The dimens ionless parameters are larger, implying the inertial forces become less si gnificant. It is worth no ting the buoyancy and pressure forces scale with respect to 2 0t, demonstrating a greater sensitivity to the time constant than the viscous terms. Performing the same dimensional analysis on the conservation of energy for the viscous region and the inviscid region respectively yields 2 * 0 0 0 0 * * * * 2 0 0 0 0 0 * * 0 0 0 * * * * *) ( ) ( } ){ ( } ){ ( ) ( r v t h r T r k r T k r L h t T k z P v t P h P z h v r h v t hz z z r 3-61 } ){ ( } * ){ ( ) (* * * * * * 2 0 0 0 0 0 * * * 0 0 0 * * * * *z T k z r T r k r T k r L h t T k z P v r P v t P h P z h v r h v t hz r z r 3-62

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103 Again, three dimensionless parameters s how up. They can be interpreted as showing the relative importance of the flow work, the heat transfer, and the viscous dissipation. The term 0 0 h is a measure of the initial energy in the system, and shows up in the denominator of all three dimensionless parameters. It is interesting to note the flow work parameter appears independent of th e time constant, while the heat transfer parameter has a direct relation with the time constant and the viscous term is inversely proportional to the time constant. For smalle r time constants, the viscous terms are relatively more important than the heat transf er terms. However, if the time constant increases, the convection velo cities decrease and the ther mal conductivity terms increase in relative value. To fully pose the problem in dimensi onless terms, the bound ary conditions and initial conditions must also be non-dimensi onalized. Looking at the vapor region, the initial conditions are expressed as P*(r*,z*,0)=1 T*(r*,z*,0)=1 zv (r*,z*,0)=0 rv (r*,z*,0)=0 The boundary conditions in the vapor boundary layer become * * *) , ( P t z P * * *) , (liqP t h r P * * *) , ( T t z T "* 0 0 0 2 0 0 * * *) , ( k Q t T k L h t z R r T "* 0 0 0 2 0 0 * * *) , ( k Q t T k L h t Z r r T * 0 0 * * *) , ( z T k k k t h r z T kliq gas liq gas 0 ) , (* * t z R vz * * *) , ( z zv t z v 0 ) 0 (* * t r vz * * *) , (liq z zv t h r v 0 ) , (* * t z R vr * * *) , ( r rv t z v

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104 0 ) 0 (* * t r vr 0 ) , (* * t h r vr Boundary conditions in the freestream are * * *) , (BLP t z P * * *) , (liqP t h r P * * *) , (BLT t z T 0 ) , 0 (* * * t z r T "* 0 0 0 2 0 0 * * *) , ( k Q t T k L h t Z r z T * 0 0 * * *) , ( z T k k k t h r z T kliq gas liq gas 0 ) , 0 (* * t z r vz 0 ) , (* * t Z r vz 0 ) , 0 (* * t Z vr 0 ) , (* * t Z r vr Two other dimensionless parameters app ear in the boundary c onditions. The first is simply the ratio of the dimensionle ss thermal conductivity be tween the liquid and vapor space. Choosing the same dimensionl ess constant could ha ve eliminated the parameter. The second relates the heat flux to the temperature gradient at the Neumann boundary condition. In this case, the dime nsionless parameter can be simplified by remembering the dimensional time constant is the initial energy in the system divided by the heat flux.

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105 CHAPTER 4 HYDROGEN SAFETY To validate the analysis conducted in Ch apter 3, a liquid hydrogen test program was initiated. Any serious discussions regard ing use of hydrogen, eith er as a liquid or a gas, must include factors pertaining to its safe use. For this dissertation, such considerations are taken with in two separate contexts; fi rst, safety of liquid hydrogen specifically as it relates to th e experimental system designed for data gathering for this work, and second, general hydrogen safety pr inciples that must be followed for the evolution to a hydrogen energy based economy to take place. This chapter will focus primarily on safety principles necessary for the specific experimental set-up, with general safety concerns included as applicable. NASA KSC has historically been one of the world’s largest consumers of liquid hydrogen, and aerospace use of hydrogen has helped lead to the development of many of today’s systems in use in industrial applications. NASA’s hydrogen safety specification(51) is the primary reference for this chapter, although the National Fire Protection Association(52) (NFPA) and Department of Transportation(53,54) (DoT) codes were considered as well. There is also an aerospace industry standard that is in development (AIAA), but this work draws heavily on the NASA standard and was not refe renced in this chapter. Hydrogen Properties Hydrogen is a nontoxic, non-corrosi ve gas that is colorless, odorless, and tasteless, and is therefore difficult to dete ct with human senses. It forms a diatomic molecule with a molecular weight of 2.06. In nature, hydrogen has two isotopes; hydrogen with an

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106 atomic mass of 1, and deuterium, with an atomic mass of 2. The ratio of ordinary hydrogen to deuterium is 3200/1. Due to th e small molecular size, gaseous hydrogen is difficult to contain in a leak free manner, and liquid storage is even more difficult due to the low temperatures required. The NBP of hydr ogen is 20.3 K, with a triple point of 13.9 K and a critical temperature of 33. 2 K. A T-s diagram for liquid hydrogen(9) is shown in Figure 4-1. The NBP of hydrogen is the s econd lowest of any element, only liquid helium is lower. Hence, NBP hydrogen will freeze out any contaminants except helium, so care must be taken in LH2 systems to el iminate any contaminants, especially air. Hydrogen is unique in that it exists in two separate molecular forms, depending on the direction of spin of the individual atoms. In ortho-hydrogen, the atoms spin in the same direction, whereas para-hydrogen at oms spin in opposite directions. Normal hydrogen, or hydrogen gas at room temperature is a mixture of 75% ortho and 25% para. However, this mixture varies with temperatur e, so one refers to equilibrium hydrogen as the equilibrium mixture percen tage at a given temperature. At the NBP, equilibrium hydrogen is 99.8% para-hydrogen. This conversion from ort ho to para is significant since there is a heat of convers ion associate with the change. This heat of conversion is due to the momentum change required as one atomic nucleus reverses spin direction, and this is an exothermic process. The heat released is significant, greater than the heat of vaporization at the NBP. Energy effici ent handling of liquid hydrogen requires accounting for this heat of c onversion, and catalysts are usually used to speed up the conversion process so the heat can be rem oved at a higher temp erature. During hydrogen system design processes, care must be taken to account for other changes in thermal and transport properties, depending on the equilibrium mixture.

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107 Figure 4-1 Hydrogen T-s diagram (Flynn)

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108 Hydrogen possesses a very low mass density; its vapor is buoyant in air even at a temperature of 23K. Combined with a high diffusion coeffici ent, hydrogen leaks disperse readily in the atmosphere. Knowledge of hydrogen convection and diffusion patterns is helpful in designing hydrogen storage facilitie s, in order to minimize chances of a detonable mixture forming. Another intere sting property of hydroge n is the low JouleThompson inversion temperature of 193 K. Hy drogen is one of thr ee gasses with a JT temperature this low, helium and neon bei ng the others. This re quires precooling of a high-pressure gas stream to below this temp erature before an isenthalpic expansion will produce a refrigeration effect Room temperature hydrogen he ats up during an isenthalpic expansion process. Combustion Hazards Combustion theory describes a “fire tria ngle” consisting of three sides necessary for combustion; fuel, oxidizer, and an ignition source. Obvi ously in the case of hydrogen systems, the presence of hydrogen indicates the presence of a fuel. One characteristic of hydrogen fuels is they need very little ignition energy to init iate a reaction. The minimum ignition energy usually descri bed is 0.017 mJ, or 1000 times less than a spark generated by static electricity. An ignition source s hould always be assumed, and common ignition sources include static electricity, lightning, particle impacts, metal rupture/fracture, friction, hot surfaces, adiabatic compression, shock waves, and heat from smoking, open flames and welding. The best practice for eliminating hydrogen fires is therefore to minimize mixing with an oxidizer. However, an other characteristic of hydrogen fires is the large range of flammability limits in air. The lower flammability limit (LFL) of hydrogen in air is 3.9% and the upper fl ammability limit (UFL) is 75%. A small hydrogen leak has the potential to build up the concentration to a flammable limit, so care

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109 should be taken to design the storage system to allow for any leaks to disperse quickly. This is best accomplished by minimizing conf inement of the hydrogen, for instance to allow for a vent path out of a facility at a hi gh point or to create a forced flow into and out of a facility. In order to safely address concerns associated with hydrogen combustion, knowledge of the combustion process is necessa ry. Once a spot in a fuel/oxidizer mixture is raised to its ignition te mperature, combustion begins. This reaction then heats the adjacent mixture above the ignition temperatur e and the combustion can proceed thru the entire mixture that is in the combustible ra nge. The speed of the combustion is a function of several variables and generally depends on th e rate of heat transfer in the mixture. Usually this flame speed is of the order of magnitude of a fe w meters per second, and this is referred to as deflagration. However, mixtures in the range of 18% to 59% hydrogen can undergo a detonation. In this case, com bustion occurs without the limitation of heat transfer because a shock wave forms that is strong enough to heat the mixture above the ignition temperature. The combustion speed then becomes supersonic, the speed of the shock wave. Detonations are caused by suffi ciently strong ignition sources within a detonable mixture range, or if there is suffici ent confinement or turbulence in an existing flame. While deflagrations have pressure ratios of the order of magnitude of 8, detonations have pressure ratios that can ex ceed 100. Normal pressure relief devices can usually handle the overpressure resulting fr om deflagration, but not detonation. In addition, the pressurization rate is so much faster in det onations that vent paths cannot keep up with the pressure wave. Therefore detonations are much more destructive than deflagrations and systems shoul d be designed to minimize de tonation hazards. This is

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110 accomplished by minimizing confinement, such as internal rooms with four walls or internal pipes with smaller diameters, as well as reducing turbulence in internal flows like that caused by flow restrict ions and flow path changes. Diluents should be used, especially in vent lines, to reduce the possi bility of detonable mi xtures from forming. In the event of a hydrogen fi re, personnel responding must be trained in the best practice for fighting hydrogen fi res. A hydrogen flame is invi sible and has a low thermal emissivity, so personnel cannot see or feel the fire until they enter the actual combustion zone. There is no smoke present, and all co mbustion products rise in the atmosphere. Proper training can ensure personnel are aware of this danger and do not enter into a hydrogen combustion area. While there have been instances of small hydrogen fires being extinguished with chemical suppressa nts, these methods are unreliable, and may actually allow the hydrogen leak to build up to a detonable mixt ure. The best practice is to isolate the leak from the hydrogen suppl y, and spray water on surrounding surfaces to prevent the fire from spreading. Eventually the fire will self extinguish once the fuel source has been isolated. All the existing explosive hazards testi ng for liquid hydrogen has been completed with liquid hydrogen at its normal boiling point so special consideration must be given for densified hydrogen. This is primarily due to increased mass of hydrogen in a given storage volume, however the reaction dynamics will also change when the additional sensible heat of the subcooled liquid is considered. A small-scale simulation was modeled using subcooled LOX and LH2 and the results indicated an explosive yield of 23 % should be expected, which is well below the yield normally used for normal boiling point propellants. However, there always ex ists the possibility th e subcooled propellants

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111 could warm up to the saturation state, so th e study recommended no change in the safety standards.(55) Hydrogen Embrittlement Hydrogen can attack metals in a number of ways. Generally, what occurs is a diffusion of hydrogen atoms in the lattice of the me tal, and the result of this attack is the mechanical properties of the materials are significantly altered. Collectively this phenomenon is referred to as hydrogen em brittlement, although physically there are three different types of embrittlement. First, environmental hydrogen embrittlement occurs when metals and alloys are plastically de formed in a hydrogen environment, such as compression on springs. The effect is magnified in high-pressure systems. Next, internal hydrogen embrittlement occurs when hydrogen is absorbed during some manufacturing process, such as welding, electroplating, or acid treating. Fi nally, hydrogen reaction embrittlement occurs when absorbed hydrogen ch emically reacts with the parent metal, forming a weaker hydride. This reaction is increased during high temp erature processes. No matter what the physical process, hydr ogen embrittlement reduces the tensile strength, ductility, and fracture toughness of materials. Crack propagation occurs more readily, and brittle failures occur more frequently. Knowledge of the system environment a nd material properties is essential in designing for reduced hydrogen embrittlement hazards. High-pressure processes increase the hazards, and high temperatures incr ease reaction embrittlement hazards. The embrittlement hazard is increased with prol onged exposure time and the concentration of hydrogen present has a great effect. Reduci ng stress on components reduces the hazard, and a highly polished surface will permit less hydrogen intrusion than a rough surface. Microcracks or stress fractures are to be avoided since these are embrittlement entry

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112 points. To design for minimum hazard, hydrogen components shoul d be manufactured for a hydrogen environment. Thicker overall parts reduce stress and surfaces should be polished. If possible, oxide layers that re strict hydrogen absorption can be used. EDM processes should be minimized, since dielectr ic fluids used contain hydrogen that is released during ionization. Pr oper welding techniques to redu ce the exposure to hydrogen should be followed. Certain alloys should be avoided, in cluding cast iron, nickel and nickel alloys, and some stainless steels such as 410 SS and17-7 pH SS. Aluminum alloys in the 1100, 6000, and 7000 series are not susceptible to embrittlement and 300 series stainless, oxygen free copper, and titanium are generally considered safe as well. For our application, we used 304 stainless steel in every wetted part, pl us our pressures and tensile stresses were so low that embrittlement was not a concern. Cryogenic Hazards Not specifically hydrogen related, general safety principles du ring use of cryogenic systems must be maintained. Cryogenic li quids are stored far below atmospheric temperature, so nature requires heat transfer to occur from ambient to the inside of the storage vessel. Such heat l eak is unavoidable but proper in sulation can minimize the total amount. This heat leak also leads to boil-off of the hydrogen, creating a pressure rise in the system. This pressurization rate is generally small if the vessel is properly insulated and can be accommodated by two means. First, the quantity of heat leaking into the tank can be removed by mechanical refrigeration be fore boil-off of the hydrogen occurs. Such zero-boil-off systems may be desirable in ma ny cases and have been discussed at length earlier in this work. The other method is to a llow for a small pressure rise before boil off gasses are vented thru a relief valve. This has been the method typically preferred in the past. In this case, sizing of th e relief valve is critical. The capacity for flow in the relief

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113 valve must be matched to the maximum possi ble boil-off rate, otherwise pressurization above the maximum operating pressure (MOP ) may occur. NASA safety standards(56) require the relief valve to be sized to accomm odate flow resulting in complete loss of insulation of the vessel, plus any internal heat generation fr om ortho to para conversion. Typically this means assuming the vacuum inte rnal to the annulus of a dewar has failed, and convection heat transfer now occurs betw een the inner and outer vessel. As an added precaution, redundancy is required in this function, preferably using non-mechanical relief. Icing or other freezing constituents may cause blockage of relief valves, and burst disks may be less susceptible. A primary re lief valve set at 100% of maximum operating pressure coupled with a burst disk set at 116% MOP satisfies this intent. In addition, single relief valves must be installed in ev ery flow passage that has the possibility of being isolated from the vessel relief system Finally, at the compone nt level, internal wetted parts must be designed to preclude the possibility of trapping liquid or cold vapor in an internal space, such as passages of closed ball valves or lobed pumps. Low temperatures can create physical h azards to the human body. Cryogenic burns, similar to heat burns, damage tissues. This can occur either from direct contact with a liquid or contact with surfaces exposed to liquid hydrogen. Proper equipment for protection, such as cryogenic gloves and ap rons, are essential. In most cases, vacuum jacketed insulation, or other high quality insulation, eliminates the potential for accidentally touching cold surfaces. Asphyxia tion can occur when personnel enter areas where oxygen has been displaced by hydrogen or other gasses, such as nitrogen or helium purges. In confined spac es, oxygen monitors are require d. Poorly insulated liquid hydrogen components have the capab ility of forming liquid air. As this liquid air warms,

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114 the nitrogen component will evaporate leaving a liquid with enriched oxygen content. This has the potential of crea ting a combustion hazard, as most substances combust in the presence of pure oxygen. Ensuring the liquid hydrogen lines are well insulated mitigates this risk. For this work, all proper pe rsonnel protective equipment was available, minimizing the low temperature hazards. A ll relief valves were sized properly. Continuous oxygen monitoring wa s available during periods of purging operations, and hydrogen detectors were used to detect leaks. All lines and components were vacuum jacketed except the vent line, and vent pro cesses were limited in dur ation and frequency. Facility Design Knowledge regarding hydroge n hazards is essential in the proper design of a hydrogen facility. The order of preference in siting systems is always as follows; outdoors, in a separate building, in a speci al room, inside a shared room. Depending on the total quantity stored, some of these options are considered forbidden. For instance, quantities above 1140 liters are not permitted to be stored in anyt hing but outdoors or a separate building. All quanti ties above 2270 liters must be stored outdoors. The system used for this work has a maximum storage volume of 140 liters, technically too small to fall under either NFPA or NSS specifications, however, for the purposes of safety the system was considered to be covered by these codes. The system was allowed to be stored inside a shared ro om. Liquid hydrogen storage shoul d always be above grade, allowing for ease of access and quick detecti on of leaks. Tables correlating the total storage quantity to safe distance, referre d to as Q-D tables, dictate the minimum separation between the storage area and facilities or areas wh ere personnel are present. Access to this exclusion area is limited to trained personnel with the proper personnel protective equipment. All equipment inside the exclusion area must be approved for use

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115 to ensure no ignition sources are present, and any operation inside the area must have reviewed and approved operational procedures Barricades may be used to limit the extent of the exclusion area, and dikes and impoundments are necessa ry if there are any oxidizers or other flammable materials stored nearby. All storage vessels should be designed per the ASME Boiler and Pressure Vessel Code, Section VIII, except for portable storage used in transportation, which must conform to DoT regulations. Storage vessels should be labeled with the content, capacity and maximum allowable working pressure (MAWP). The tank should be protected by barriers if there is the presen ce of rotating or reciprocating mechanical equipment nearby. A remote operated valve should be provided as close as possible to the storage tank to allow for isolation of the stor age content in the event of a leak. All piping systems must conform to ASME B31.3. Electrical bonding sh all be present across all joints, and the entire system shall be grounded. Piping sh all allow for flexibility, to account for coefficient of thermal expansion as the system chills down. In most cases, bellows are provided for flexibility, although flexhoses, U bends, or low coefficient of thermal expansion materials such as Invar may be used. Supports shall account for this flexibility, using rollers where possible to constrain the system in only one degree of freedom. Piping shall also be labeled with content, MA WP, and flow direction. Storage systems must have proper vent a nd pressure relief systems. Relief system design requirements have been discussed in pr evious sections. The pressure relief path shall be connected to an approve d vent stack. Venting to th e atmosphere is acceptable if the flowrate is below 0.5 lb/sec, any higher vent flowrates should be burned in a flare stack. In either case, the vent system sh all be designed to prevent air or moisture

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116 intrusion into the vent. Moisture can form ice blockage during venting of cold gasses, obstructing the vent path. Air intrusion allows for the formation of combustible mixtures. The overall flow velocity of the vent shoul d be kept to a minimum, to preclude the possibility of generating enough ignition ener gy and to prevent turbulent mixing, which may aid in formation of detonations. The vent stack must have a purge capability to keep oxygen out of the system. Ground vent stacks sha ll be 25 feet above grade, and roof vent stacks shall be 16 feet a bove the roof level. In all cases vent stacks should be positioned away from air intakes or other mechanical systems, and should have lightning protection in the form of a 30-degree cone around the top of the vent. In the event the hydrogen is stored inside a special room or building, provisions for the design of that facility mu st be made. Use of lightwe ight, non-combustible materials is necessary, and walls, ceilings and floors s hould have a minimum 2-hour fire protection rating. All windows must be shat terproof glass or plastic, a nd doors shall open outward to facilitate easy egress. Emergency venting shall be accommodated in the event of a detonation, and the vent must open with a maximum pressure of 25 lb/ft2. Adequate ventilation is required to prevent the accumu lation of hydrogen above a concentration of 1%. The minimum vent area shall be 1 ft2/1000 ft3 of room volume, and shall be located at the top of the room. The room shall be designed to avoid ceiling peaks and trapped pockets such as false ceilings. The hydrogen system shall be 100% covered with water spray systems, but care must be taken to a void water deluge into a vent line. Any electrical systems within 3 feet of hydrogen connections mu st be certified as Class 1, Group B, Division 1 per NFPA Section 70, and Class 1, Group B, Division 2 within 25 feet. Any system containing hydrogen shall have adequate instrument ation and controls

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117 to ensure that operation is within acceptable limits, and shall have adequate alarms and warnings if operation falls outside of accep table limits. Means of detection hydrogen leakage must be employed. Fixed hydrogen det ectors shall be used at likely leak points such as tanker connections, and portable hydrogen detectors s hould be used during operations where hydrogen may accumulate. Th e detectors must have short response times and must be capable of detection concentrations of 1%, or 25% of the LFL. Management and Operations Historical data regarding causes of pa st hydrogen accidents reveal system and hardware failures are seldom the sole cause of the incident. Often, there are a number of individual events that form a chain of events leading to an accident, and if any of those events was prevented the chain would be disr upted and the incident could be avoided. More often than not, improper management or ope rations is one of the key events leading to an accident, so care should be taken to ensure this cause is avoided. The most important preventative meas ure is proper management of hydrogen systems and the operations. Safety reviews must be held at a number of points in the project life cycle. Design reviews to achi eve a fail safe design must be held, and the design must incorporate all the requirements discussed above. The system should be single fault tolerant before failure that can l ead to loss of life, injury or major system damage. A detailed hazards analysis by an engineer knowledgeable in hydrogen systems should be performed prior to first operation. All operations sh all require approved written procedures, and the procedures must be maintained at the operational site. Once in the operational phase, good housekeeping mu st be maintained. Any combustible materials, including weeds, rags, wood, and car dboard, must be kept 25 feet away from any vessels or lines that may store hydrogen. Egress routs mu st be kept free and clear,

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118 and must be marked properly. Practice of emergency planning or procedures should periodically be performed. It is important that area control be enforced to ensure people not knowledgeable about the operation are kept away. Conclusion Once the proper research and education wa s completed, these safety principles were used to design, construct, and operate a small liquid hydrogen storage system. This storage system, discussed in Chapter 5, cont ained an integrated refrigeration system. Although this type of system had not been developed previously, and the size of the system developed technically did not require adherence to the safety standards, the principles learned in this chapter were i nvaluable in the following chapters. If used properly, liquid hydrogen systems are as safe as other flammabl e hydrocarbon systems.

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119 CHAPTER 5 TEST SYSTEM DESIGN AND ANALYSIS The next major step was to design and fa bricate a sub-scale system capable of testing concepts introduced in Chapter 2 and validating the models from Chapter 3 while conforming to safety standards addressed in Chapter 4. Funding was obtained in collaboration with Florida Solar Energy Center through the NAS A Hydrogen Research for Florida Universities Program. The devel opment process included a preliminary design and analysis phase, followed by a generati on of a system specification used for procurement of the test cryostat, reviews of the detailed design drawings made by the cryostat vendor, acceptance testing of the cryos tat after delivery, and finally the detailed design and fabrication of the cryostat support systems. Preliminary Design and Analysis Preliminary design requirements consisted of the need to effectively demonstrate the operational concepts discu ssed in Chapters 2 and 3. Major components needed would be a hydrogen storage vessel, a refrigeration system to remove heat, instrumentation and data acquisition, fluid supply and distribution, vacuum system, and safety and leak detection. The general design path was to determine the system size in terms of storage volume, then estimate the heat leak in that storage system. The refrigeration system is then sized to accommodate that heat leak combined with any heat removal required by the gas liquefaction rate. On ce the sizing was complete, s upporting systems such as instrumentation, pneumatics, and vacuum systems could be selected. Constraints on system size were dictated by budgets as well as safety specifications.

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120 Hydrogen Storage The required volume of the hydrogen storage wa s set at 150 liters. This volume is similar to familiar lab scale dewars that hold 180 liters, but was reduced to bring the total volume down below the minimum NFPA 50B guidel ine of 150 liters. This classified the cryostat as a lab scale research vessel, not a definite storage site. However, the volume was still expected to be large enough to pe rform long time liquefacti on operations and to observe stratification in the densified liquid. The storage vessel was to be made as efficient as possible as determin ed by proven design characteristics.(57) Many operations were to be performed belo w atmospheric pressure, so there was a requirement for the inner tank to be vacuum tight. Maximum operating pressure in the dewar was set at 358 kPa. Primary and seconda ry relief from overpressurization at 100% and 116% of the system MOP (required by ASME code) was satisfied by a relief valve and burst disk respectively. In addition, a vacuum relief valve for vacuum annulus protection was specified. The minimum temperature expected for the liquid hydrogen was 14 K, just above the triple point temperature of 13.9 K. Sa turated LH2 at this temperature has a density of .0769 g/cm3. Therefore, the maximum e xpected mass stored in the system was 11.5 kg. Cryogenic Refrigerator Once the storage system has been sized, a cryogenic refrigerator, or cryocooler must be identified that is capable of cooling the system. Based on a rule of thumb that the product loss rate of a new, well designed la rge dewar is less than 5% per day, an estimated heat leak can be calculated. The heat required to vapori ze 7.5 liters of liquid

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121 hydrogen at the NBP over 24 hours is found to be approximately 3 W. At a minimum, to achieve ZBO, a cryocooler that can produce 3 W at 20 K is needed. If liquefaction is also require d, refrigeration to remove th e sensible heat of the gas between atmospheric temperatur e to the liquid temperature ( 3652 J/g) plus the heat of vaporization (443 J/g) must also be supplied. Additionally, the heat of conversion between ortho and para hydrogen must removed (703 J/g). Assuming the need to fill the dewar every 40 days, a mass flow rate of 0.0033 g/s of hydrogen gas is required. The refrigerator must then be capable of removing the following amount of heat; Q =0.0033 g/s *(3652 J/g + 443 J/g + 703 J/g) = 16 W 5-1 Combining the liquefaction requirement with the heat leak requirement, a cryocooler capable of at least 19 W at 20 K mu st be used. Literature and web searches identified several candidates, mostly Gi fford-McMahon style pulse tubes or stirling cycles, so no requirement was impose d for any particular manufacturer. The cryocooler also needed to be integrated into the storage system in an efficient manner, to exchange heat between the cryoc ooler cold head and the liquid hydrogen at the bottom of the tank. Details for this in terface design, including penetration at the bottom of the tank vs. at the t op using a heat pipe or copper bar to transfer heat to the bottom, were left to the vendor building the cryostat. One critical property that needed to be estimated was the free convection coefficient of liquid hydrogen. A simple heat exchanger had to be designed to effectively transfer the refrigeration from the cryocool er to the liquid, and the only mechanism was free convection. Literature reviews did not reveal any experimental values, so heat transfer correlations had to be used. The simplest HX to in corporate was flat straps of

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122 oxygen free copper anchored to the coldhead and this could be approximated as a vertical flat plate. Church ill developed a correlation fo r this geometry, which gives(58) 2 27 / 8 16 / 9 6 / 1] ) ) P r 492 0 ( 1 ( ) ( 357 0 825 0 [ L LRa Nu 5-2 The Prandtl Number for liquid hydrogen at 20 K is found from the refrigerant property database refPROP to be Pr = 1.224. The Rayleigh Number is found from * ) ( *3L T T g Raw L 5-3 The volumetric thermal expansion coefficient is defined as PT ) ( 1 5-4 and using refPROP to find the st ate variables is found to be K 1 14 0 average between 15 K and 20 K. The average kinematic viscosity between 15 K and 20 K is s cm20018 0 and the average thermal diffusivity is found to be s cm20015 0 The total length of the c opper straps is set as 10 cm, long enough to reach within 5 cm of the bottom of the tank. Assuming a cold head te mperature of 14 K and a liquid temperature of 20 K, the Rayleigh Number is estimated as 3.4 x 1013. This high of a Rayleigh number implies the dominant form of heat transfer in this system will be convection and the natural convective flow will be turbulent. Later operational scenarios where the temperature gradient is not as large will reduce the overall heat flux and the flow regime will transition to laminar. From this the Nusselt number is calculated to be 3765. Finally, the convection coefficient is found, knowing the thermal conductivity of LH2 and using the following relation

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123 L k Nu hL* 5-5 to be K m W h2436 This is a significantly high heat transfer coefficient and means the heat exchange should be an efficient proce ss. A calculated total surface area of roughly 100 cm2 is required for the heat exchange. Instrumentation and Data Acquisition Data acquisition needs were dictated by th e type of planned operations. On the cryostat itself, a probe with five silicon diode sensors was necessary to measure temperature of the liquid as a function of liquid level. Other diodes were used to monitor the health of the cryocooler a nd to control temperature. The cryostat also needed pressure transducers for both the inner ve ssel and the vacuum jacket. It was also anticipated than mass flow of the product gas to be liquefied would be measured by a mass flowmeter. The large thermal mass and the low heat tran sfer rates in the system eliminated the need for a high-speed data acquisition (daq) system. Labview 7.0 was used as the daq software, utilizing a program written by Dr. Baik at FSEC. Fieldpoi nt network modules were the interface between the instrumenta tion and the daq computer. The fieldpoint modules used have a 16-bit an alog to digital converter. Fluid Distribution The following four fluid interfaces were re quired for the cryostat; a liquid fill and withdraw port (” VJ), vent port (” tube), liquefaction su pply port (3/8” tube), and a gas supply port (3/8” tube). The liquefacti on port and the gas supply port introduced gas at two separate locations, one wrapped ar ound the cryocooler cold head for conduction heat exchange, and the other to introduce vapor bubbles at the bottom of the tank. The

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124 tank relief valve and burst disk were flow through type with the outlet plumbed to the vent system. All shut off valves were speci fied as manual globe va lves. In addition a pressure building leg was added to allow fo r self-pressurization, with regulation for pressure control. Gaseous nitrogen, helium, and hydrogen K bo ttles would be used as a commodity supply system. Appropriate K bottle regulators were purchas ed, including high and low pressure gauges and shut off valves. Liquid nitr ogen could be used to facilitate chilldown. Vacuum System The performance of any good cryostat depends directly on the quality of its vacuum system. To ensure good performance and to enha nce flexibility in the laboratory, a high capacity, dual pump vacuum system was procured from Leybold(59). The first stage of this system is a rotary vane mechani cal pump capable of pumping speeds of 35 m3/hr, and an ultimate low pressure of 10-3 torr. The second stage consists of a TurboVac turbomolecular pump with pumping speed of 55 l/s and an ultimate low pressure of 10-9 torr. Vacuum pressures are measured using a Combivac CM31 universal vacuum gauge, combining a Thermovac pirani instrument for higher pressures (atmospheric to 10-3 torr) and a Penningvac cold cathode sensor for lower pressure (10-2 -10-9 torr). A built in RS232 interface allows data to be sent to the daq computer. Safety and Leak Detection System To measure any hydrogen leakage, a catalyt ic portable hydrogen leak detector was purchased for the laboratory. The detector works by sensing the heat generated by combustion of hydrogen and oxygen on the surf ace of a palladium catalyst. During normal operations the detector sensor was positioned above the cryostat to detect leaking hydrogen gas that is buoyant, but the sensor could also be used as a point detector during

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125 some transient operations to measure leak age at a specific interface. A portable O2 monitor was used to ensure any helium or nitrogen leakage woul d not create an oxygen deficient atmosphere in the enclosed labor atory. All electric al connections on the cryostat were specified to be built explosion proof per Class 1 Group B Division 2 of NFPA 70. Vendor supplied equipment, such as temperature and pressure monitors that were not explosion proof, were specified to be enclosed in a purged environment, meeting the intent of NFPA 70 Cryostat Specification Following completion of the preliminar y design, a cryostat specification was produced and distributed to a variety of vendors for bids. This specification used the sizing and operations require ments previously analyzed, and incorporated all the necessary design and fabrica tion requirements imposed by cryogenic standards. All construction was to be stainless steel, with the inner vessel conf orming to ASME Boiler and Pressure Vessel Code Section VIII, and the vacuum jacket to Section VIII and Section IX. Tubing was specified by ANSI B31.3. A number of test requirements, such as x-ray of welds, cold shock, leak test, and pr essure test were also specified. The vendor was required to submit a number of test re ports and certifications as well as the fabrication and assembly dr awings. A final cleaning requ irement and shipping details were included as well. The full system sp ecification, as well as a preliminary test schematic, is included in Appendix A. Cryostat Detailed Design Cryogenic Technical Services, of Longmont, Colorado was selected to fabricate the cryostat, primarily due to the experience of the owner Glen McIntosh with liquid hydrogen. Glen added several innovative design features, especially in the area of the

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126 pressure buildup system (PBU). His expertise in designing and fabri cating low heat leak vessels eliminated the need for a shield around the inner ta nk. The cryocooler chosen was a G-M, connected to the top fla nge of the dewar with a heat pi pe to transfer heat to the bottom of the tank. A detailed de sign is shown in Figure 5-1. T5 T4 T3 T2 T1 T6 T7 T8 Figure 5-1 Cryostat design detail (Cryogenic Technical Services)

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127 Cryostat Construction The inner vessel is 20 inch SS 304 tubing, w ith a cylindrical section 25.5 inch long and two elliptical end caps. The total volume is 157 liters, and has a surface area of 1.56 m2. 45 layers of dexterous paper and alumini zed mylar, 1 inches thick, serve as the multi-layer insulation (MLI). The inner vessel is primarily supported by the 12-inch long, 8-inch diameter 304 SS neck. There is also a low conductivity G-10 bottom support. The cryocooler cold head is installed down the leng th of the neck, offset from the center, and thin stainless steel baffles suppr ess and radiative heat transfer in the neck of the dewar. One design feature added is the incorporation of a flange at the top of the vacuum shell, to allow the entire inner vesse l to be removed. Another fl ange at the top of the neck allows removal of the cryocooler coldhead, h eat pipe, and inner vesse l instrumentation. A total of four lines were connected to the inner vessel. The liquid fill and drain line, VJ outside the dewar, was 3/8 inches ID, .049 inch wall thickness, and had a conduction path of 12 inches long. This lin e had a bayonet connection interface, and ran to the bottom of the inner ve ssel. The vent line was 5/8 inches OD, had 0.049-inch wall thickness and had a path length of 12 inches. It connected to the high point of the inner vessel, and had external tees to the pressure transducer, the vent stack, the PBU leg, and a shut off valve. The liquefaction inlet line is 3/8 inch OD tube, w ith .049 wall thickness and a conduction path of 12 inches. This line is brazed onto the cold end of the heat pipe for good conduction heat transfer, and has a s hut-off valve at the warm interface. The PBU system was a unique challenge. In most storage vessels, the PB U line is connected to the bottom of the tank, has a number of coils wrapped in the VJ annulus, and has a shut off valve and regulator outside the dewar at th e top of the system. In this case, the PBU system uses a liquid trap to minimize heat leak when not in operation. In deeply

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128 subcooled systems, there is no vaporization occurring immediately in the PBU line, so there is no vapor backpressure preventing the liquid from flowing ove r the liquid trap and into the uninsulated portion of the PBU line. This would dramatically increase the total heat leak in the cryostat to th e extent that the cryocooler would not be able to overcome this heat leak, and subcooling would not be achie vable. The simple solution to this is to move the PBU isolation valve to the bottom of the tank, but this design is complicated since the valve stem would be inverted and liquid could be present at the valve stem packing. This situation is unacceptable since heat leak would increa se and there could be leakage problems at the dynamic seal at th e top of the valve stem. CTS proposed an innovative solution to this problem, placi ng the valve body and poppe tt at the bottom of the tank and using a stainless steel cable as a link between the valve seat and the manual actuator at the top of the system. The PBU line, 3/8 inches OD and 0.049 inch wall thickness, then runs downstream of this valv e a total of 23.5 inches until it exits the vacuum annulus and enters the vaporizer se ction at the bottom of the tank. The PBU regulator is at the top of the tank. There is some additional heat leak associated with this cable, but this small heat leak is negligible. Knowing the details of constr uction, a more exact calcula tion of the total tank heat leak can be made. This number is estim ated by adding the contributions from the radiation around the area of the dewar with the conduction do wn the dewar neck and all tube penetrations, and adding in a cryocooler heat leak co ntribution given by the vendor cc c c hlQ L T T kA T T hA Q ) ( ) ( 5-6 where h is the overall heat transfer coe fficient across the MLI calculated from the modified Lockheed correlation(42).

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129 The total heat leak for the cryostat is now estimated to be 8.7 W, more than doubled compared to the origin al estimate based on the 5 % pe r day rule of thumb. This is due to the fact that the small vessel has mo re parasitic heat loads than larger dewars due to the scaling of heat leak being relate d to area (r squared) compared to volume (r cubed). Details of this heal leak calcula tion, made using an Excel spreadsheet, are included in Appendix B. The final instrumentation design for the cryostat included 8 Lakeshore DT-400 series silicon diode temperature sensors, with 4 wires each, calibrated at the factory. The sensitivity of these diodes is +/22 mK(60,61). Five of these diodes were installed on a G10 support down the height of the tank, sp aced every 5 inches, with T1 reading the product (usually vapor) temperature at the top of the vessel and T5 reading the product (usually liquid) temperature at the bottom of the vessel. T6 is the cryocooler cold head temperature, T7 is the temperature at the top of the heat pipe, and T8 is the temperature at the bottom of the heat pipe. This arrange ment allowed for visibility into liquid temperature stratifications, as well as cryocool er performance, heat pipe performance, and the effectiveness of the cryocooler to heat pipe thermal connection. A Taber Industries pressure transducer factory calibrated with a reso lution of 0 .05 psia, monitors the inner tank pressure from a tee off the vent port(62). An American Magnetics capacitance based liquid level pr obe was included to better estimate the total volume of liquid in the tank, but it never seemed to function consistently and the data was not used. Cryogenic Refrigeration A Cryomech AL330 Stirling type G-M cryocooler was selected for the refrigeration system. The AL330 is capable of producing 40W at 20 K, 15 W at 15K and has a no load temperature of 12 K. A capacity curve is shown in Figure 5-2(63). The cold

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130 head package, consisting of a rotary valve, displacer, regenerative heat exchanger, and copper cold mount, weighs 44 lbs and is c onnected to the compre ssor by two gaseous helium lines and an electrical power feed. The CP970 compressor is oil lubricated and water cooled. The compressor power requirement is 220 VAC, 3 phase, 60 Hz, and uses a total of 7.5 KW. At 20K, this gives a speci fic power of 187.5 W/W, not very efficient but the cryocooler is very reliable. 0 20 40 60 80 100 120 140 160 180 0102030405060 Temperature (K)Power (W) Figure 5-2 Cryocooler AL330 capacity curve (Manufacturer Spec) The heat pipe is a 2 1/2 inch diameter tube, 26 inches long with an internal volume of 127 in3. It is th ermally anchored at the top to the cold head, using invar screws for low thermal expansion and Apezion N vacuum grease to enhance heat transfer between the two polished oxygen free copper su rfaces. The heat pipe copper heads are machined on the inside surface with parall el fins, to increase the condensation and evaporation surface area. The heat pipe has a charge port that has an interface outside the dewar, for changing the working fluid if the te mperature range requires it, or to refill any

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131 leakage that may have occurred. The bo ttom copper mass on the heat pipe has the liquefaction line soldered to th e outside surface, and four flex ible copper straps, .75 inch wide by 5 inches long, designed to exceed th e required heat transf er area by giving 194 cm2 of surface. Acceptance Testing The cryostat was delivered to FSEC in October, 2003. Following unpacking and visual inspection, the system was set up in the Chemistry Laboratory. The instrumentation was powered up and the vacuum level on the vacuum jacket was verified to be good. The vacuum pump was connected to the inner vessel and this was evacuated to 10 microns, following which a vacuum decay check was performed. The pressure rose 7 microns in 6 hours. Vacuum leak ra tes can be quantified by the equation(64) t P V T Q / * )} 273 /( 273 { 79 5-7 Where Q is the leak rate in sccm, V is the vol ume in liters, and P is the pressure in Torr. The estimated leak rate becomes 0.0036 s ccm. After the vacuum decay, the cryocooler was started and a temperature of 14 K was reach ed on the cold head. At this point the heat pipe had not been charged. All diodes functioned as expected. Support Systems Once the acceptance testing was complete, th e cryostat was positioned into the lab where the testing was to take place. Previously, a hole was cut into the outer wall and a 1” vent pipe was installed and placed several feet above roof level. A K-bottle rack was purchased as well as nitrogen, helium and hydr ogen K-bottle regulators. For the gaseous hydrogen supply system, a MKS mass flow mete r was installed to control and measure the quantity of hydrogen entering the system. The flowmeter had a range of 0-50 slm and an accuracy of 0.05 slm(65). Flexible copper tubing wa s used to connect different

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132 elements, and swagelok compression fittings were used for all gas connections. Check valves were used to minimize the potential for system contamination. A liquid nitrogen laboratory scale dewar was purchased to ai d in the initial chilldown, and a foam insulated, metal bellows flexhose was used to connect the LN2 to the cryostat. A picture of the completed test set up is shown in Figure 5-3.

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133 Figure 5-3 Liquid hydrogen cr yostat test arrangement

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134 CHAPTER 6 LABORATORY TESTING AND DATA ANALYSIS A series of tests were conduc ted at the Florida Solar En ergy Center in the summer of 2004. Total quantities of LH2 were limited by the laborat ory managers to keep the liquid mass under 2 kg, for safety purposes. Testing was terminated on August 12 2004, when the approach of Hurricane Charley cr eated the need for system deservicing and safing. Zero boil off, liquefaction and densific ation were all achieved Future plans call for further testing in 2005-2006 in a de dicated lab space where quantity-distance concerns are minimized. The test de scription and data analysis follow. Liquid Nitrogen Chilldown Testing with cryogens started on June 22, 2004. The cryocooler was not operating and the system was at ambient temp erature. It was decided that a stored cryogen supply would be used for the system chilldown to save time, as opposed to using the cryocooler refrigeration power. No read ily available supply of liquid hydrogen was found in small quantities for this purpose. Th e estimated total mass of the cryostat that would need to be chilled down was 150 kg, mostly stainless steel. Jacobs (66) has provided a method of estimating total liquid require for chilldown of cryogenic pipelines, and using this method approximately 4800 liters of liquid helium is required. This estimate assumes only the latent heat is used for ch illdown, as opposed to cross country pipelines where sensible heat can also be a contributing factor due to longer dwell times in the equipment. Liquid helium was determined to be too expensive. The solution was to use liquid nitrogen to chill down to 77K, then drain and purge the liquid nitrogen using

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135 gaseous helium, evacuate then turn on the cryocooler and supply gaseous hydrogen to complete the chilldown process. The total volume of LN2 needed wa s estimated to be only 84 liters. Figure 6-1 shows the data fr om the initial phase of this chilldown. At the start of the test, all valves on th e system were closed and the system was evacuated to a pressure of 0.02 psia. The v acuum annulus was evacuated to a vacuum in the range of 1x10-4 Torr. All temperatures we re reading in the range of 297 K. A portable, 160 liter dewar of liquid nitrogen was connected to the liquid fill and drain line, and the dewar supply valve and the liquid hydrogen drain valve were opened. The system vent valve was then opened. Unfort unately, the supply dewar pressure was not vented prior to the transfer and the valve was not opened slowly enough. As liquid nitrogen entered the warm hydrogen storage tank, it vaporized a nd expanded beyond the flow capability of the inch vent line. Fros t was observed at the outlet of both the relief valve and the burst disk, indi cating cold vapor flow out of these devices. The liquid nitrogen supply valve was closed and the system pressure began to decrease. The nitrogen storage pressure was vented and supply valve was very slowly opened to reestablish the chilldown process. Figure 6-2 shows more detail of the over pressurization of the system. Note the pressure increasing in surges, as is expected in a chilldown process as liquid flashes off, creating a localized pressure spike that redu ces further liquid flow. In spite of these spikes, the overall pressure increases in a fair ly linear profile until the burst disk relieves at 64.5 psia (49.8 psig), slightly higher than the 45 psig specification. It is worth noting there was no corresponding decr ease in pressurization rate when the relief valve opens, indicating the flow capacity was not sufficient to relieve that quantity of gas.

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136 0 50 100 150 200 250 300 0204060 Time (min) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-1 Liquid nitrogen chilldown 0 20 40 60 80 100 9.710.210.7 Time (min)Pressure (psia) Figure 6-2 Hydrogen dewar overpressurization Pressure continued to increase until the de lta pressure between tanks reached a point where the liquid mass flow rate into the system equaled the gaseous mass flow rate out of the system. Once the frost was observed on the relief line, the liquid nitrogen supply

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137 valve was closed, and pressure decreased to match the atmospheric pressure. Later, after the chilldown was complete and while the system was open to ambient, a new burst disk was installed to provide a redundant method of overpressure protection. Looking at the temperature profiles during th e chilldown in more detail (Figure 6-3), notice the lowest diode (T5) quickly reaches the liquid state (97.8 K, 96.5 psia) and remains liquid during the flow interruption. The liquid temperature decreases after the flow stops since the vapor pressure is decrea sing. T5 eventually reaches 77 K (NBP) as the pressure in the tank vents to ambient. Si milarly, T4 initially reaches the liquid point, but turns to vapor shortly afte r the flow is terminated. The other three diodes in the temperature rake are gradually decreasing in temperature, even when the flow is stopped initially. This is due to the fact that li quid nitrogen is boiling off in the bottom of the tank, removing heat from the saturated liqui d as the vapor pressu re drops. Once the depressurization rate decreased enough, the ta nk heat leak and heat capacity of the semiwarm metal overcomes this cold vapor supply and the ullage temperatures seek to stabilize at a higher temperature. Another in teresting point is the temperatures on the cryocooler and heat pipe themselves, which gr adually decrease in temperature compared to the diodes on the rake. This is due to the much larger thermal mass associated with these locations taking longer to chill. After the burst disk rupture had been diagnosed and determined not to be a constraint on further testing, the liquid n itrogen supply valve wa s reopened. Figure 6-4 below shows details on this process. The n itrogen dewar had been vented to a much lower pressure and the lack of a burst disk gave a larger path to vent, so the system pressurized in a much more controlled manne r. Extra care was also used to open the

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138 50 100 150 200 250 300 9111315 Time (min) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-3 Liquid nitrogen chilldown detail supply valve more slowly. The maximum syst em pressure was only 28 psia during this chilldown sequence. Data shows that T5 incr eased slightly as the pressure increases, following the liquid saturation line. T6 a nd T4 quickly reached liquid temperature, followed by T3 about 18 minutes after the start of flow. Flow was terminated at T+51 10 30 50 70 90 110 25354555 Time (min) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-4 Comple tion of chilldown

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139 minutes, when the liquid level was approaching T2. Pressure in the system vented to ambient, accompanied by a drop in saturated liquid temperature. Shortly after the pressure reached ambient, the T3 measurement increased past the saturation temperature, indicating enough liquid boiled off to leave th e diode in the vapor region. Another interesting phenomenon was observed in the te mperature profiles in the liquid. During flow, all liquid temperatures were equal, indi cating mixing of the liquid. Shortly after the flow was stopped the temperature of the upper liquid layers decreased (T3, T4) compared to the lowest liquid layer (T 5). Evaporation at the surface caused liquid temperatures to decrease, but there was a time delay before the natural convecti on currents created a normal temperature gradient in the liquid. The tank, half full of liquid nitrogen was left open to atmosphere overnight to ensure a complete chill down. By Thursday June 24 at 11:00 am, a stable temperature profile was r ecorded with T4 and T5 reading 77K, T3 reading 95K, T2 reading 117K, and T1 readi ng 138K. At this point the tank drain and purge was performed. LN2 Drain and Purge Drain and purge of the liquid nitrogen was started on June 24 at 10:45 am. A data overview of the next four hours is shown in Figure 6-5. First the system vent valve was closed. The system immediately began self -pressurizing. A gaseous helium K-Bottle was connected to the system and the line was evacuated to eliminate any contaminants. The system was then pressurized to 18.2 psia. A series of 5 positive pressure purge and vent cycles was completed. Once the rema ining liquid was expelled, two helium purge and vacuum cycles were completed to rem ove all the gaseous nitrogen, which would solidify at liquid hydrogen temperatures. Fina lly, after all the nitrogen was removed and the system was still under vacuum the cryocooler was turned on.

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140 10 30 50 70 90 110 130 150 170 190 050100150200 Time (min) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-5 Liquid nitr ogen drain and purge More insight on the system behavior can be found by examining the data in greater detail. Figure 6-6 shows the tank pressure profile during the purges, drains, and evacuation. Starting at 18.2 psia, the gaseous helium inlet valve was opened to pressurize to 20.7 psia. The system vent valve was then opened starting the first purge cycle. When the pressure decreased to 17.5 psia, the vent was closed to repressurize. This was repeated five times, to get the nitrogen u llage replaced with helium. While this is occurring, enthalpy from the warm helium is causing liquid nitrogen to boil. Notice the pressurization and depressurizati on rate decreases as the boil off leaves a greater ullage volume. At the end of the fifth cycle, the gas supply valve is closed and the vent valve is closed. The system is repressurized to 18.5 ps ia and the liquid withdraw valve is opened. There is a noticeable slope change in the depressurization curve when comparing a gas vent to a liquid withdraw. As most of th e liquid is drained, the system reaches near

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141 0 5 10 15 20 0204060 Time (min)Pressure (psia) Figure 6-6 Tank drain and purge pressure cycles ambient pressure and valve is closed. Ne xt, two evacuations ar e performed using the vacuum pump, with a backfill of gaseous helium in between. The system remained evacuated until the following day when the gaseous hydrogen was introduced into the system. Temperature profiles during this operation are shown in detail in Figure 6-7. All five purge and vent cycles are clearly eviden t in the ullage temperature measurements. By the second purge cycle, enough warm gas had entered the system that the liquid level had reached the T4 level. After this point, T4 behaves in a similar manner to the other ullage temperatures, except the final pressurization cycles during the liqui d withdraw procedure created much higher temperature spikes in T4 that T3, T2, and T1. Liquid stayed in the bottom of the tank through all five purge cycles, as is evident by the lowest tank temperature continuing to track the saturation lin e. After the five purge cycles, the liquid withdraw valve was opened. Most, but not all of the tank was drained. Note the

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142 65 75 85 95 105 115 125 0204060 Time (min) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-7 Tank drain and purge temperature profile differences in behavior between the diodes in gas vs. diode in liquid. The ullage temperature drops initially as the pressure de creases, and during this phase it is measuring the gas temperature directly thru convection. Eventually the temperat ure decrease stops, although the pressure continues to decrease. The liquid diode d ecreases in temperature as the pressure drops, roughly follo wing the saturation line. At this point it was decided to do a second drain operation, and the system was repressurized to 16 psia. The drain valve was reopened and the system vented to ambient. The vacuum pump was reconnected and turned on and this time it appeared the remaining liquid was removed from the tank. The T5 reading began increa sing, along with all th e other temperatures, and the decision was made to turn on the cryocooler. When the cryocooler was started (Figure 6-8), the cold head temperature was reading 182K. Within 30 minutes, the temperat ure had decreased to 22K, and many of the other temperatures near th e top of the tank were decrea sing. However, the lower tank

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143 temperatures and the bottom heat pipe temperature did not start decreasing until the heat pipe was charged with gaseous hydrogen. The charge operation caused an immediate spike in cold head temperature due to the en thalpy of the warm ga s entering the pipe, and this spike is also ev ident in the upper tank temperatures. Once the heat pipe was fully charged, the lower heat pipe temperat ure immediately began decreasing as the refrigeration power was pumped down the le ngth of the pipe by the internal hydrogen gas. Within 30 minutes, the lower heat pipe temperature had completed its chilldown. The delta temperature between the cooler and the heat pipe end was approximately 0.7K, which is very efficient considering there wa s thermal contact resistance between the top of the pipe and the cold h ead, and thermal resistance down the length of the pipe. One puzzling piece of data is that the expected temperature prof ile was established with the exception of the lowest diode T5. This temp erature did not decrease as quickly as the others, and remained the warmest of all the te mperatures during this phase of operation. 10 30 50 70 90 110 130 150 170 190 123143163183203 Time (min) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-8 Cryocooler chilldown in vacuum

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144 This is potentially explained by the internal configuration of the tank, with the internal G10 support tube partially blocki ng the radiation path between T5 and the heat pipe cold mass. With little pressure in the tank, the primary heat transfer mechanism would be radiation. The cryocooler was left on overnight to achieve maximum chill down and the next morning the hydrogen liquefaction process began. Hydrogen Liquefaction After the cryocooler operated overnight, th e cold head temperature and heat pipe temperature were reading approximately 15.5 K. The cold head temperature was actually experiencing temperature oscilla tions of a magnitude near 1.5 K, which were damped out by the thermal mass of the heat pipe. Ulla ge temperatures varied between 28 K and 37 K, and were still decreasing slightly. Ar ound 10:20 am on 6/25/04, hydrogen gas at room temperature was introduced into the vessel. Figure 6-9 below show s this operation, from start of gas flow until termination of gas fl ow 4.5 hours later. The temperature and 0 10 20 30 40 50 60 23242526272829 Time (hr) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Mdot (slm) Figure 6-9 Hydrogen li quefaction on 6/24/04

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145 pressure profiles are driven by the mass flow rate into the vessel, as is expected since the enthalpy from the warm gas introduces the en ergy in the system while the cryocooler tries to remove this thermal energy. If the ma ss flow rate exceeds what the cryocooler can liquefy, the pressure increases. Accurate c ontrol of the mass flow rate of gaseous hydrogen was somewhat difficult since the only means of control were globe valves that had imprecise adjustments, with fluctuati ng pressures upstream and downstream of the valve, and in some cases, vibration from the cryocooler displacer that caused changes in valve positions. Future modifications to the experimental set up will include the addition of a mass flow controller. As soon as the gas flow was initiated into th e vessel, the temperatures started to rise on all thermocouples, with the exception of T5. Recall that during the overnight chilldown T5, the lowest thermocouple on th e rake, was expected to read a lower temperature than T1 thru T4, but in fact it did not. This was attributed to the fact that the dominant heat transfer mechanism in the ta nk ullage at that time was radiation, not convection, and T5 was shielded from a direct view of the lower end of the heat pipe. However, as soon as gas was introduced into the system, convecti on became the primary means of heat transfer, and T5 initially cooled off as stratification of the gas occurred. When the gas pressure was sufficient so as to allow T5 to read the temperature accurately (around 0.5 psia), the measurement began to rise At this point, the expected temperature profile was recorded in T1 thru T5. As the pressure continued to increase, greater convective heat transfer began to occur between the heat pipe end (T6) and the measurement on the rake, and T5 began to decr ease again. This continued until the heat pipe and cold head warmed up beyond the boili ng point of the hydrogen in the heat pipe.

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146 At this point, heat transfer down the heat pipe was limited to convection instead of a phase change, and the heat transfer down the pipe was restricted. T6 began to increase as a result, and this caused T5 to start increas ing as well. This initial warm up phenomenon is shown in greater detail in Figure 6-10. At this point the decision was made to increase gas flow in the tank to get to the point where the internal pressure was a bove atmospheric, so as to minimize the possibility of air leaking into the syst em. The valve was opened numerous times to increase flow, but the flow rate decayed immediately afterward. Eventually the k-bottle regulator pressure was decreased to mini mize delta pressure, and flow rates became somewhat more controllable. Pressure change s in the tank were directly related to the value of the mass flow rate. This is shown graphically in more detail in Figure 6-11, with the slope of the pressure curve related to the magnitude of the mass flow rate. Some effort was made to determine the mass flow rate that gave a constant pressure in the tank, such a flow rate would roughly approximate the liquefaction rate of the cryocooler (neglecting ortho-para conversi on losses). There were two pe riods of time when the tank pressure was roughly constant, corresponding to flow rates of 6.6 standard liters per minute and 4.3 slm. However, there were still too many transient effects at this time to come to any conclusions. From this data it is easy to numerically integrate the mass flow rate with respect to time to obtain the total quantity of hydrogen in the system. This resu lt is shown in Figure 6-12. During the course of the day, a to tal of 2000 standard liters of gaseous hydrogen was introduced into the tank. Knowing the standard volume of hydrogen gas in the tank, combined with the total volume of the tank, the specific volume of the hydrogen can be

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147 15 20 25 30 35 40 45 50 55 60 65 2323.123.223.3 Time (hr) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-10 Temperature transi ents during initial gas flow 0 5 10 15 20 232425262728 Time (hr) P (psia) Mdot (slm) Figure 6-11 Mass flow rate a nd pressure during liquefaction computed. The hydrogen mass is found to be 0.164 kg and the specific volume is .91 m3/kg When this is combin ed with the tank pressure, th e thermodynamic state of the hydrogen can be found.

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148 0 700 1400 2100 232425262728 Time (hr)Volume (std liters) Figure 6-12 Total hydrogen volume in tank At the time the mass flow is shut off, the pressure is 12.6 psia, so a quick check of hydrogen properties shows the state point to be in the vapor region. At this point, no hydrogen liquid has been produced, just cold vapor, however as th e cryocooler continued to operate the vapor pressure continued to decrease and when the pressure reached the saturation point (11.89 psia) liquid droplets st arted to form. By the next morning the pressure had dropped to 3.78 psia, well inside the two-phase region. Another interesting point is where the hydrogen inside the heat pipe becomes saturated again, which is evident by the sharp decrease in heat pipe te mperature and change in the slope of the ullage temperature curves. Figure 6-13 shows this event in more detail. Hydrogen Densification Around 4:00 pm on June 25, the hydrogen flow was terminated and the cryocooler remained on overnight to continue to refrig erate the hydrogen remaini ng in the tank. As

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149 18 20 22 24 26 28 30 26.52727.52828.5 Time (hr) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-13 Heat pipe saturation was discussed above, the hydrogen was not yet saturated when the flow was terminated, but shortly thereafter it reached the satura ted state. The following morning the tank pressure and temperature had stabilized to an expected condition. The pressure was 3.88 psia and the temperatures varied between 16.5 K and 18.7 K. There were several unexplained jumps in temperature and pressure measurements, but at this time it is undetermined whether this represents some phys ical process or an error in the way the data files were manipulated. In either case, the state of the fl uid is known at this time. The specific volume is still 0.91 m3/kg, since no changes occurred either to the system volume or the mass overnight. The saturated vapor specific volume is 2.49 m3/kg, and the saturated liquid specific volume is 0.0134 m3 /kg. The quality of the fluid is then found to be 36% or a total liquid mass of 0.06 kg. The density of the saturated liquid is 74.7 kg/m3, an increase of 5.5% over the norma l boiling point of the liquid. Figure 6-14 below shows temperature and pressure prof iles during this densification period.

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150 0 2 4 6 8 10 12 14 16 18 20 579111315 Time (hr) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) Figure 6-14 Overnight densification The system was allowed to continue to pump down over the weekend, with the exception being a quick period on June 28 when the cryocooler was turned off for a relocation of the system within the lab for safety purposes. The system warmed up slightly during this time, with the largest incr ease in temperature being in the cold head. This is expected since the temperature measur ement that is most susceptible to increases is the cold head due to conduction down the length of the regene rator portion of the cryocooler. The warm up data is shown in Figure 6-15 below. From this figure it is obvious the heat pipe never reached the unsat urated state. On June 29, liquefaction operations restarted, as shown in Figure 6-16. This operation was slightly different from before since there was a small amount of li quid already in the tank and the system was completely chilled down, as opposed to the ha rd vacuum on the system prior to the start of the first operation. As such, there were slightly different temper ature profiles. Note that the lowest temperature measurements did not increase at nearly the same rate as the

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151 upper measurements. This is probably due to th e thermal mass of refrigeration stored in the system from cooling overnight. The heat pipe temperature and T4 and T5 on the rake did not increase above 21 K, in fact T5 seem ed to stay within the temperature saturation 0 5 10 15 20 25 30 35 40 45 50 4949.55050.551 Time (hr) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-15 System relocation warm up line indicating it remained in liquid. Refere nce Figure 6-17 for details. The heat pipe remained partially filled with liquid, allowing for maximum heat transf er to the bottom of the tank. Again, there was some trouble main taining a constant hydr ogen flow rate. At the end of the day, integration showed the total volume of hydrogen inside the tank had risen to 3153 standard liters. There was some behavior in the tank that was not expected. Once the hydrogen gas flow was terminated, the pressure began to decrease as expected, since the cryocooler was condensing the ullage gas. However, the ulla ge temperatures fairly quickly collapsed to the saturated state, equaling the liquid temperature. The ullage

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152 0 5 10 15 20 25 30 35 40 45 012345 Time (hr) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Mdot (slm) Figure 6-16 Continuing liquefaction 0 5 10 15 20 25 01234 Time (hr) P (psia) T5 (K) T6 (K) Figure 6-17 Liquid temperature and pressure saturation curve remained saturated for approximately 30 mi nutes, and then the expected temperature gradients began to reappear in the ullage. Th is behavior was not observed on the first day, due to the fact that there was still no liqui d in the tank at the time the gas flow was

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153 terminated. Similar behavior was observed to some extent on all subsequent days the hydrogen flow was terminated. Figure 6-18 be low shows this ullage collapse graphically. 16 17 18 19 20 21 22 23 24 3.754.254.755.255.756.256.75 Time (hr) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-18 Ullage collapse Hydrogen flow and liquefaction operations continued for the next several days on first shift only, with only slight changes in data. Plots are shown in Figures 6-19 and 6-20 for the next two days. At the end of these two days, a total of 7565 standard liters of hydrogen had been liquefied. At this point, hydrogen flow was terminated for the next week, and densification operations continue d around the clock. After one week of densification, the stabilized temperature at the bottom of the system remained 16.7 K, roughly equal to the temperature achieved at the end of an overnight chilldown. A second bottle of gaseous hydrogen was purchas ed and connected to the system, and liquefaction operations recommenced. Following another week of de nsification, the liquefac tion operations began again on July 12. A second K-bottle of gaseous hydrogen was connected. Liquefaction

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154 0 5 10 15 20 25 30 35 212631364146 Time (hr) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Mdot (slm) Figure 6-19 Liquefaction on 6-30-04 0 5 10 15 20 25 30 35 46485052 Time (hr) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Mdot (slm) Figure 6-20 Liquefaction on 7-1-04 occurred on first shift all five days that week, with very similar temperature and pressure profiles as was recorded previ ously. At the end of the w eek, a total of 15,214 standard liters of gaseous hydrogen had been liquefied, or 1.25 kg. This is eq ual to 17.65 liters of

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155 liquid in the tank. At this time it was decide d no further liquefaction would be allowed in the small laboratory that was being used, due to safety constraints. Further liquefaction would occur once the outdoor hydrogen test facility was completed. Zero Boil Off Although no further liquefaction was allowed, the system remained partially full of liquid hydrogen. Testing was performed to determine the minimum cryocooler run time necessary to maintain the hydrogen in the tank without boil off losses. This was done for two reasons; first, to minimize the energy expended, and second, to minimize the excessive noise in the lab that the G-M refr igerator caused. Figure 6-21 shows the typical temperature and pressure prof iles of the ZBO testing for two days. The cryocooler was turned off for 8 to 9 hours on first shift, then turned back on at the start of second shift and allowed to cool overnight. Pressure rise in the tank reached 33 psia, below the relief valve set point, so no venti ng occurred. The cryocooler ge nerally took about 7 hours to recondense the boil-off and achieve the dens ified condition again. Since there was no way to turn on and off the cryocooler automa tically, the cooler continued to operated over third shift and was then turned off at the start of the next first shift. Future performance upgrades to the system will include a control system to automatically start the cryocooler when the pressure reaches a se t point (33 psia), and turn off the cooler when the low point pressure is reached. The ZBO operations continued until August 12, when securing for Hurricane Charley dictated the system be drained and purged of H2. Looking at a plot of the non-dimensional te mperature profile for a shorter time period gives a better physical understanding of the heat transfer processes taking place inside the tank. From an energy balance of a defined region inside the tank, assuming no mixing, the functional dependence of the non-di mensional temperature (T*) becomes

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156 ) *, ( Bi Fo x f T 6-1 where Fo is the Fourrier numb er and Bi is the Biot number. This functional dependence 0 20 40 60 80 100 120 140 010203040 Time (hr) P (psia) T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T8 (K) Figure 6-21 Zero boil off operations can be found knowing the exact geometry of the system. The geometry of the vapor region is a cylinder with variable temperatures up the length of the wall and a constant warm temperature at the top of the tank. For this case, T1* thru T4* exhibit the same behavior since they are all in the same va por region and only the difference in location gives a variation in temperature. T8* is influenced more by conduction down the cryocooler and has different temperature profil es. Similarly T5* and T6* are both in the liquid region and the heat transfer mechanis m also is different than the vapor region.

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157 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 222426283032 Time (hr)(T-Ti)/(Tf-Ti) T1* T2* T3* T4* T5* T6* T8* Figure 6-22 Non-dimensional thermal stra tification during se lf pressurization Measurement Uncertainty Analysis Any well-executed experiment must incl ude accounting for uncertainty in the measurements. These errors manifest themselv es in two ways, bias errors and precision errors. Bias errors are fixed, constant com ponents of the total error, whereas precision errors are random and due to repeatability of measurements Although bias errors are often thought to be eliminated by calibration of the instrument s, there are s till installation bias errors present. In this case, these in stallation bias errors for the calibrated silicon diode temperature measurements come from an imperfect heat exch ange with the surface they are bonded to.(67) The main focus of this chapter is to obtain a general knowledge of the thermodynamic behavior of hydrogen in an inte grated refrigeration and storage system. This focus means much of the work is an examination of data collected for the thermodynamic variables, and not as much emphasis is placed on data reduction equations where errors and uncertainty can pr opagate. This simplifies the uncertainty

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158 analysis. For example, two primary propertie s to be measured are the temperature and pressure, and the instrumentation vendor has provided a calibration report for both of these measurements. For example, the pressure is calibrated to an accuracy of +/0.05 psia. There is also a bias error associated with the analog to digital signal. With a 16-bit analog to digital converter, there is a preci sion bias of approximately 0.00153 psia. The addition of these individual uncertainties gives the overall measurement uncertainty. Knowing the uncertainty, error bars in the y dire ction can be added to these plots. Figure 6-23 is another view of Figure 6-21 (ZBO opera tions), with only T6 and the tank pressure shown, and the measurement uncertainty bars are included. Figure 6-24 shows these error bars for the pressure and temperature (T6) respectively for a blown up section of Figure 6-23. From this it is apparent that the uncertainty in these m easurements is so small, it is not visible in the “big picture” plots that make up the bulk of this chapter. 0 20 40 60 80 100 120 140 010203040 Time (hr) P (psia) T6 (K) Figure 6-23 ZBO operations with P and T error bars

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159 16.5 16.7 16.9 17.1 17.3 17.5 17.7 17.9 00.20.40.60.81 Time (hr)T6 (K) 4 4.5 5 5.5 6 6.5 7 7.5 8 00.20.40.60.81 Time (hr)Pressure (psia) Figure 6-24 Expanded section plot s of P and T with error bars There are several places in th is chapter where data reduc tion calculations are made. In these cases the uncertainty can pr opagate into the derived expressions.(68) An example is Figure 6-24, which shows the total mass in th e tank as it is calculated by the expression dt m M* 6-2 Knowing the mass flow rate measurement has a calibration uncertainty of 0.05 slm, and the A/D conversion bias is 0.002 slm, the total uncertainty of the mass flow is +/-0.052 slm. Adding these uncertainties into the Ex cel database and integr ating over time, the total uncertainty of the hydrogen mass can be calculated. Figure 6-25 is a revised graph of Figure 6-12, with an upper and lower uncertainty plotted. From this analysis, there is a final uncertainty of 1.6% in the tank mass ov er the period of time considered. This total uncertainty is much greater than the uncertain ty at any one specific measurement point, since the errors can propagate over time.

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160 0 700 1400 2100 23242526272829 Time (hr)Hydrogen Volume (std liters) Figure 6-25. Mass uncertainty estimates

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161 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS A novel hydrogen liquefaction, storage and distribution system has been proposed for space launch vehicle servicing applications This system integrates a closed cycle helium refrigerator into the liquid space of th e storage tank, removing the heat leak into the system from the surroundings and controlling the state of the hydrogen by varying the total heat interactions. This offers a potent ial for reduced operations cost combined with advanced servicing capabilities. Chapter 1 provides background research in the current state of the art in liquid hydrogen storage. Present systems lose up to 50% of the liquid hydrogen per year. These losses are a byproduct of normal heat leak into the system, h eat leak via tanker transportation operations, or chill down of wa rm parts of the system. Research into past zero boil-off studies have been conducted, and economic analysis applied future launch vehicles have been presented. In addition, on site liquefaction gives greater flexibility to the entire propellant supply chain, minimizing the reliance on commercial liquid hydrogen suppliers. Current and proposed methods of propellant conditioning, or densification, were also discussed. Chapter 2 details the concept of the proposed system and the economic and safety advantages over the current state of the ar t. The behavior of the system is addressed from a qualitative st andpoint and potential issues are addressed. A projected vision of what a full-scale system would be is also presented. Chapter 3 provides the quantitative analys is of the system behavior from the thermodynamic perspective. First, an Excel based model of the storage system

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162 thermodynamic behavior is developed. This model uses the integral forms of the conservation of mass and cons ervation of energy and makes an assumption of bulk fluid properties in the liquid and vapor region. The heat leak is modeled using the modified Lockheed Martin MLI correlation combined with Fourier’s law of conduction down solid supports. The state of the liquid and gas in the system is modeled for a variety of system operations. Where possible, the model is co mpared to experimental data gathered in Chapter 6. Discrepancies in the data and th e model are noted. These discrepancies are attributed to assumptions made in the heat leak calculation (assum ption of isothermal system) and transient effects that are no t accounted for by the bulk fluid property assumption. A two-part correction factor is pr oposed to account for these changes. First, a linear correction factor with respect to system liquid level is added, then, a time dependent logarithmic correction is added to a ccount for transient eff ects. This proposed factor is added to the model and predicted results match experimental results more accurately. This model can be used for gr ound or space based mission design, including estimating on orbit hold times, required cooling capacities for zero boil off, and predictions of propellant densification low temperature load points. Second, a thermodynamic model of the pro posed liquefaction cycle is developed. This is a novel cycle that achieves cooli ng in a combined manner by expanding hydrogen at high pressure while other steps in the cycle remove heat via a closed loop helium refrigeration cycle. The details of the cycl e are provided, and an Excel based model is developed. This model uses a number of in puts, including heat exchanger, compressor, and turbine efficiencies, variable temper ature storage states, and input hydrogen flowrates. The model then iterates to find problem solutions for a range of variables

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163 including hydrogen and helium compression ratio, helium high and low temperature turbine mass flow rates, and required inte rmediate temperatures downstream of the recuperative heat exchanger. The model shows there is a small range of acceptable operating temperatures for a given set of hyd rogen and helium pressures, and the favored operating pressure for this cycle is around 1200 kPa for the helium side and 2200 kPa for the hydrogen side. The last section of Chapter 3 addresses th e true physical behavior of the hydrogen in the storage system. An energy balance be tween the heat leak across the insulation and the free convection heat leak inside the tank shows normal temperature gradients between the walls and the fluid is less than 0.1K. During transient operations, this gradient may increase. Using this temperature gradient, pr edictions are made on the heat transfer and hydrodynamic flow regimes. The Reynol ds number and the Grashof number are computed for this liquid an d vapor regions. Then, the fu ll conservation equations in differential form are presented, and using an order of magnitude an alysis the equations are simplified. These equations are transien t and 2 dimensional, and include a viscous boundary layer region and an inviscid core flow. Finally, a unique form of these equations is presented in dimensionless form using dimensional constants derived from the initial state of the fluid and the thermal boundary conditio ns. The significance of the choice of dimensional constants and dime nsionless parameters is discussed. Chapters 4, 5, and 6 focus on an experi mental apparatus designed to test the proposed system. Chapter 4 is a safety an alysis of liquid hydrogen systems, with a particular emphasis on densified fluids cooled below the normal boiling point. Previously unpublished data on subcooled hydr ogen explosive equivale nce is included.

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164 Chapter 5 details the experimental system de sign and fabrication effort. Several unique design features were needed to accommodate the densified hydrogen, including redesign of the self-pressurization system and design of a liquid hydrogen heat exchanger. Finally Chapter 6 shows the results of approximatel y 6 weeks worth of testing, including data analysis on hydrogen liquefaction, densific ation, and zero boil-off operations. Pressure control via mass injection is achieved during some liquefaction operations. At the end of this effort, the conclusion that has been reached is the integrated refrigeration and storage system as proposed within appears to offer many benefits. Numerical analysis and experime ntal data confirm that the sy stem behavior is acceptable. A number of recommendations can be made to further this effort in the future. First, a detailed computational fluid dyna mics model should be developed to more accurately predict system behavi or. Prior to this model development, experimentation to determine heat and mass transfer coefficients of liquid hydrogen in the natural convection mode should be made. The verification of these transport properties will allow for greater model fidelity. Once more accurate anal ysis and experimentation are done at this level, a large-scale testbed (greater than 10, 000 gallons) should be developed. This will allow further testing of operational concepts that could not be completed in the small testbed due to size, funding and safety constraints, including recovery of chill down losses, pressurization with non condensable ga sses, methods of temperature stratification management, and efficient liquefaction includ ing staged refrigeration and ortho-to-para hydrogen conversion at multiple temperatures.

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165 APPENDIX A CRYOSTAT SYSTEM SPECIFICATION Liquid Hydrogen Dewar and Cryocooler Assembly Configuration and Performance Requirements General: The entire assembly shall be de signed to store subc ooled liquid hydrogen, with a maximum pressure of 52 psia and a minimum temperature of 14K, and shall be considered portable. A cryocooler cold head shall be integrated into the dewar to provide refrigeration for subcooling of the NBP hydrogen. This entire assembly shall be designed for, and suitable for use with liquid and/or ga seous hydrogen service. Refer to Fig. 1 for representative configuration. The assembly shall be designed and built to allow for maximum flexibility to access and modify internal components, including access to disconnect the pressurization coil. Size and dimensions: Inner tank volume sha ll be between 140 and 150 liters. Four liquid/gas interface ports shall be provided fo r connection with the experimental system. Liquid fill/withdraw port shall be inch ID vacuum jacket line with manual shut-off valve at the end. Vent port shall be 1/2 in ch line with manual shut-off valve at the end. Liquefaction supply port shall be 3/8 inch line with manual shut off valve at the end. Gas supply port shall be 3/8 inch line with ma nual shut-off valve at the end. Mechanical connections on valve outlets are TBD. Pressurization: Dewar assembly shall have the capability of self-pressurization thru internal vaporizer. Pressure level sha ll be adjustable thru a vaporizer regulator.

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166 Overpressurization protection: Dewar inner vessel shall be equipped with relief valve to prevent overpressurization. RV sha ll be set at maximum ope rating pressure. RV shall be in line type to allow for connection to external vent system. Capacity of relief system shall be capable of relieving pressure buildup in the event of loss of vacuum. Dewar inner vessel shall be equipped with bu rst disk set at 116% of maximum operating pressure. Vacuum jacket: Vacuum annulus shall in clude spacers, multi-layer super-insulation (MLI), and a chemical gettering system. A su itable vacuum pump out port, preferably a 1 CF flange, standard for high vacuum use, shall be provided for the vacuum annulus. A vacuum relief valve shall be provided to ensure overpressurization of the vacuum annulus does not occur. Heat leak: Total assembly heat leak sha ll be minimized (10 W at 14 K or less) to reduce size of selected cryocooler assembly Radiation shielding such as LN2 jacket, vapor cooled shield, or mechanical cooling (cryocooler 1st stage) are acceptable if required to meet heat leak specification. Cryocooler interface: Cryocooler cold head shall be in the inner vessel to facilitate transfer of energy from the liquid hydrogen to the cryocooler. Cryocooler compressor shall be outside the vacuum annulus and can be located some small distance away from the assembly. Cryocooler shall be sized to provide at least 30W cooling at 20K. Cryocooler shall be optimized for long term reliable operation an d not necessarily for overall thermodynamic efficiency. Heat exchanger: A fin type heat exch anger shall be added to the cryocooler coldhead to increase surface area and allow for greater heat exchanger to the liquid

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167 hydrogen. One fin shall be hollow with perforations to allo w for connection to liquefaction supply line. I nstrumentation: Dewar shall be instrument ed to provide temperature profile of the liquid hydrogen. Temperature probe shall have sensors spaced at a minimum of every 4 inches. Temperature probe shall have the capability of quantifying liquid level. Additional temperature sensors shall be cap able of measuring cryocooler cold head temperature. Tank pressures shall be monitored using pressure transducer. Design, Fabrication, Inspection and Testing Requirements Inner Vessel: The inner ve ssel shall be designed, fa bricated, and tested in accordance with ASME Code, Section VIII, Di vision I for a design pressure of 52 psia, and a service temperature range of 14 K to 3 00 K. The inner vessel shall be designed to withstand an internal vacuum (0 psia) and ex ternal (vacuum jacket) pressure of 15 psia. Vacuum Jacket: VJ shall be designed, fa bricated, and tested in accordance with ASME Boiler and Pressure Vessel Code, Sec tion VIII and Section IX. For a service temperature of 14 K to 300 K, the VJ shall be designed for both 1) an internal vacuum (0 psia) and 15 psig external pressure, and 2) an internal pressure (the greater) of 35 psig or two times the VPR valve relief pressure and 0 psig external pressure. Bellows: Any bellows shall be designed, fabricated, and tested in accordance with ASME B31.3 and the Standards of the E xpansion Joint Manufacturers Association (EJMA). Normal movement shall not exceed 75% of the maximum rated movement for a design cycle life of 7,000 cycles. Materials: All dewar materials shall be 304/304L or 316/316L stainless steel, unless otherwise approved.

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168 Radiographic Testing: All vessel we lds shall be subject to 25% random radiographic testing. Do not use liquid penetrant on welds. Pressure Test: Pressure ve ssels shall be pressure tested in accordance with ASME Code, Section VIII except that a pneumatic pressure test shall not be at less than 125% of the design pressure. After a hydrostatic pressure test, component surfaces shall be completely dried and passivated. Cold Shock: Prior to leak test, the comp leted assembly shall be cold shocked with liquid nitrogen. After completion of cold shock test, assembly shall be allowed to return to ambient temperature, using an ambient nitr ogen purge if necessary. Moisture shall be prevented from forming on (the inside of) components as the assembly warms. Leak Test: The completed assembly shall be leaked tested by pressurizing process lines/component to 30 psig with (pure and dry) helium. During the test no leakage shall be detected using a helium mass spectrome ter connected to the vacuum annulus, previously evacuated to 0 psia. The helium mass spectrometer shall be calibrated to a sensitivity of 1x10-9 standard cubic centimeters per second (sccs). Final Cleaning: After the successful completion of all testing, the entire assembly shall be commercially oxygen cleaned (per standard “Linde” speci fication). Prior to shipping, with the assembly at ambient temp erature and at (or above) 0 psig, the vacuum level shall not significantly change (i.e., approx. 1 micron) over a 48 hour period, and shall be stable at less than 15 microns (micro-meters of Mercury). Submittals Fabrication and assembly drawings for assembly, including dimensions, line sizes/schedules, and material specifications.

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169 Vessel heat leak and design code calculations. Welding procedure specifications (WPS ’s), procedure qualification records (PQR’s), and welder perform ance qualifications (WPQ’s). Non-destructive test pe rsonnel qualifications. Mill test reports. Radiographic records, radiographs, and weld map. Test reports and certifications. Shipment Assembly shall be packaged for shipme nt such that the cleanliness level is maintained and to prevent moisture intrusion. Assembly shall be restrained from motion during shipment and evenly supported (no concen trated support loads) All ports shall be capped with the appropriate mating fitting. A ssembly shall be shipped with a nitrogen blanket pressure between 5 to 10 psig. The pressure port shall be equipped with an appropriate gauge and vent valve (for vent ing the assembly to ambient pressure upon arrival). An obvious and conspicuous caution, stating “CAUTION: ASSEMBLY UNDER POSITIVE PRESSURE”, shall be placed on the assembly for shipping (which will be immediately seen upon opening the shipping container, but able to be easily removed without damaging the assembly).

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170 LH2 GH2/GHe MLI FILL VLV VACUUM ANNULUS VAPORIZER REG VAPORIZER ISO VLV VENT VLV LIQUEFACTION SUPPLY VLV COPPER FINS COLD HEAD GAS SUPPLY VLV PROBE CRYOTRACKERSD SD SD SD SD SD SD SD SD SD RV BD P FLANGE HEAT PIPE RADIATION SHIELD CRYOCOOLER Figure A-1 System Specification Schematic

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171 APPENDIX B HEAT LEAK CALCULATION Radiation Tank Geometry Volume157,000cm3 Radius25.4cm Length64.7cmTOTAL Area15,600.0cm2 Insulation density11.8#/cmRadiation1.75W Insulation layers45#Neck2.424209W Warm boundary T300KTubes2.440476W Cold Boundary T20.2KCooler1.97W Insulation K1.121625W/m2Total8.58W Radiation H/L1.75W Conduction Neck ID20.32cm Thickness0.0381cm Length30.48cm Warm Boundary T300K Cold Boundary T20.2K Material304 K-h3060W/m K-c16.30W/m Heat leak2.424209W Feedthru #1Feedthru #3 ID0.9525cmID0.9525cm OD0.1244cmOD0.1244cm Length25.4cmLength25.4cm Warm Boundary T300KWarm Boundary T300K Cold Boundary T20.2KCold Boundary T20.2K Material304Material304 K-h3060W/mK-h3060W/m K-c16.30W/mK-c16.30W/m Heat leak0.581717WHeat leak0.581717W Feedthru #2Feedthru #4 ID1.59cmID0.9525cm OD0.1244cmOD0.1244cm Length25.4cmLength59.7cm Warm Boundary T300KWarm Boundary T300K Cold Boundary T20.2KCold Boundary T20.2K Material304Material304 K-h3060W/mK-h3060W/m K-c16.30W/mK-c16.30W/m Heat leak1.029544WHeat leak0.247498W

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172 APPENDIX C DENSIFICATION SAMPLE MODEL Initial Conditions P101kPa-63.322 T20.27K M5411g V150000cm3 Fluid n-hyd Heat leak8.80W PT h XhHrho-g M-g H-grho-f V M-fH-l t Q kPaK c m3J/gJg/cm3 m g /g Jg/cm3 m g / J / W 10120.270.0185-273.13-14778910.00134100.2164390.07085310.8-1494330-32.394 10020.230.0184-273.55-14801580.0013299.3162780.07085311.7-1496436-32.151 9920.200.0182-273.97-14824330.0013198.5161170.07095312.5-1498550-31.905 9820.160.0180-274.39-14847180.0013097.6159560.07095313.4-1500674-31.657 9720.130.0179-274.81-14870120.0012996.7157950.07105314.3-1502807-31.407 9620.100.0177-275.24-14893160.0012895.9156340.07105315.1-1504950-31.154 9520.060.0176-275.67-14916300.0012695.0154730.07105316.0-1507102-30.900 9420.030.0174-276.10-14939530.0012594.1153120.07115316.9-1509264-30.643 9319.990.0172-276.53-14962860.0012493.3151500.07115317.7-1511437-30.383 9219.960.0171-276.96-14986300.0012392.4149890.07125318.6-1513619-30.121 9119.920.0169-277.39-15009840.0012291.5148280.07125319.5-1515811-29.856 9019.880.0168-277.83-15033480.0012090.7146660.07125320.3-1518015-29.589 8919.850.0166-278.27-15057230.0011989.8145050.07135321.2-1520228-29.319 8819.810.0164-278.71-15081100.0011888.9143440.07135322.1-1522453-29.047 8719.770.0163-279.15-15105070.0011788.1141820.07145322.9-1524689-28.771 8619.740.0161-279.60-15129160.0011687.2140210.07145323.8-1526936-28.493 8519.700.0160-280.05-15153360.0011486.3138590.07145324.7-1529195-28.212 8419.660.0158-280.50-15177680.0011385.4136970.07155325.6-1531465-27.928 8319.620.0156-280.95-15202120.0011284.6135360.07155326.4-1533747-27.641 8219.580.0155-281.40-15226680.0011183.7133740.07165327.3-1536042-27.351 8119.540.0153-281.86-15251370.0011082.8132120.07165328.2-1538349-27.058 8019.500.0151-282.32-15276180.0010881.9130510.07175329.1-1540669-26.762 7919.460.0150-282.78-15301130.0010781.0128890.07175330.0-1543001-26.462 7819.420.0148-283.24-15326200.0010680.1127270.07175330.9-1545347-26.159 7719.380.0146-283.71-15351410.0010579.3125650.07185331.7-1547706-25.852 7619.340.0145-284.18-15376760.0010378.4124030.07185332.6-1550079-25.542 7519.300.0143-284.65-15402250.0010277.5122410.07195333.5-1552467-25.229 7419.260.0142-285.12-15427890.0010176.6120790.07195334.4-1554868-24.911 7319.220.0140-285.60-15453670.0010075.7119170.07205335.3-1557284-24.590 0 20 40 60 80 100 120 05000100001500020000Time (s)Press (kPa)10 12 14 16 18 20 22Temp (K) Press Temp

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173 APPENDIX D ACRONYMS AND SYMBOLS Acronyms A/D analog to digital AIAA American Institute of Aeronautics and Astronautics ASME American Society of Mechanical Engineers CTE coefficient of thermal expansion daq data acquisition DoT Department of Transportation ET External Tank FOM Figure of Merit FSEC Florida Solar Energy Center G-M Gifford McMahon GRC Glenn Research Center GSE ground support equipment HHV higher heating value HX heat exchanger ISRU In Situ Resource Utilization J-T Joule-Thompson KISS keep it simple, stupid KSC Kennedy Space Center LC launch complex LEO low earth orbit LFL lower flammability limit LH2 liquid hydrogen LHS left hand side LN2 liquid nitrogen LOX liquid oxygen LRU line replacement unit MAWP maximum allowable working pressure MLI multi layer insulation MOP maximum operating pressure NASA National Aeronautics and Space Administration NBP normal boiling point NFPA National Fire Protection Association NSS NASA safety standards PBU pressure build up Q-D quantity-distance RHS right hand side RLV reusable launch vehicle

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174 SBIR Small Business Innovative Research SS stainless steel UFL upper flammability limit USAF United States Air Force VJ vacuum jacket ZBO zero boil-off Units g grams gpm gallons per minute J joules K degrees Kelvin kg kilogram kJ kilojoules kPa kilopascals kW kilowatts kW-hr kilowatt-hour m3 cubic meters psi pounds per square inch psia pounds per square inch absolute psig pounds per square inch gauge sccm standard cubic centimeters per minute SLPM standard liters per minute Symbols A Area E energy F force vector yg gravitational acceleration Gr Grashof number h specific enthalpy h heat transfer coefficient k thermal conductivity L characteristic length m mass flow rate m mass Nu Nusselt number P pressure Pr Prandtl number Q heat transfer rate refQ refrigeration heat transfer

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175 HLQ heat leak radQ radiation heat transfer conQ conduction heat transfer Ra Rayleigh number Re Reynolds number s specific entropy t time T temperature u velocity in horizontal direction v velocity in vertical direction V volume V velocity vector W work y liquid yield % thermal diffusivity volumetric expansion coefficient specific heat ratio coefficient of viscosity density kinematic viscosity

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176 LIST OF REFERENCES 1. Peschka, W., Liquid Hydrogen – Fuel of the Future, Springer-Verlag Wein, New York, NY, 1992 2. Culp, A.W., Principles of Energy Conversion, 2nd Edition, McGraw-Hill Inc., New York, NY, 1991 3. Sutton, G.P., and Bilbarz, O.; Rocket Propulsion Elements; Wiley Interscience, New York, NY, 2001 4. Rudiger, H., and Seifers, H.; Liquid Hydr ogen Storage System for Urban Bus; .; Hydrogen Energy Progress X; Proceedings of the 10th World Hydrogen Energy Conference; Internationa l Association of Hydrog en Energy, Orlando FL,1994 5. Kocer, K., and Veziroglu, T.N.; Liquid Hydrogen Powered Commercial Aircraft; Hydrogen Energy Progress X; Proceedings of the 10th World Hydrogen Energy Conference; International Association of Hydrogen Energy, Orlando FL, 1994 6. GasPak V 3.41, Thermophysical and Transport Properties Database, Horizon Technologies, 2003 7. Flynn, T.M., Cryogenic Engineering, Marcel Dekker Inc., New York, NY, 1997 8. West, J.E., The Economics of Small to Medium Liquid Hydrogen Facilities, CryoGas International, pg 28-33, May 2003 9. Barron, R.F., Cryogenic Systems 2nd Edition, Oxford University Press, New York, NY, 1985 10. Hynek, S. and Fuller, W., Hydrogen Storag e within the Infrastructure, Proceedings of the 10th World Hydrogen Energy Conferen ce, International Association of Hydrogen Energy, Orlando FL, 1994 11. Gen H2, CryoGas International, pg 45, May 2003 12. Pehr, K., Aspects of Safety and Acceptance of LH2 Tank Systems in Passenger Cars, Proceedings of the 10th World Hydrogen Energy C onference, International Association of Hydrogen Energy, 1Orlando FL, 994 13. Methods of Distributed Scale Liquefaction for Natural Gas and Hydrogen; Professional Development Short Co urse; Prometheus Energy Company

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177 14. Strobridge, T.R.; Cryogenic Refrigerator s – An Updated Survey; NBS Tech Note 655; Boulder CO, 1974 15. Add on Study to Prepare Design Details for a Re-Liquefier on the Complex 39 LH2 Tank, Martin Marietta Corp. 1977 16. Rosso, M.J., and Golben, P.M., Capture of Liquid Hydrogen Boil-Off with Metal Hydride Absorbers, Ergenics Inc., SBIR Final Report, 1986 17. Egan, G.J., and Gier, H.L., Capture an d Reliquefaction of Hydrogen Boiloff at Shuttle Launch Site, Final Report, NAS10-11401, Hydrogen Consultants, SBIR Final Report, 1991 18. Notardonato, W.U., Baik, J.H. and Mc Intosh, G.E, Operational Testing of Densified Hydrogen Using GM Refrigerati on, Advances in Cryogenic Engineering, Volume 49, pg 64-71, Plenum Publishers, New York NY, 2004 19. Larson, Wiley and Pranke, Linda; Human Spaceflight – Mission Analysis and Design; McGraw Hill, New York NY, 2002 20. Investigation of External Refrigeration Systems for Long Term Cryogenic Storage, Lockheed Missiles and Space Report A981632, 1971 21. Giellis, R.T., Long Term Cryogenic Stor age Study, US Air Force, AFRPL TR-82071 22. Kittel, P., Cryocoolers for the Human and Robotic Exploration of Mars, Cryocoolers10, pg 815-821, Plen um Press, New York NY, 1999 23. Plachta, D.W., Hybrid Thermal Control Te sting of a Cryogenic Propellant Tank, Advances In Cryogenic Engineering Volu me 45, pg 465-472, Plenum Press, New York NY, 2000 24. Hastings, L.J., An Overview of NA SA Efforts on Zero Boiloff Storage of Cryogenic Propellants, Cryogenics 41, pg 833-839, Elsevier Science Ltd., New York NY, 2002 25. Plachta, D.W., Results of an Advanced Development Zero Boil-Off Cryogenic Propellant Storage Test, NASA TM-2004-213390, 2004 26. Kittel, P., Propellant Preservation Using Re -Liquefiers, Cryogenics 41, pg 841-844, Elsevier Science Ltd., New York NY, 2002 27. Lak, T., and Lozano, M., Advancement in Cryogenic Propulsion System Performance Through Propellant De nsification, AIAA-96-3123, 1996 28. Ewart, R., and Dergance, R., “Cryogenic Propellant Densification Study”, Final Report NASA Lewis Research Center Contract Number NAS3-21014, 1977

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178 29. DeWitt, R,. and Hardy, T., “Slush Hydrogen Technology Development for Application to the National Aero space Plane”, NASA TM 102315, 1989 30. Tomsik, T., “Recent Advances and Ap plications in Cryogenic Propellant Densification Technology”, NASA TM-2000-209941, 2000 31. Notardonato, W.U.; NASA Strategic Launc h Initiative Propellant Densification Program, Results of the Base Period Work and Future Plans, Proceedings of the 19th International Cryogenic Engineeri ng Conference; pg 533-537, Narosa Publishing, New Delhi India, 2002 32. Notardonato, W., “Densified Propellant Operability Analysis”, NASA KSC White Paper, 2002 33. Notardonato, W.U., Propellant Densifica tion for the Human Exploration of Mars, Proceedings of AIAA 37th Joint Propulsion Conferen ce, Indianapolis IN, 2002 34. Rhodes, R; Propellant Cost Fact ors: NASA KSC White Paper; 2003 35. NSTS 3600 Launch Commit Criteria; NASA KSC, 2005 36. Gisteau-Baguer, G.; Helium Refrigerat ion; Cryogenic Society of America; Chicago, IL, 2004 37. Filina, N.N., and Weisend, J.G.; Cryogenic Two Phase Flow; Cambridge University Press; New York NY, 1996 38. Anderson, J.D.; Modern Compressible Flow; McGraw Hill; New York NY, 1990 39. Li, X., and Xu, L.; Investigation on Performances of Non-Loss Storage for Cryogenic Liquefied Gas; Cryogenics 44 pg 357; 2004 40. Tholmes, L.A. and Schwartz, S.H.; Th e Thermodynamics of Space Storage of Liquid Propellants; Douglas Aircra ft Company Internal Report ;1967 41. Younglove, B.A.; Thermophysical Proper ties of Fluids: Argon, Ethylene, Parahydrogen, Nitrogen, Nitrogen Trifluor ide, and Oxygen; J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 1, pp. 1-11, 1982 42. Spadley, I.E., Nast, T.C., and Frank, D.J. ; Experimental Studies of MLI Systems at Very Low Boundary Temperatures; Advan ces in Cryogenic Engineering, Vol.35; pg 407-413, Plenum 1990 43. McMordie, R.K.; Steady State Conduction with Variable Thermal Conductivity; Journal of Heat Transfer 84: pg 92-93 44. White, F.M.; Viscous Fluid Flow; McGraw Hill; New York NY, 1991

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179 45. Majumdar, A., and Steadman, T.; Numerical Modeling of Thermal Performance of Cryogenic Test Tank at Kennedy Sp ace Center; CESAT Interim Report, 2005 46. Tannehill, J.C., Anderson, D.A., and Pletcher, R.H.; Computational Fluid Mechanics and Heat Transfer; Taylor and Francis; New York NY, 1997 47. White, F.M.; Fluid Mechanics; McGraw Hill; New York NY, 1999 48. Oosthuizen, P.H., and Naylor, D.; Intr oduction to Convective Heat Transfer Analysis; McGraw Hill; New York NY, 1999 49. Nunn, R.H,; Intermediate Fluid Mechanics; Hemisphere Publishing Corporation; New York NY, 1989 50. Bejan, A.; Convection Heat Tran sfer; Wiley, New York NY, 1984 51. NSS 1740.16 NASA safety Standard fo r Hydrogen and Hydrogen Systems; 1995 52. NFPA 50B; Standard for Liquid Hydrog en Systems at Consumer Sites; 1999 Edition 53. CFR 29 1910.103; Occupational Health and Safety Standards 2206, Hydrogen; 1981 54. Title 49 CFR Parts 171-190; US Departme nt of Transportation; Specifications and Regulations 55. Explosive Equivalence of Subcooled Li quid Hydrogen and Liquid Oxygen; USAF Report Number 07805-004-001-1; 2001 56. KSC STD Z-0009; Standard for Design of Cryogenic Ground Support Equipment; 1973 57. Scurlock, R.; Low Loss Tanks and Dewars; Cryogenic Society of America; Chicago IL, 2004 58. Churchill, S.W., and Chu, H.S,; Correlating equations for Laminar and Turbulent Free Convection from a Vertical Plate; International Journal of Heat and Mass Transfer, Vol 18, p1323; 1975 59. Combivac CM31 Operating Instructions; Leybold Vacuum 60. Model 218 Temperature MonitorUsers Manual; Lake Shore Cryotronics, Inc. 61. Calibration Report 376905; Lake Shore Cryotronics, Inc. 62. Calibration Report 20002647, Taber Industries

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180 63. Operations and Maintenance Manual -G-M Cryocooler AL330 and Helium Compressor CP970; Cryomech Inc 64. Hansen, S.; Leaks: The Good, the Bad, and the Ugly; Bell Jar, Volume 7, No. 1 Winter 1998 65. MKS 358C Mass Flow Meter Instru ction Manual; MKS Instruments 66. Jacobs, R.B.; Liquid Requirements for the Cool-Down of Cryogenic Equipment; Advances in Cryogenic Engineering, Vol. 8, Plenum Press 67. Coleman, H.W., and Steel, W.G.; Experimentation and Uncertainty Analysis for Engineers; Wiley Interscience, New York, NY, 1989 68. Uhl, V.W., and Lowthian, W.E.; Uncertai nty Analysis for Engineers; American Institute of Chemical Engineers; New York, NY, 1982 69. Exploration Crew Transportation Syst em Requirements Document; Version Preliminary – Revision B 8 Nov 2004

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181 BIOGRAPHICAL SKETCH William Notardonato is a Mechanical Engineer working for NASA at Kennedy Space Center (KSC). Mr. Notardonato’s specialty is design and development of advanced cryogenic systems, with an em phasis on thermodynamic control of liquid hydrogen. He has been working at KSC since 1988, and has held a variety of jobs in different fluid systems, including hydraulics, pneumatics, life support, hypergolics, and cryogenics. Mr. Notardonato earned a bachelor’s degr ee in aeronautical e ngineering from the Ohio State University in 1988. After join ing NASA, he earned a master’s degree in mechanical engineering from the University of Central Florida in 1992. He was accepted for a KSC Graduate Fellowship and attended cla sses at the University of Florida in 2000. Since that time, he has been working on hi s dissertation part time while keeping his present duties at work. Mr. Notardonato has published 10 papers relating to cryogenics and advanced materials testing.


Permanent Link: http://ufdc.ufl.edu/UFE0013786/00001

Material Information

Title: Analysis and testing of an integrated refrigeration and storage system for liquid hydrogen zero boil-off, liquefaction, and densification
Physical Description: Mixed Material
Language: English
Creator: Notardonato, William Usilton ( Dissertant )
Sherif, Sherif Ahmed ( Thesis advisor )
Peterson, Dr. ( Reviewer )
Chung, Dr. ( Reviewer )
Ingley, Skip ( Reviewer )
Chow, Dr. ( Reviewer )
Sullivan, Dr ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Mechanical Engineering thesis, Ph. D.
Dissertations, Academic -- UF -- Mechanical and Aerospace Engineering

Notes

Abstract: While hydrogen was first liquefied in the laboratory by Sir James Dewar in 1898, it was not until the beginning of the space age in the 1950s that large-scale production of liquid hydrogen was common. Since then, the methods used by NASA to produce, liquefy, store and distribute hydrogen for launch vehicle applications have not changed. Specifically, gaseous hydrogen is produced from natural gas, liquefied in large scale plants by performing external work on the gas and then expanding it, transported to the launch site via tanker trucks and stored in large ground tanks in the saturated state until it is loaded into the vehicle during launch countdown. During the process, heat leak and tank pressurization create boil-off losses, and chill-down of the transport lines cause more product losses. Other handling issues, including low liquid density, large thermal transients, leakage and safety concerns, and two phase flow problems have given liquid hydrogen a reputation for being a difficult fluid to store and control. This dissertation proposes a novel method of liquefying and storing hydrogen by incorporating a closed-cycle helium refrigerator into the storage tank. There are numerous advantages to this system. Localized production and liquefaction eliminates the need for transportation of hazardous liquid hydrogen, minimizes heat flow into the system, and reduces the number of personnel required at the launch site. Proper design of the refrigerator also allows for densification of the liquid, increasing the amount of propellant loaded into the flight tank. In addition, subcooling below the normal boiling point allows the liquid to store more refrigeration energy, leading to less boil off losses or eliminating boil off completely, and possible allowing for recovery of chill down losses. Subcooled propellants also provide greater thermal margin before onset of evaporation and two-phase flow. Details of these performance and economic benefits are provided in Chapter 2. While there are benefits, refrigerated and subcooled cryogens behave in a different manner than saturated liquids. These behavior issues must be investigated prior to large-scale incorporation in future launch systems. The conservation equations have been presented, and simplification of these equations in a 2-dimensional transient mass and energy model has been developed. Chapter 3 presents some results of the predicted behavior. A small testbed has also been proposed, designed, and fabricated for experimental validation of this model, and initial testing has occurred to validate the proposed concepts of liquefaction, zero boil off and densification. Results of this initial round of tests are provided in Chapter 6.
Subject: densification, hydrogen, liquefaction, zbo
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 195 pages.
General Note: Includes vita.
Thesis: Thesis (Ph. D.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 003757749
System ID: UFE0013786:00001

Permanent Link: http://ufdc.ufl.edu/UFE0013786/00001

Material Information

Title: Analysis and testing of an integrated refrigeration and storage system for liquid hydrogen zero boil-off, liquefaction, and densification
Physical Description: Mixed Material
Language: English
Creator: Notardonato, William Usilton ( Dissertant )
Sherif, Sherif Ahmed ( Thesis advisor )
Peterson, Dr. ( Reviewer )
Chung, Dr. ( Reviewer )
Ingley, Skip ( Reviewer )
Chow, Dr. ( Reviewer )
Sullivan, Dr ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Mechanical Engineering thesis, Ph. D.
Dissertations, Academic -- UF -- Mechanical and Aerospace Engineering

Notes

Abstract: While hydrogen was first liquefied in the laboratory by Sir James Dewar in 1898, it was not until the beginning of the space age in the 1950s that large-scale production of liquid hydrogen was common. Since then, the methods used by NASA to produce, liquefy, store and distribute hydrogen for launch vehicle applications have not changed. Specifically, gaseous hydrogen is produced from natural gas, liquefied in large scale plants by performing external work on the gas and then expanding it, transported to the launch site via tanker trucks and stored in large ground tanks in the saturated state until it is loaded into the vehicle during launch countdown. During the process, heat leak and tank pressurization create boil-off losses, and chill-down of the transport lines cause more product losses. Other handling issues, including low liquid density, large thermal transients, leakage and safety concerns, and two phase flow problems have given liquid hydrogen a reputation for being a difficult fluid to store and control. This dissertation proposes a novel method of liquefying and storing hydrogen by incorporating a closed-cycle helium refrigerator into the storage tank. There are numerous advantages to this system. Localized production and liquefaction eliminates the need for transportation of hazardous liquid hydrogen, minimizes heat flow into the system, and reduces the number of personnel required at the launch site. Proper design of the refrigerator also allows for densification of the liquid, increasing the amount of propellant loaded into the flight tank. In addition, subcooling below the normal boiling point allows the liquid to store more refrigeration energy, leading to less boil off losses or eliminating boil off completely, and possible allowing for recovery of chill down losses. Subcooled propellants also provide greater thermal margin before onset of evaporation and two-phase flow. Details of these performance and economic benefits are provided in Chapter 2. While there are benefits, refrigerated and subcooled cryogens behave in a different manner than saturated liquids. These behavior issues must be investigated prior to large-scale incorporation in future launch systems. The conservation equations have been presented, and simplification of these equations in a 2-dimensional transient mass and energy model has been developed. Chapter 3 presents some results of the predicted behavior. A small testbed has also been proposed, designed, and fabricated for experimental validation of this model, and initial testing has occurred to validate the proposed concepts of liquefaction, zero boil off and densification. Results of this initial round of tests are provided in Chapter 6.
Subject: densification, hydrogen, liquefaction, zbo
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 195 pages.
General Note: Includes vita.
Thesis: Thesis (Ph. D.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 003757749
System ID: UFE0013786:00001


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Table of Contents
    Title Page
        Page i
        Page ii
    Dedication
        Page iii
    Acknowledgement
        Page iv
        Page v
    Table of Contents
        Page vi
        Page vii
        Page viii
    List of Tables
        Page ix
    List of Figures
        Page x
        Page xi
        Page xii
    Abstract
        Page xiii
        Page xiv
    Current state of the art in hydrogen liquefaction, zero boil-off, and densification
        Page 1
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    Proposed integrated refrigeration and storage system
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    Analysis of governing equations
        Page 40
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    Hydrogen safety
        Page 105
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    Test system design and analysis
        Page 119
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    Laboratory testing and data analysis
        Page 134
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    Conclusions and recommendations
        Page 161
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    Appendices
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    References
        Page 176
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    Biographical sketch
        Page 181
Full Text







ANALYSIS AND TESTING OF AN INTEGRATED REFRIGERATION AND
STORAGE SYSTEM FOR LIQUID HYDROGEN ZERO BOIL-OFF,
LIQUEFACTION, AND DENSIFICATION













By

WILLIAM USILTON NOTARDONATO


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

William Usilton Notardonato






























To the men and women of NASA KSC and their operations contractors for their
dedication and commitment in performing an often-unappreciated role of preparing and
launching spacecraft.








ACKNOWLEDGMENTS

I have a number of people to thank from NASA Kennedy Space Center, including

Roy Bridges, who set up the Kennedy Graduate Student Fellowship, Joe Porta, my boss,

who let me take the time to do the research work; and a number of KSC cryogenic

engineers who lent their expertise, including but not limited to Robert Johnson, James

Fesmire, Zoltan Nagy, Carl Exline, Diane Stees, and Maria Littlefield. In addition, a

number of industry sources, including people at PHPK, Praxair, Sierra Lobo, Air Liquide,

and NIST have contributed their expertise. I am also particularly indebted to Dr. Jong

Baik of the Florida Solar Energy Center, my partner, who did the laboratory set up and

much of the testing, and Dr. Glen McIntosh of CTS, for significantly contributing to the

design and fabrication of the cryostat.

I express my sincere gratitude to all my committee members for agreeing to take

the time to help my work and review this document. Specifically, I wish to thank Dr.

Peterson and Dr. Chung for all of their help and guidance while I was revising this

dissertation, Dr. Chow for a number of discussions and projects worked between KSC

and UCF, and Dr. Sullivan and Dr. Ingley for agreeing to step in late and take over for

other departed members. I also would like to thank all the professors I had at UF for

rekindling my desire for learning about advanced engineering concepts. Finally, and

most importantly, I acknowledge and thank Dr. Sherif for his time, patience, and

guidance over the past five years.




This work would not be possible without the support of my immediate family, and

for this I am very grateful. I thank my parents Mary-Lou and Joe for all their support

over the years and for stressing the value of a good education. I also recognize Loretta

Parenteau for her support and help with my family during the year I was in Gainesville.

Finally, and most importantly, I thank my wife Celeste for all of her patience,

understanding, support, praise, motivation, and help over the past five years. I could not

have done it without her.








TABLE OF CONTENTS

page

ACKNOW LEDGM ENTS ................................................................................................. iv

LIST OF TABLES .......................................................................................................... ix

LIST OF FIGURES ............................................................................... ........................... x

ABSTRACT..................................................................................................................... xiii

CHAPTER

1 CURRENT STATE OF THE ART IN HYDROGEN LIQUEFACTION, ZERO
BOIL-OFF, AND DENSIFICATION ....................................................................1...

Hydrogen Liquefaction.................................................................................................2
Linde-Hampson Cycle...........................................................................................6
Pre-Cooled Linde-Hampson Cycle.....................................................................8
Linde Dual Pressure Cycle ................................................................................ 11
Claude Cycle .................................................................................................. 12
Large Scale Hydrogen Liquefaction Plants......................................................... 14
Zero Boil Off .................................................................... ..... ............................ 15
Ground Applications ........................................................................................ 15
Space Applications ..............................................................................................19
Hydrogen Densification............................................................................................ 21
Launch Vehicle Operations ..................................................................................... 25
S u m m ary ....... .......... .................. .................................. ....................................... 2 7

2 PROPOSED INTEGRATED REFRIGERATION AND STORAGE SYSTEM.......28

Integrated Refrigeration and Storage Concept ........................................................ 28
System Behavior....................................................................................................... 31
Behavior Issues ..................................................................................................... 36

3 ANALYSIS OF GOVERNING EQUATIONS....................................................... 40

Therm odynam ic Analysis of Liquefaction Cycle.................................................... 41
Cycle Description .............................................................................................. 41
M odel Developm ent ..........................................................................................44
Analysis .......................................................................................................... 46




Therm odynam ic Analysis of Storage System .......................................................... 55
Definitions and Assum options ............................................................................ 55
Conservation of M ass ........................................................................................ 58
Conservation of Energy..................................................................................... 59
Equation of State .................................................................................................62
Operational Sim plifications............................................................................... 62
Closed Storage With Heat Transfer To the System (Self Pressurization)...........63
Open Storage With Heat Transfer To The System (Boil off) ..........................69
Closed Storage With Zero Net Heat Transfer (Zero Boil Off)......................... 72
Open System With Heat Transfer Out Of The System (Liquefaction) ............73
Closed Storage With Heat Transfer Out Of The System (Densification) ...........76
Corrected m odel ............................................ ................................................ 79
Storage Fluid Analysis............................................................................................. 81
Conservation of M ass ........................................................................................ 89
Conservation of M om entum ................................................ ........................... 90
Conservation of Energy..................................................................................... 94
Sum m ary.............. .... ........................ ........................ ........................ 95
Solution Procedure .................................................................. ....................... 96
Boundary Conditions........................................................................................... 97
Dim ensionless analysis.................................................... ............................... 100

4 HYDROGEN SAFETY .......................................................... ............................... 105

Hydrogen Properties ................................................................ ........................... 105
Com bustion Hazards............................................................................................... 108
Hydrogen Em brittlement .............................................................. ......................... 111
Cryogenic Hazards.................................................................................................... 112
Facility Design..................................................... ............................................... 114
M anagem ent and Operations .................................................. ............................... 117
Conclusion .................................................................................... ....................... 118

5 TEST SY STEM DESIGN AND ANALYSIS.............................. ......................... 119

Prelim inary Design and Analysis .............................................. ............................ 119
Hydrogen Storage................................................................... ........................ 120
Cryogenic Refrigerator...................................................................................... 120
Instrum entation and Data Acquisition............................................................. 123
Fluid Distribution ......................................................................................... 123
Vacuum System ................................................................................................. 124
Safety and Leak Detection System .................................................................... 124
Cryostat Specification............................................................... .............................125
Cryostat Detailed Design................................................................. ...................... 125
Cryostat Construction........................................................................................127
Cryogenic Refrigeration ................................................... ............................ 129
Acceptance Testing.......................................................................... ...................... 131
Support System s ............................................................................ ........................ 131




6 LABORATORY TESTING AND DATA ANALYSIS......................................... 134

Liquid N itrogen Chilldow n.................................................................................... 134
L N 2 D rain and Purge .............................................................. ............................... 139
H ydrogen L iquefaction ....................................................................... ................... 144
H ydrogen D ensification........................................................... ........................... 148
Z ero B oil O ff .............................................. ..................... ... ....................... 155
Measurement Uncertainty Analysis.......................................................................... 157

7 CONCLUSIONS AND RECOMMENDATIONS.................................................161

APPENDIX

A CRYOSTAT SYSTEM SPECIFICATION.............................................................. 165

Configuration and Performance Requirements .....................................................165
Design, Fabrication, Inspection and Testing Requirements ...................................167
S u b m ittals .................................... ............................. ............................ 16 8
S hip m ent ............................................ ........... ........................................................ 169

B HEAT LEAK CALCULATION.............................................................................. 171

C DENSIFICATION SAMPLE MODEL................................................................. 172

D ACRONYMS AND SYMBOLS........................................................................... 173

LIST O F R EFER EN C E S ............................................................................................... 176

BIOGRAPHICAL SKETCH ......................................................................................... 181








LIST OF TABLES


Table page

1-1 Ideal work of liquefaction for cryogenic fluids.........................................................4...

1-2 Ideal work input and density for liquefaction vs. pressurization of hydrogen .............5

3-1 O operational scenarios ........................................... ................................................ 63








LIST OF FIGURES


Figure page

1-1 Ideal liquefaction process T-s diagram and system schematic..................................3...

1-2 Linde H am pson schem atic................................................................ ......................7...

1-3 Linde H am pson T-s diagram .....................................................................................7...

1-4 Pre-cooled Linde Hampson schem atic .........................................................................9

1-5 Pre-cooled Linde Hampson T-s diagram.................................................................10

1-6 C ascade cycle schem atic ............................................................................................ 10

1-7 Linde dual pressure cycle schem atic ....................................................................... 11

1-8 Linde dual pressure cycle T-s diagram .................................................................... 12

1-9 C laude cycle schem atic ........................................................... ............................. 13

1-10 C laude cycle T-s diagram ...................................................................................... 14

1-11 Zero loss storage economy ic analysis ..................................................................... 19

1-12 Saturated liquid hydrogen density, enthalpy, and vapor pressure .........................23

3-1 Proposed Liquefaction Cycle Schematic...............................................................42

3-2 Acceptable Intermediate Temperatures as a Function of Helium Compression ........48

3-3 Compression Work vs Intermediate Temperature (P2=120 kPa)............................49

3-4 Compression Work vs Intermediate Temperature (P2=1200 kPa)..........................50

3-5 Turbine Mass Flow Rates and Cycle Work..............................................................51

3-6 H eat R ejection at HX 3 and H X 4 .............................................................................. 52

3-7 Cycle Work vs Temperature for a Range of Hydrogen Pressures........................... 53

3-8 Cycle W ork vs Hydrogen Pressure............................................. ........................... 54




3-9 Cycle W ork vs H elium Pressure............................................................................... 54

3-10 Sim plified system representation........................................................................... 57

3-11 Self pressurization temperature and pressure vs. time ..........................................66

3-12 Self pressurization tank quality and phase volume vs. time..................................67

3-13 Self pressurization rates for variable liquid level..................................................68

3-14 Self pressurization (m odel vs. data) ...................................... ............................... 68

3-15 Liquid and vapor mass during boil off ................................................................71

3-16 Boil off time dependence on pressure .................................................................71

3-17 Cryocooler performance and heat leak vs. temperature ........................................72

3-18 Comparison of predicted vs. actual liquefaction rate ............................................75

3-19 Predicted densification temperature and pressure ..................................................77

3-20 Densification rates for variable liquid levels.........................................................77

3-21 Predicted vs. actual densification rates..................................................................78

3-22 Corrected model vs. densification data...................................................................82

3-23 Corrected model vs. pressurization data................................................................82

3-24 Proposed system representation.............................................................................. 84

3-25 Predicted Free Convection Velocity....................................................................86

3-26 Predicted Free Convection Reynolds Number ......................................................87

3-27 Predicted Grashof N um ber............................................... .............................. 88

4-1 H ydrogen T-s diagram ................................................................. ....................... 107

5-1 C ryostat design detail ............................................................................................ 126

5-2 Cryocooler A L330 capacity curve ......................................................................... 130

5-3 Liquid hydrogen cryostat test arrangement........................................................... 133

6-1 Liquid nitrogen chilldow n ...................................................................................... 136

6-2 Hydrogen dewar overpressurization...................................................................... 136




6-3 Liquid nitrogen chilldown detail ............................................................................ 138

6-4 Completion of chilldown................................................................. ...................... 138

6-5 Liquid nitrogen drain and purge ...................................................... ...................... 140

6-6 Tank drain and purge pressure cycles..................................................................... 141

6-7 Tank drain and purge temperature profile .............................................................. 142

6-8 Cryocooler chilldown in vacuum ........................................................................... 143

6-9 Hydrogen liquefaction on 6/24/04........................................................................... 144

6-10 Temperature transients during initial gas flow ..................................................... 147

6-11 M ass flow rate and pressure during liquefaction.................................................. 147

6-12 Total hydrogen volume in tank............................................................................. 148

6-13 Heat pipe saturation............................................................... ............................ 149

6-14 Overnight densification ......................................................... ........................... 150

6-15 System relocation warm up ................................................... ............................ 151

6-16 Continuing liquefaction.............................................................. ....................... 152

6-17 Liquid temperature and pressure saturation curve............................................... 152

6-18 Ullage collapse .................................................................................................... 153

6-19 Liquefaction on 6-30-04................................................................. ..................... 154

6-20 Liquefaction on 7-1-04......................................................................................... 154

6-21 Zero boil off operations ................................................................. ...................... 156

6-22 Non-dimensional thermal stratification during self pressurization ....................... 157

6-23 ZBO operations with P and T error bars............................................................... 158

6-24 Expanded section plots of P and T with error bars............................................... 159

A-1 System Specification Schematic........................................... .............................. 170








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

ANALYSIS AND TESTING OF AN INTEGRATED REFRIGERATION AND
STORAGE SYSTEM FOR LIQUID HYDROGEN ZERO BOIL-OFF,
LIQUEFACTION, AND DENSIFICATION

By

William Usilton Notardonato

December 2006

Chair: S. A. Sherif
Major Department: Mechanical and Aerospace Engineering

While hydrogen was first liquefied in the laboratory by Sir James Dewar in 1898, it

was not until the beginning of the space age in the 1950s that large-scale production of

liquid hydrogen was common. Since then, the methods used by NASA to produce,

liquefy, store and distribute hydrogen for launch vehicle applications have not changed.

Specifically, gaseous hydrogen is produced from natural gas, liquefied in large scale

plants by performing external work on the gas and then expanding it, transported to the

launch site via tanker trucks and stored in large ground tanks in the saturated state until it

is loaded into the vehicle during launch countdown. During the process, heat leak and

tank pressurization create boil-off losses, and chill-down of the transport lines cause more

product losses. Other handling issues, including low liquid density, large thermal

transients, leakage and safety concerns, and two phase flow problems have given liquid

hydrogen a reputation for being a difficult fluid to store and control.




This dissertation proposes a novel method of liquefying and storing hydrogen by

incorporating a closed-cycle helium refrigerator into the storage tank. There are

numerous advantages to this system. Localized production and liquefaction eliminates the

need for transportation of hazardous liquid hydrogen, minimizes heat flow into the

system, and reduces the number of personnel required at the launch site. Proper design of

the refrigerator also allows for densification of the liquid, increasing the amount of

propellant loaded into the flight tank. In addition, subcooling below the normal boiling

point allows the liquid to store more refrigeration energy, leading to less boil off losses or

eliminating boil off completely, and possible allowing for recovery of chill down losses.

Subcooled propellants also provide greater thermal margin before onset of evaporation

and two-phase flow. Details of these performance and economic benefits are provided in

Chapter 2.

While there are benefits, refrigerated and subcooled cryogens behave in a different

manner than saturated liquids. These behavior issues must be investigated before

large-scale incorporation in future launch systems. The conservation equations have been

presented, and simplification of these equations in a 2-dimensional transient mass and

energy model has been developed. Chapter 3 presents some results of the predicted

behavior. A small testbed has also been proposed, designed, and fabricated for

experimental validation of this model, and initial testing has occurred to validate the

proposed concepts of liquefaction, zero boil off and densification. Results of this initial

round of tests are provided in Chapter 6.







CHAPTER 1
CURRENT STATE OF THE ART IN HYDROGEN LIQUEFACTION, ZERO
BOIL-OFF, AND DENSIFICATION

Hydrogen has many favorable properties that make it attractive as a secondary

energy carrier. Hydrogen is very abundant. It is believed to make up 90% of the mass in

the universe, and is the ninth most common chemical element on Earth. Combustion of

hydrogen is clean, with the major combustion products being water and heat.(1) With a

higher heating value (HHV) of 142,000 J/g, hydrogen carries more energy per unit mass

than other fuels.(2) This is particularly useful for space applications as liquid

hydrogen/liquid oxygen rockets have the highest specific impulse of any combination of

chemical propellant currently in use.(3) For this reason, NASA and the US Air Force

(USAF) have been interested in hydrogen as a propellant for space vehicles since the late

1950s. More recently, there is much interest in using hydrogen as an energy carrier in

transportation applications, including automobiles, busses, and aircraft.(45)

Use of hydrogen does have some negative aspects however. Hydrogen gas has

very low mass density, so volumetric concerns limit it use to small applications.

Hydrogen can be stored as a gas in a solid matrix such as metal hydrides, but these

systems are not mass efficient for space use. The most practical storage method for

hydrogen fuels has been as a low temperature liquid. Hydrogen has a normal boiling

point (NBP) of 20.27 K, and the density at this point is 70.79 kg/m3. Its critical point has

a pressure of 1315 kPa and temperature of 33.2 K, and the triple point has a pressure of

7.2 kPa and a temperature of 13.9 K.(6) While NASA and USAF have pioneered methods







for large scale production, storage, and distribution of liquid hydrogen, there are issues

that must still be addressed before liquid hydrogen gains more widespread use as a

practical energy carrier. Hydrogen requires large quantities of energy to liquefy, and

since it is stored far below ambient temperature, heat leaks into the storage vessels

creating evaporation and product losses. In addition, although liquid hydrogen density is

789 times greater than gaseous hydrogen, it is still a very low-density fuel and requires

large, well-insulated storage vessels. These issues will be addressed in the present

chapter.

Hydrogen Liquefaction

One factor delaying development of widespread use of hydrogen in the economy is

the difficulty of storing and distributing large quantities. Gaseous storage requires

extremely large volumes and storage in a metal hydride requires heavy storage tanks and

addition of energy to drive the hydrogen out of the storage state. Liquid hydrogen has the

potential to eliminate these concerns, but the process of liquefying hydrogen is energy

intensive. Many different cycles have been proposed and used for hydrogen liquefaction,

ranging from small-scale laboratory use to large liquefaction plants capable of producing

60 tons per day of liquid hydrogen.(7) A challenge associated with liquid production and

storage is the need for development of small- to medium-scale distributed liquefaction

systems that have efficiencies of the same order of magnitude as the large-scale

liquefaction plants. This allows for localized production of hydrogen gas optimized for

the specific location coupled with localized efficient liquefaction for higher energy

storage densities. (8)

Generalized descriptions of procedures for hydrogen liquefaction exist in cryogenic

technology literature. (1,7,9) These methods all rely on taking a purified gas at room








temperature and cooling it to the extremely low temperature of 20.3 K, the normal boiling

point of hydrogen. In order to compare these systems, the thermodynamically ideal

process first must be identified. The optimum cycle from the thermodynamic perspective

is the Carnot Cycle, which consists of two reversible isothermal processes and two

reversible adiabatic processes. This cycle would be the ideal refrigeration cycle, however,

the liquefaction process is not a closed cycle but an open cycle where mass is

continuously liquefied at the cold end and must be re-supplied at the warm end.

Therefore the ideal liquefaction process can be taken as the first two steps of the Carnot

cycle, namely a reversible isothermal compression of the gas to a suitably high pressure,

followed by an isentropic expansion where the gas completely condenses in the expander.

Refer to Figure 1-1 for details on this process depicted on a T-s diagram.(9) However, the

high pressure required for complete liquefaction of hydrogen, 105 bar, makes this process

technically not feasible. The minimum work required for this ideal liquefier can be

determined and used as a benchmark for comparison with real processes.


COMPRESSOR r
1f- 2
mh

2 1




p=const EXPANDER






/ LIQUID

S
RESERVOIR

Figure 1-1 Ideal liquefaction process T-s diagram and system schematic








The First Law of Thermodynamics for steady flow with one inlet and one outlet,

neglecting kinetic and potential energy change between the initial and final state, can be

written as

Q-W = th(h, h,) 1-1

From the Second Law of Thermodynamics for an ideal reversible process, an entropy

balance on the heat exchange process gives

Q=rhJT-ds or Q=ThTl(s2-s,) 1-2

Combining equations 1-1 and 1-2 and knowing s2 is equal to S3 we find the minimum

work required for liquefaction can be expressed as

W
--= TI(s-s,)- (h, -h,) 1-3


From equation 1-3 we find the minimum work required to liquefy a gas (assuming the

initial and final pressure are equal) depends on the initial state of the gas and the type of

gas to be liquefied. Some common cryogenic fluids are listed in Table 1-1 along with

their NBP and their ideal work of liquefaction. Note that hydrogen requires the highest

work input for liquefaction, more than even liquid helium, which has the lowest NBP of

any fluid.

Table 1-1 Ideal work of liquefaction for cryogenic fluids
Gas Normal Boiling Point (K) Ideal Liquefaction
Work (J/g)
Helium 3 3.19 8178
Helium 4 4.21 6819
Hydrogen 20.27 12,019
Neon 27.09 1335
Nitrogen 77.36 768
Argon 87.28 479
Oxygen 90.18 636
Methane 111.7 1091










As an interesting side note regarding hydrogen storage for automotive use, US

manufacturers tend to favor high-pressure hydrogen gas storage over liquid storage,

which differs from some European auto manufacturers. Storage pressures range from the

present 5000-psi systems to proposed 10000-psi systems.(10) Reasons cited for this

preference include longer storage times, since there is no boil as with liquid systems, less

systems complexity, and less energy input required. The advantages to liquid storage are

greater energy density and hence greater range, and inherent purity of liquid hydrogen as

opposed to gas. (9'1112) Table 1-2 shows the relative energy costs associated with ideal

liquefaction systems as compared to ideal gas compression systems for 5000 and 10000

psi. Ideal isothermal compression is given by the equation


W = PoV, In( ) 1-4
0

although this is not attainable in real life. A more realistic process is the adiabatic

compression process, expressed as


W = ( _I)Po {( )Y 1} 1-5


This table also shows the density of the product. From this table it is apparent that there is

still significant energy cost associated with high-pressure gas storage.

Table 1-2 Ideal work input and density for liquefaction vs. pressurization of hydrogen
Ideal Work Input Density

kJ/kg kg/m3

Liquid 12019 70.8

10000 psi fluid 8603 38.7

5000 psi fluid 7468 22.9










Now that a baseline liquefaction work requirement for ideal systems has been identified,

actual liquefaction processes can be compared. A parameter called the Figure of Merit

(FOM) is defined as ideal work required divided by the actual work required, and varies

between 0 and 1.

Linde-Hampson Cycle

The most simple liquefaction system is the Linde-Hampson system, which uses a

Joule Thomson (J-T) valve for isenthalpic expansion of the gas. The basic Linde-

Hampson system is unacceptable for use in hydrogen systems because of that isenthalpic

expansion, since the J-T coefficient for hydrogen at ambient temperature is negative.

This means the expansion of hydrogen gas at ambient temperature will create a heating

effect. It is not until the hydrogen gas reaches 205 K, its maximum inversion temperature

that the J-T coefficient becomes positive and refrigeration may occur upon expansion.

However, the Linde Hampson cycle will be discussed here because many of the same

principles are used in other cycles.

A simple schematic of the Linde-Hampson cycle is shown in Figure 1-2'9), and the

cycle state points are represented in the T-s diagram shown in Figure 1-3(9). First, the gas

is compressed isothermally from a low pressure Pi to a high pressure P2. The high-

pressure warm gas stream then passes through an isobaric heat exchanger (HX), being

cooled from the cold low-pressure gas stream. Next, the gas undergoes an isenthalpic

expansion back to the original low pressure though a flow restriction, and enters the two-

phase region. Here, some fraction of the process stream is withdrawn as a liquid, and the

remaining vapor is used to cool the high-pressure gas stream before being re-compressed









for another round though the cycle. Make-up gas, equal in mass to the liquid withdrawn,


is added prior to the compression step.


COMPRESSOR


HEAT EXCHANGER


m-mf


JT
VALVE


Make up gas


RESERVOIR


Figure 1-2 Linde Hampson schematic







2




T N1.


Figure 1-3 Linde Hampson T-s diagram








A control volume energy balance for the heat exchanger, expansion valve, and

liquid tank, using the same assumptions as before, allows one to solve for the liquid yield.


h h h 1-6
m h, hf

Applying a similar energy balance to the compressor gives the work per unit mass

liquefied to be

W h, -hf
-)[T, *(s, -s,-)-(k -h)] 1-7
m / h, h2

This is an ideal analysis that does not take into account imperfect heat exchange, pressure

drops in the system, heat leak into the system, and assumes isothermal compression.

Nevertheless, this analysis will give a liquid yield of about 7% for liquid nitrogen

systems, and has a typical LN2 FOM of 0.115.

Pre-Cooled Linde-Hampson Cycle

The basic Linde-Hampson cycle can be used as a hydrogen liquefier if the high-

pressure gas stream is cooled below the J-T inversion temperature prior to undergoing

expansion in the valve. This system, referred to as the pre-cooled Linde-Hampson, is

shown schematically in Figure 1-4(9) and the cycle state points are shown in Figure 1-5.(9)

A secondary refrigerant, most commonly liquid nitrogen in either an open or closed

cycle, is used to decrease the temperature of the gas prior to entering the recuperative

heat exchanger. Again using an energy balance for the control volume including the two

heat exchangers, expansion valve and receiver tank, a relation for the liquid yield can be

found to be

-h h2 (h, -h( ) 1-8
S-hf mh (kh-h )









and the ideal work requirement per mass of gas liquefied becomes


--= -[T (s, s2 (-h2 )+ -(h h)] 1-9
my y m


The final term represents the additional work required by the refrigerant compressor.

There are added complexities with this type of system, and careful design is required to

find the optimum refrigerant flow rate. Typically this type of system will raise the FOM

for a nitrogen liquefier to a value of 0.168. Variations on the pre-cooled Linde-Hampson

include the Cascade cycle, where the refrigerant is pre-cooled by another cycle, which in

turn could be pre-cooled by another cycle. A simple schematic of a cascade system is

shown in Figure 1-6.(9)



b c




REFRIGERANT
LOOP



a d
C HEAT EXCHANGER
COMPRESSOR r HEAT EXCHANGER




1h WCl VALVE

S T 5


RESERVOIR


Figure 1-4 Pre-cooled Linde Hampson schematic





10







/2
Refrigerant BP

3 6
T /
P=-const



4 h=const /







S

Figure 1-5 Pre-cooled Linde Hampson T-s diagram


Figure 1-6 Cascade cycle schematic








Linde Dual Pressure Cycle

Another modification to the basic Linde-Hampson cycle is to add an intermediate

pressure compression to the system, so not all the gas is compressed to the final pressure.

This reduces the total work requirement somewhat and allows some of the heat to be

removed from the gas at a higher temperature, making the process more efficient in terms

of work required per unit mass liquefied. A schematic of the dual pressure cycle is

shown in Figure 1-7(9) and the T-s diagram is shown in Figure 1-8.(9) The liquid yield is

found to be


y = 1-10
h hf m (h, -hf)


And the ideal work per mass liquefied is


-=-[T,* (s-s2)-(h -h,)- {T -s,)-(h,- h,)] 1-11
mf y mt


2
LOW PRESSURE HIGH PRESSURE HEAT EXCANGER
COMPRESSOR rl COMPRESSOR Qr2
1 2 3 8

VALVE
5
rh[ .1 ` I


rn rnf -in2
|ma
Make up gas


RESERVOIR


Figure 1-7 Linde dual pressure cycle schematic




















6T










S

Figure 1-8 Linde dual pressure cycle T-s diagram

Claude Cycle

Another typical cryogenic liquefaction cycle, commonly used in hydrogen

liquefiers, is the Claude cycle. This system is shown schematically in Figure 1-9(9) and

the state points are shown in Figure 1-10.(9) The major difference between this and other

cycles discussed so far is the first stage of expansion is done through a work-extracting

turbine. This expansion is typically approximated as isentropic, and this allows the

hydrogen to be cooled more efficiently than isenthalpic expansion, and cooling will occur

no matter what the initial temperature. The refrigeration produced in the first stage

expander is used to pre-cool the remained of the gas, so heat can be removed more

efficiently at a higher temperature. A second stage J-T expansion is used for final








liquefaction, for simplicity since turbines typically cannot tolerate large liquid flow. An

additional benefit of large scale Claude systems is the work produced in the turbine

expander is used to help compress the gas, reducing the total work required. Liquid yield

can be approximated as


Sh, -h2 e (h-h) 1-12
h,- h (-h1-12


And the ideal work per unit mass liquefied is

W1 m
=- [T-(s -s2)- (h- )-- (h -he)] 1-13
mf y m


There are many variations of the Claude cycle in use, not just for liquefaction of

hydrogen but in many cases refrigeration of helium as well. This cycle can be combined

in many ways with dual-pressure systems and pre-cooled systems. In some cases work is

recovered in the outlet of the turbine but in others with work is dissipated in a braking

system.


Q,
COMPRESSOR / HEAT EXCHANGER HEAT EXCHANGER HEAT EXCHANGER
1 | 2 | ---- 3 --4 | ---
i--- ___ -i ----- --v Z ----AiW--f--WW-9-
8 7
5



SJT
3 VALVE

W EXPANDER 6


Make up gas e
E__ LIQUID


RESERVOIR


Figure 1-9 Claude cycle schematic


















T S=const








4 s



S

Figure 1-10 Claude cycle T-s diagram

Large Scale Hydrogen Liquefaction Plants

Several large-scale hydrogen liquefaction plants are in operation around the world

and supply the majority of liquid hydrogen currently consumed. Details of the exact

cycles used are considered proprietary but in general the plants use variations on the

Claude cycle with a dual pressure system, and include several stages of isentropic turbine

expansions before the final J-T expansion step for liquefaction. (17'13) These plants have

been designed and optimized for the specific conditions of the local economy, and

compromises between capital costs (typically the number of stages of turbine expansion

and heat exchanger effectiveness) and operating costs (electrical input and maintenance)

have been analyzed for economic efficiency. Generally, plants in the US also include a







liquid nitrogen pre-cooling stage while this practice has not been favored in Europe as

much.

Surveys of existing large scale liquefaction plants as well as thermodynamic

analysis has found that these systems typically operate at efficiencies approaching 40% of

the Carnot ideal cycle.(14) This calculates that the total work required per mass of gas

liquefied is typically around 30,000 kJ/kg. Obviously this is significant since this is

approximately 22% of the HHV of the hydrogen.

Another factor to consider is the ortho-para conversion, and the energy associated

with this exothermic reaction. Details of the ortho to para hydrogen conversion are

given in Chapter 4. The optimum method of removing the heat of conversion is to use a

catalyst to speed up the conversion process and remove the heat at the highest

temperature possible. Current plants perform the catalyst step and heat removal in a

number of discrete temperature points, but prototypes have been built and tested that

perform conversion and heat removal in a continuous process.

Zero Boil Off

Ground Applications

One common feature of liquid hydrogen systems, indeed of cryogenic systems in

general, is the fact that they are never in thermodynamic equilibrium with their

surroundings. Heat transfer from the ambient temperature to the cryogenic storage

temperature will always occur, no matter how good the thermal insulation systems are. If

the liquid is subcooled, the heat leak increases the sensible heat of the liquid, and if the

liquid is saturated the heat leak is absorbed by the latent heat of vaporization and boil off

occurs. This boil off increases the vapor pressure in the tank until the maximum

operating pressure is reached, and product losses occur as the excess vapor is vented








through the pressure relief system. As a side note, although the term boil off is in general

use in the cryogenic industry to describe this product loss, heat leaks into the tank are

typically so small that no nucleate boiling is actually occurring. A more accurate term

would be surface evaporation.

Due to the cost of producing hydrogen from natural gas feedstock, liquefying it at a

central plant, and then shipping it to the final destination, it appears economically

attractive to ensure that boil off losses are minimized or perhaps even eliminated. NASA

has been investigating zero boil off (ZBO) systems for many years at the Kennedy Space

Center (KSC). Martin Marietta proposed a hydrogen reliquefier for the LC-39 complex

in 1977 that would remove the heat that leaked into the tank by compressing the cold

vapor at the top of the tank and then expanding it isenthalpically to obtain cooling in a

modified basic Linde-Hampson system.(15) The compressors would operate at ambient

temperature, with the compressor inlet stream cooling the compressor outlet stream, after

the heat of compression was removed at ambient temperature. The compressor and

coldbox were to be installed at the top of the LH2 tank at LC-39. Review of the

thermodynamics and economics of the system indicated the approach was feasible,

however the idea was never implemented because NASA management was concerned the

work at the pads would impact the upcoming maiden launch of the Space Shuttle. In

1991, Ergenics Inc. proposed a system that would capture boil off losses in a metal

hydride bed.016) The captured gas would then be compressed in a hydride compressor,

pre-cooled with liquid nitrogen, and expanded in a J-T expansion system. The analysis

done indicated the system could be sized to capture not just the normal boil-off of the

hydrogen tank, but also losses during tanker offload operations, from chill down of the








transfer lines as well as losses from tanker venting. This approach required the

development of a large metal hydride storage system as well as a 2-ton per day liquefier

that would only operate a few weeks per year. This proposal was rejected partly for the

reason of complexity of a transient refrigeration system operating in batch processes, and

concerns over reliability in such a design. At this same time, a Phase II SBIR contract

was awarded to Hydrogen Consultants Inc. to prove the concept of a metal hydride

compressor design that could run a J-T refrigeration system. 17) This system was sized to

provide just enough refrigeration to overcome the steady heat leak into the tank, and the

concerns over thermal transients was eliminated since the system was designed to operate

continuously, using dual regenerative hydride beds. The program did produce working

hardware, but there were technical issues with the J-T expansion device freezing and

sticking during operation. In addition, the measured efficiency of the system was just

8.5% Carnot, poor by comparison with other cryogenic refrigerators. In all three cases

discussed above, the hydrogen was allowed to vaporize, and then work was performed on

the vapor to compress it prior to expansion and reliquefaction.

Despite the lack of success in creating a zero boil off system at KSC in the past,

there are still sound economic advantages to recapturing hydrogen losses from boil off.

In the case of liquid hydrogen at Kennedy Space Center a quick analysis shows the

potential payoff for such a system.(18) Assume KSC pays a rough cost of $5.40 per kg of

LH2 (not a true cost). This includes the cost to produce the hydrogen from the natural

gas, cost to chill the hydrogen from its ambient temperature to a saturated vapor, cost to

liquefy the vapor, the cost to ship the hydrogen to KSC in the tanker (plus losses in the

transfer process), the cost to offload it to the KSC storage vessel, and profit for the







vendor. Now, after all the energy and effort that went into that process, every 20 J of

heat that leaks into the storage vessel creates a loss of 1 gram of product. From an energy

ratio standpoint, the equation is

m* hfg
Ratio = m h 1-14
E H2production +m h300K-21K +m hfg + Eshipplng +Etransferloss


It is difficult to estimate all the energy put into the entire process, especially the

production process, but 88% of the enthalpy removed from the hydrogen during the

liquefaction process occurs between ambient temperature and the saturated vapor state.

However, when the liquid boils off and vents from the tank, this stored refrigeration is

vented to atmosphere. This heat leak can be intercepted without creating boil off losses

and the only energy cost to the system is the energy that goes into refrigeration.

Assuming a refrigeration temperature of 20 K, an efficiency of 35% Camot, and an

electrical energy cost of $0.09 per kW-hr, a ZBO system equates to buying hydrogen for

$0.50 per kg. There would be capital costs to be amortized over the life of the system,

and these are not included in this simple analysis. Any additional operations (manpower)

cost associated with this refrigeration will be offset by operational reductions in tanker

offloads. There are safety benefits from the elimination of tank venting as well as

reducing the number of transient operations.

Some estimates of the economic savings associated with ZBO ground systems are

shown in Figure 1-11. There are a variety of cases analyzed, from current Shuttle launch

operations to projected Crew Launch Vehicle and Heavy Launch Vehicle launch rates.

The options include only recovery of boil off in the pad tanks, recovery of boil off and

tanker losses, and finally recovery of boil off, tanker losses, and chill down losses. This

figure shows the estimated payback time for the system is between 2 and 6 years.









35
2004 fixed hydrogen price
30 2004 labor rates

25

"20 -- HLV ZBO
e 20

'a 5 1
I-




50 CLV breakeven point
0 ^ --- -------- i ----- i ----
0 2 4 6 8 10
Time (years)


Figure 1-11 Zero loss storage economic analysis

Space Applications

In addition to developing ZBO systems for large-scale ground use, NASA has

actively worked on developing a ZBO system for in space cryogenic storage. In this

instance, the primary concern of product loss is magnified by the penalties imposed by

the rocket equation. The cryogen in this case, fuel and oxidizer for a future propulsion

stage, is considered payload for the launch vehicle and is subjected to the same small

payload mass fraction as other payloads. As an example, consider an in space cryogenic

depot situated in low Earth orbit (LEO). For every kilogram of product delivered, 6.5

kilograms of propellant are required for the launch vehicle to deliver it to LEO. The ratio

becomes 12.9 to 1 for a depot at the LI point, and 22 to 1 for hydrogen delivered to the

surface of Mars.(19) Thus product loss from heat leak can make the use of cryogenic

propellants prohibitive for many missions, unless zero boil off systems are developed.

Lockheed Missiles and Space first proposed the use of cryogenic refrigerators for

long-term space missions in 1971(20), and the USAF investigated similar concepts in








1982(21). At the time, cryocooler development was not at the required level of

development in terms of low mass and flight quality reliability to warrant inclusion in

systems at that time. Advances in flight quality cryocoolers in the 1980's and 1990's,

especially using Stirling and pulse tube cycles, have made their use more attractive.

Analysis of proposed hydrogen storage systems as feedstock for In Situ Resource

Utilization (ISRU) systems for Mars exploration determined that ZBO made sense if the

mission duration lasted longer than 45 days.(22) That is, less mass was added by the

incorporation of a cryocooler and its associated power generation and heat rejections

systems than was lost by boil off and the associated increase in tank size if the mission

lasted longer than 45 days. Partially due to this analysis, NASA funded a series of

experiments to determine the optimum integration methods of cryocoolers in

microgravity cryogenic storage systems.

Initial testing at NASA Glenn Research Center (GRC) in 1999 was a proof of

concept demonstration using an existing off the shelf cryocooler and a condensing heat

exchanger in the vapor space of the tank. Test results were positive, showing constant or

negative hydrogen vapor pressure slopes over the duration of 77 hours, but this

configuration was not representative of actual space conditions, as there are no gravity

forces that would separate the liquid and vapor phases. (32 Two phase flow handling in

zero-g is the key technology that must be demonstrated. A more representative flight like

test, performed at NASA Marshall Space Flight Center in 2001, used a circulatory system

with a hydrogen pump drawing liquid from a liquid acquisition device and flowing it

through a heat exchanger coupled with a cryocooler cold head. The cooled liquid then

exited out a spray bar vent tube designed to provide destratification independent of ullage







and liquid positions in zero-g. The bulk hydrogen was maintained in the saturated liquid

state, and refrigeration energy provided was exactly balanced by heat leak into the tank.

Again, this cryocooler was not a flight quality unit but a commercial unit purchased off

the shelf.(24) Testing ZBO concepts with a flight like cooler was accomplished in 2003 at

NASA GRC. This test was performed with liquid nitrogen and a Northrop Grumman

High Efficiency Cryocooler developed for the USAF. A submerged mixer pump was

included to provide forced liquid nitrogen flow across a heat exchange surface, which

was coupled to the cryocooler by a heat pipe and a flexible conductive link.

Unfortunately, degradation in the system insulation performance over time led to larger

than expected heat leak, and true ZBO conditions were never achieved. However,

important information regarding integration of flight like cryocoolers with storage vessels

was proven.(25)

In all the above cases, ZBO systems were proposed and tested that depended on the

incorporation of a closed cycle refrigeration system to remove heat that had leaked into

the tank. NASA Ames Research Center has proposed and performed a first order

efficiency analysis on a system that uses the vapor from boil off as the working fluid in a

refrigeration cycle. 26) This analysis shows it is advantageous from an efficiency point to

directly perform work on the fluid to be maintained, primarily due to the fact that there is

no temperature difference required to promote heat exchange at the low temperature end

of the system. This concept, similar to ground based studies mentioned earlier, has not

been proven in a test environment.

Hydrogen Densification

One performance enhancement under consideration for the next generation of space

launch vehicles is densification of the cryogenic propellants. Propellant densification









refers to cooling the cryogens below their normal boiling point. Decreasing the

temperature of liquid hydrogen from 20.3 K to 15 K increases the density from 70.8

kg/m3 to 76.0 kg/m3, an improvement of 7.3%. This density increase has a

corresponding decrease in vehicle propellant tank volume and mass, reducing the overall

dry mass of the vehicle. In addition to reduction in tank sizes, propellant densification

has other performance benefits. Liquid hydrogen has a vapor pressure of 13 kPa at 15K,

compared to 101 kPa at the normal boiling point. Lower vapor pressures mean lower

tank operating pressures while still meeting the engine inlet net positive suction pressure

required to prevent cavitation. This lower tank pressure can result in thinner tank walls,

further reducing dry mass. Higher propellant density also results in smaller engine

turbomachinery for a given mass flow rate, or increased safety margins by reducing the

rotational speed on existing sized turbopumps. Finally, subcooled propellants can provide

greater cooling power to the engine nozzles and combustion chambers due to the

increased enthalpy gain prior to boil off, possibly making cooling passages smaller or

minimizing chill down losses. All of the above reductions in vehicle dry mass have a

cascading effect on the rest of the vehicle subsystems, resulting in mass reductions in

airframes and aerodynamic surfaces, orbital maneuvering systems, thermal protection

systems, landing gears and other systems. Studies by NASA contractors have estimated

that propellant densification can result in the reduction of Gross Lift Off Weight by 12%

to 20%, depending on the vehicle design and number of stages.(27) Figure 1-12 plots

liquid hydrogen density, enthalpy, and vapor pressure as a function of temperature

between the critical point and triple point.(6)
































Figure 1-12 Saturated liquid hydrogen density, enthalpy, and vapor pressure

Because of the advantages that densified propellants offer, NASA and the

Department of Defense have been interested in their potential use for many years. The

National Bureau of Standards performed densified propellant property studies in the

1960's, usually producing the necessary refrigeration by evaporative cooling.

Evaporative cooling refers to the technique of vacuum pumping the ullage space in a LH2

tank to reduce the vapor pressure, leading to evaporation of some of the liquid. The heat

of vaporization needed for this evaporation is provided by the remaining liquid, creating a

cooling effect. Union Carbide analytically investigated several slush hydrogen production

techniques in the same timeframe. During the 1970's, Martin Marietta studied the

concept of using a 50% slush LH2 mix with triple point oxygen in a single stage to orbit

launch vehicle. Using slush hydrogen has increased benefits over subcooled liquids,

primarily due to a density increase of almost 16% over normal boiling point hydrogen,

and one of the recommendations from the report was to concentrate on hydrogen slush

development only.(28) At this point, propellant densification was considered an immature


350 0.09

0.08
300 -
0) 0.07
250
C 0.06
S200- 0.05 -- P (psia
I h(J/g'
150- 0.04 rho (glcmn3
0.03
100-
0 0.02
50 -
0.01

0 0
13 18 23 28 33
Temperature








technology and NBP liquids were chosen as the propellants on the Space Shuttle. Further

slush hydrogen work was accomplished during the National Aerospace Plane program in

the late 1980's, with batch production of slush hydrogen being accomplished in 2000-

liter quantities by the freeze-thaw method of evaporative cooling at NASA Glenn

Research Center.(29) Operational and handling issues associated with pressurization,

transfer, mixing and sloshing, and instrumentation was investigated. Although slush

hydrogen offers significant performance benefits over subcooled liquids, technical issues

with its use (including filtering, mixing to ensure homogeneous states, and mass gauging)

has led NASA to primarily consider subcooled liquids above the triple point in most

current studies.

More recently, NASA and aerospace contractors have considered using subcooled

hydrogen on a modified Shuttle system, the X-33, and other 2nd Generation Reusable

Launch Vehicles (RLV). Many of the funded programs in this area have concentrated on

development of a densification production system. NASA GRC and Lockheed Martin

have developed and tested subscale liquid hydrogen and liquid oxygen densification units

based on the evaporative cooling method.(30) The largest hydrogen unit was capable of

cooling 3.6 kg/sec of NBP hydrogen to 15 K, and the oxygen unit cools 13.6 kg/sec of

NBP LOX to 66.6 K. In addition to production testing, tanking tests of the X-33

structural test article tank were completed. Tank loading procedures, including

recirculation of warm propellants, were tested using subcooled LH2. However, safety

and operational concerns with using subatmospheric boiling bath heat exchangers and

cold compressors led NASA to solicit alternate technologies to producing subcooled

propellants for the 2nd Gen RLV program. Refrigeration cycles that were chosen for







further development included orifice pulse tube refrigerators, a mixed gas J-T cycle

refrigerators, and a packed column cooling tower design based on evaporation of liquid

into a non-condensable gas. All three technologies were chosen based on the promise of

simplicity and reliability of operation once development issues had been addressed.(31)

After two years of development, these projects were not extended when the 2nd Gen

RLV program transitioned into the Next Generation Launch Vehicle program and

densified hydrogen fell out of favor compared to RP-1. However, operability

assessments by NASA KSC during this program led to questions regarding the manner in

which densified propellants would be implemented at the launch site.(32) This operability

assessment is the basis of the proposed integrated refrigeration and storage system

discussed in this dissertation. Other propellant studies have shown the mass savings

associated with using densified oxygen and methane for ascent vehicles on the surface of

Mars, coupled with an ISRU production facility.(33)

Launch Vehicle Operations

NASA has developed techniques for servicing spacecraft and launch vehicle

cryogenic propulsion systems since the late 1950's. Techniques have evolved as

hardware and software capability has developed, and each current program has some

vehicle and pad specific systems and operations required. However, the basic approach

remains similar, and servicing capabilities (in terms of quality of propellant loaded) are

nearly identical. These systems, or derivatives of them, are capable of meeting the needs

of an in space cryogenic depot, provided this depot uses propellant at or above the normal

boiling point, and free venting of boil off in space is permitted. Conditioning of

propellants via advanced ground storage systems has the potential to minimize cost and

safety risks, while maximizing launch performance.








The current method of large-scale cryogenic storage and distribution is very similar

across all programs at Kennedy Space Center and Cape Canaveral Air Station. Cryogens

(Liquid Hydrogen and Liquid Oxygen) are produced off site, delivered via tanker trucks,

and transferred to ground storage tanks days or weeks prior to launch. Cryogens in the

tanks are stored as a saturated liquid, and boil off gas is not recovered. During launch

countdown, as late as possible into the count, the cryogens are transferred to the flight

tank, and in the event of a launch scrub, are drained back into the ground storage tanks.

Details on how this is accomplished vary across programs.

Hydrogen for the Space Shuttle Program is purchased from Air Products New

Orleans plant and delivered via 13000-gallon road tankers. Periodic sampling of tankers

is done to ensure the propellant meets purity specifications. Waves of up to five tankers

can be offloaded at a time, and two waves can be done in a day. Prior to offload, transfer

lines are purged with gaseous helium and sampled. The tank is vented and valves are

opened to start chill down. Product losses from tank venting and transfer line chill down

are free vented at the top of the pad storage tank. After offload is complete, transfer lines

are purged of hydrogen. The pad storage tank holds 850,000 gallons of liquid, with 10%

ullage on top. The tank has a vacuum jacket and perlite bulk fill insulation. The cross-

country lines 10" ID, 1500 feet long and are vacuum jacketed (VJ) with multi-layer

insulation (MLI). The storage tank is pressurized using vaporizer heat exchangers.

Prior to launch, the tank must be filled to 700,000 gallons, which is enough for

three launch attempts. Loading of the STS external tank (ET) begins at T-6 hours on the

countdown clock. Purges to the various disconnect cavities is initiated and transfer line

blanket pressure is vented. The ET vent valve is opened, chill down line valve is opened,











and chill down of cross-country lines begins. Then the storage tank is self-pressurized,

and slow fill (1000 gpm) to the lower ET liquid level sensors is completed. The main

transfer valve is then opened and fast fill to 98% initiated, with flow rate of 8500 gpm.

When the ET ullage pressure rate reaches a limit, LH2 topping at 775 gpm is initiated

until the upper liquid level sensor reads 100% wet. Then the replenish valve controls the

flow to maintain 100%, usually less than 300 gpm. At T-1:57 minutes, replenish mode

terminates. Overall, 383,400 gallons is loaded into the ET, with 48,000 gallons lost

during chill down and 40,000 gallons lost during replenish. These vapor losses are

burned in a flare stack. If the launch is scrubbed, drainback procedures are initiated.

Summary

The state of the art in ground processing of cryogenic propellants is considered

mature, and KSC operators have over 50 years of experience in this type of operations.

There are performance enhancements that can be made. Of these, local production and

liquefaction of hydrogen offers benefits of eliminating tanker operations, and zero boil

off storage can eliminate wasteful product losses. Hydrogen densification has

performance benefits for the flight vehicle. NASA has invested significant funds to

investigate these systems over the past 30+ years, but has never fielded an actual

operating system. There are many reasons for this, but the most powerful of these has

always been a lack of confidence that the benefits would outweigh the operational

impacts, and conservative forces in management were unwilling to try something

different. This work is an attempt to change some of these positions.







CHAPTER 2
PROPOSED INTEGRATED REFRIGERATION AND STORAGE SYSTEM

The current state of the art in hydrogen liquefaction, storage and distribution for

space launch systems has successfully served its intended purpose for the past 50 years.

However, there are possible improvements that can be made that will make liquid

hydrogen use more economical, reliable, and safe than current systems. This chapter will

describe the basic concept of such a system, will explain the significance of the

development, and will qualitatively describe the thermodynamic behavior of the system.

Later chapters will detail designs of an experimental system built to test these concepts,

and data analysis of initial liquefaction, zero boil off and densification tests will be

presented.

Integrated Refrigeration and Storage Concept

The optimum design of a liquid hydrogen storage and distribution system is highly

dependent on the intended use of the product. For example, most industrial uses of liquid

hydrogen are in a continuous or semi-continuous process, such as a steady flow of

hydrogen to hydrogenate oils in the production of margarine or cooking oils or steady

flow of hydrogen in an anhydrous ammonia plant. In these cases, hydrogen is liquefied

only because of the transportation issues associated with supplying large quantities of

gaseous hydrogen make the process impractical. The hydrogen is ultimately used as a

gaseous product, although much of the cooling power is recuperated elsewhere in the

process. Most of the time, there is not a large quantity of liquid transfer lines, the

hydrogen is vaporized immediately downstream of the storage tank. In these cases, large









scale use of a continuous flow of gaseous hydrogen from a liquid storage system, heat

leak into the tank that creates boil off is not considered an issue, there are not many issues

associated with chill down and two phase flow in the supply lines, and there is no reason

to increase the density of the liquid in the storage tank. Current state of the art in

hydrogen storage and distribution is acceptable for these applications.

The typical usage scenario for a liquid hydrogen system in support of the space

program is very different than that in industry. The hydrogen is used in a batch process,

often with many months in between launches. During this time heat leak into the tank

leads to significant product losses, in fact only 65% of the hydrogen delivered to

Kennedy Space Center is ever actually launched aboard the Space Shuttle.(34) Another

major difference is the hydrogen is required to be a liquid at the use point as opposed to a

gas as in most major industrial operations. Not only is the hydrogen required to be a

liquid, there are strict limits on the state of that liquid that are dictated by the design of

the tank and the engine start box. For the Space Shuttle main engines, temperature

measurements on the turbopump exit and recirculation lines as well as power limits on

the recirculation pump (to detect cavitation) ensure there is liquid flowing through the

engine passages prior to start. (35 In this manner, the usage requirements between

industry and aerospace vary greatly, and current state of the art, while acceptable, is not

optimized for space use. These usage requirements are even more strict when

considering liquid hydrogen produced In Situ on the Moon or Mars. Therefore, liquid

hydrogen systems designed to minimize or eliminate heat leak and boil off, operate in a

number of batch processes with large thermal transients, and still deliver good quality








liquid when required at a use point many hundreds of meters away, are required for the

next generation of space launch systems.

What is truly needed is a novel approach to ground processing of cryogenic

propellants, as opposed to incremental improvements in existing philosophies. The new

philosophy should conform to the KISS principle, by minimizing operations, especially

ones that cause thermal transients or require opening the system to outside contamination.

This new philosophy should take advantage of advances in cryogenic engineering over

the past 20 years including efficient and reliable refrigeration systems, health monitoring

of vital components, and advanced insulation systems. Most important, the system should

offer economic and energy efficiency by minimizing boil off and chill down losses as

well as venting of high cost purge gasses like helium. One possible approach to this issue

is to integrate a closed cycle helium refrigeration system into the ground storage tank.

This integrated refrigeration system would offer the advantage of exercising more control

of the propellant thermodynamic state while still in ground storage. Such an advanced

system could serve as a liquefier, a zero boil off storage system, and possibly a propellant

densification system. Properly designed, this could provide cost, safety, reliability, and

performance benefits over current state of the art.

This work proposes to integrate a cryogenic refrigerator into a liquid hydrogen

dewar. Advantages to this proposal are numerous. First, the refrigerator can be used to

remove the heat that leaks into the vessel from the ambient environment, so there is no

pressure rise and associated boil off from the heat leak. This has obvious economic

savings, however, there are safety benefits as well since the tank is not venting gaseous

hydrogen most of the time. Second, if the refrigerator is sized properly, it can serve as a







local liquefaction system. This minimizes operations cost since fewer personnel are

required for tanker offload operations. There are less purge and sampling operations as

well since there are no tanker supply lines to inert. An added benefit is elimination of

tanker offload losses from venting the tankers and chilling down the transfer lines. Again,

there are safety and reliability benefits due to minimization of transient operations and

venting operations. A third advantage of the integrated refrigeration and storage is the

ability to control the state of the propellant. Currently, liquid hydrogen is created and

stored as a saturated liquid, although some degree of subcooling is possible with

pressurization of the liquid. This proposal allows for both subcooling for an extended

period of time as well as densification of the liquid below the normal boiling point. This

is a fundamental change in the way liquid hydrogen is stored. Currently, there is no true

thermodynamic equilibrium in a cryogenic system as there is always some degree of heat

leak between the ambient temperature and the liquid temperature. This proposal

mechanically removes this heat leak, so the cryogen can be stored in a manner similar to

thermodynamic equilibrium.

System Behavior

By integrating a cryogenic refrigerator into a storage vessel, thermodynamic

control of the cryogenic propellants can be achieved. The control of the system will be

based on the ability to change the enthalpy of the stored liquid, and depends on the design

of the system. Specifically the difference between the amount of heat removed at the

storage temperature by the refrigeration system compared to the energy entering the

system from either heat leak into the system from the warm surroundings or energy

entering the system from a mass input will determine the rate of change of the stored

enthalpy. Mathematically this is expressed as








6h
m*-= -Q,, +QHL +rhAh 2-1


There are three possible types of behaviors associated with such a system. If the

first term on the right is less than the other two, there will be a net positive flow of energy

into the system. This leads to a temperature increase, or if the fluid is saturated, an

evaporation of some of the liquid combined with a pressure increase. Eventually the

pressure will increase to the limit on the tank relief valve, and tank venting will lead to

product loss. This type of system is what is currently used at KSC.

A second type of system behavior is to balance the energy entering the tank with

the refrigeration produced, so there is no net energy input into the system. This quasi

steady state behavior is characterized by constant system pressure and temperatures,

despite the fact that the system is not truly in thermal equilibrium with the surroundings.

NASA has been studying similar systems recently for the application of long term zero

boil-off storage for space missions. Most of these studies are for closed systems with no

mass input, but some proposals have sized the refrigerator to allow for liquefaction of

some small amount of incoming propellant from an ISRU reactor.

The third type of behavior is exhibited when the refrigerator removes more energy

from the system than enters via either mass input or heat leak. This results in a decrease

in system pressure and temperature and a corresponding condensation of some of the

ullage gas. Assuming a homogeneous system, the state will follow saturated liquid line

to the triple point and then eventually the liquid completely freezes and the path follows

the sublimation curve. For systems of interest to spaceport propellant servicing, the solid

phase most probably will be avoided and refrigeration will be controlled to keep the state

above the triple point. In addition, to avoid contamination the system pressure would








probably need to be kept above atmospheric pressure by using a non-condensable

pressurization gas such as helium.

Combined with the fundamental change in behavior of the integrated refrigeration

and storage system as described above, there are a number of operational enhancements

to be considered. First and foremost, the system can be developed to be a zero loss

storage system. Better than a zero boil off system, a true zero loss system would never

have any product loss, including during chill down and transfer operations. While this

idealized case will probably never be fully achieved, capture and recovery of 50% of

current chill down losses during countdown will have substantial savings. This implies to

less venting and flaring operations at the launch pad, which is a potential safety

improvement, and requires a smaller storage vessel with less capital costs and heat leak

than the current alternative. Another ambitious goal would be elimination of boil off from

heat leak into the flight tank during loading operations. This would lead to a storablee"

form of cryogenic propellant, which has great benefits from an operational standpoint.

Storable cryogens will have extended countdown hold times, and can be useful as a rapid

response type of launch vehicle. Since flight tanks are generally insulated with foam, the

heat leak is an order of magnitude higher than what is found in the ground supply tank.

This necessitates a refrigeration system with higher capacity, but this is a benefit in itself.

Larger capacities imply greater efficiencies, and the added capacity can be used as a

liquefaction system when not in launch countdown. If liquefaction capability is built in to

the storage system, there is no need for tanker delivery of liquid, and the only supply

connection can be a pure gaseous hydrogen input at the top of the tank. This leads to less

ground support equipment (GSE), no tanker ports and transfer lines, less hazardous








operations, less thermal transients, and less potential for contamination from line

connections. Finally, when the refrigeration system is not performing zero boil off or

liquefaction operations, the capacity can be used to densify and subcool the propellant.

Densification has advantages for launch vehicle performance, as will be discussed in later

sections, however, even if launch vehicles use NBP propellants there are advantages in

densifying and subcooling on the ground. Densified, subcooled propellant acts as a

source of stored refrigeration energy that can be used as a thermal mass in liquefaction

and zero boil off applications, may allow for faster chill down times, and are easier to

transfer due to greater density and less tendency to exhibit two phase flow and cavitation.

These three new operational capabilities, ZBO or zero loss, liquefaction, and

densification/subcooling, will be discussed in greater detail below.

The added capability will come at some cost, mainly capital improvement of the

pads by adding a cryogenic refrigeration system. This capital cost will be offset by

savings in procurement by adding ZBO and liquefaction capability. If properly designed,

there should be little added operations required as a result and should be offset by

operational savings resulting from elimination of tanker operations. Close cycle helium

refrigerators using the reverse turbo-Brayton cycle are current state of the art, and need

no advanced development to be modified for this application. These systems are in use at

many large-scale magnetic labs and particle accelerators and are proven to be efficient

and reliable. Many components are also in use at open cycle liquefaction plants around

the world. Helium screw compressors are at ambient temperatures and are oil lubricated.

The only cold moving parts are the turbines, and at hydrogen temperature ranges these do

not require expansion of helium into the two-phase region. The turbines are also








mounted outside the cold box and can be replaced LRU style with no interruption in

service. The refrigerators are designed with modem controls systems are self-regulating

to provide optimum operation at a range of output conditions.(36)

In a full scale Spaceport system, the refrigeration system may be sized to remove

the heat leak in the flight tank. Flight tanks generally use Spray on Foam Insulation, so

overall heat leak may be on the order of 200 kW. When the flight tank is not loaded, the

refrigerator will be oversized. This excess capacity can either be turned down or the

system can be used as a hydrogen liquefier. On site liquefaction has operational

advantages. There are safety benefits, since there is no transportation across public

highways, no transfers of cryogenic liquids from tankers to storage tanks, and less

hazardous venting. Cost savings will occur due to less operations and transportation,

especially if the hydrogen production facility can be sized to provide economy of scale

for many sites. The entire spaceport can consist of one centralized hydrogen production

facility supplying a number of modular, self-contained liquefaction and storage sites at

each pad thru pipelines not unlike the natural gas lines in common use. There is possible

synergy with the future hydrogen economy, and the need for localized hydrogen

production and storage, and the system serves as a prototype of a future Lunar or Mars

propellant production and storage facility.

The proposed testbed will have the capability to deliver hydrogen gas to the liquid

system. After pressure reduction, the gas will be metered thru a mass flow controller. The

regulated gas stream can be delivered in three possible ports. First, the gas can be added

to the ullage space on top of the liquid, condensing at the liquid/vapor interface. Second,

the gas can bubble up thru the bottom of the tank, with the bubbles exchanging heat with







the subcooled liquid. Finally, the gas can exchange heat directly with a condensing heat

exchanger line at the cold head. For all three methods, the liquefaction rate must be

measured. To increase efficiency of the liquefaction process, the gas may be pre-cooled

with a liquid nitrogen HX or an intermediate stage of helium refrigeration, so the high

temperature enthalpy changes can be removed with less expensive refrigeration. In

addition, pre-cooling allows the addition of an ortho to para conversion catalyst to be

added. This will help remove some of the heat of conversion before the hydrogen enters

the dewar.

Behavior Issues

The proposed novel operational system will behave different than the NBP

counterpart and there will be a learning curve associated with their use. Research into

operational behavior must be addressed. The topics to be explored include pressurization

and venting of stored subcooled liquids, integrated refrigeration systems controls to

provide optimum performance during different operational phases of densification, zero

boil-off and liquefaction, determination of heat and mass transfer coefficients, and

methods of handling stratification layers. Advanced instrumentation should be developed

to accurately determine the state of the propellant quality

The vapor pressure of liquid hydrogen stored at 14 K is only 7 kPa. Having a

subatmospheric pressure inside the dewar may create safety concerns since any leak path

in the tank will draw in outside air, which will immediately freeze. While the inner tank

must be designed to hold a vacuum, that should not be the normal mode of operation.

Another issue is the tendency of the tank pressure to decrease as heat is removed from the

tank, as opposed to normal heat leak into a tank causing a pressure increase. The tank will

operate at two pressure settings, normal (extended) operation with a small positive









pressure differential, and transfer operations pressure with a higher positive pressure to

overcome line resistance and elevation changes.

Normal operational pressure will be approximately set at 140 kPa. The inside of

the tank will not be in thermodynamic equilibrium, as the cold liquid will continuously

condense the vapor at the top of the tank. To maintain positive pressure, three different

sources of ullage pressure may be considered. First, gaseous helium, non condensable at

14 K, will be used. Testing will be performed to determine the rate of pressurization of

the system using various flow rates of gaseous helium. This will depend on the heat

transfer rate between the liquid/vapor interface and the convection heat transfer in the

gaseous helium. Techniques to prevent the collapse of the ullage pressure will be

investigated, including bubbling the helium up through the liquid hydrogen to increase

heat exchange rate and pre-cool the helium. The other option for pressurization gas is

hydrogen. Liquid hydrogen from the tank will be directed to a vaporizer consisting of a

heat exchange coil, isolation valve, and pressurization regulator. The dynamics of the

system heat exchange rates will be recorded, in an attempt to balance the rate of heat

transfer between the liquid/vapor interface and the vaporizer and atmosphere. Again,

gaseous hydrogen will also be bubbled up through the liquid, although this is not

advantageous since the amount of heat entering the tank will increase using this method.

Finally, a bottle of room temperature hydrogen will be used as a pressurization source.

This gas will liquefy at the interface, so a continuous source of gas must be used to

prevent ullage collapse. This pressurization method will be discussed more when

hydrogen liquefaction is considered.








During operations that require transfer of liquid from one tank to another, tank

pressure will need to be increased to overcome friction and elevation head losses. All

three pressurization sources discussed above will also be evaluated for their suitability for

this purpose. In this case, the ullage space in the tank will be increasing as the tank liquid

level is decreasing, so the mass flow rate required will be greater than just tank pressure

maintenance. This mass flow rate must equal the rate required to fill the extra volume

plus the rate required to make up the contraction as the gas cools down. Depressurization

without venting the tank will be achieved by terminating the flow rate of pressurization

into the tank while maintaining the cooling of the hydrogen.

However, this approximation depends on perfect heat exchange between the

cryocooler and the hydrogen, and it assumes there are no temperature gradients in the

liquid (lumped capacitance method). In reality, the overall heat transfer coefficient of the

free hydrogen convection must be determined. The tank will be instrumented to allow

for monitoring of the temperature gradients in the liquid, so the total thermal energy in

the system can be calculated. Knowing the performance capabilities of the cryocooler as

a function of temperature, the rate of heat transfer from the liquid to the cold heat

exchanger can be calculated, and the heat transfer coefficient can be determined. The

cold head of the cryocooler will be designed to allow for a variety of heat exchangers to

be used. The initial cold heat exchanger will be bundled of OHFC copper extending

downward from the cold head. Future designs will include horizontal and vertical

surfaces with a variety of extended fins. The vertical position of the heat exchanger will

be variable by removing or replacing the heat pipe in the system. One enhancement

under consideration will be the addition of a mixing or stirring device in the tank. This





























39


could help the rate of heat transfer in two ways; ensuring a uniform temperature in the

tank, and creating a forced convection current across the cold HX.







CHAPTER 3
ANALYSIS OF GOVERNING EQUATIONS

In Chapter 2, the concept of the integrated refrigeration and storage system was

discussed, and the behavior of the system was addressed from a qualitative standpoint.

This chapter will look at the thermodynamic behavior from a quantitative perspective.

First, a thermodynamic model of the proposed liquefaction cycle will be developed. This

model will integrate the closed cycle helium refrigerator into the hydrogen input stream.

Details on the system operating characteristics will be presented, and a range of

acceptable intermediate cycle temperatures will be found. Optimizing the cycle

parameters, namely the hydrogen and helium compression ratios and the intermediate

temperature, to minimize the total work input will be completed. Next, a simplified

model of the storage system will be made using a two-dimensional transient mass and

energy balance approach, starting with the integral form of the conservation equations.

This model will then look at specific operational situations and predict system behavior.

Where applicable, this behavior will be compared to experimental data obtained in

Chapter 6. Corrective changes to this model will be proposed to more accurately predict

the system behavior. These changes incorporate correction factors accounting for the

variable liquid level in the system as well as non-isothermal temperature profiles in the

ullage space that lead to variations in the system heat leak. Finally, since the bulk fluid

mass and energy balance approach still falls short of a true physical model of the system,

the full conservation equations will then be presented in differential form based on an

analysis of expected flow and heat transfer regimes. Initial conditions and boundary







values will be presented to fully pose the problem. This problem formulation is an

important first step in the generation of a full solution, as CFD experts may not have the

requisite experience in understanding the behavior of the system to be modeled. These

conservation equations will then be converted to dimensionless form, using the initial

system energy and heat leak rate as dimensional constants. This will provide insight into

the system behavior from the perspective of how much heat is entering the system with

respect to how much energy was initially in the system.

Thermodynamic Analysis of Liquefaction Cycle

Cycle Description

A novel cycle for hydrogen liquefaction is presented in this section. This cycle

takes advantage of the required helium refrigeration cycle needed for maintaining the

hydrogen in the controlled storage state and uses excess refrigeration capacity to precool

the incoming hydrogen stream as well as remove the latent heat of vaporization of any

saturated hydrogen vapors downstream of the expansion valve. A schematic of this

proposed cycle is show in Figure 3.1.

Pure hydrogen from a production plant enters the cycle at point 1 and is

compressed to pressure P2 by a hydrogen compressor. HX3 removes the heat of

compression and sends the ambient temperature, high-pressure hydrogen gas to the

recuperative heat exchanger HX3. In HX3, a cold helium refrigeration system removes

heat from the hydrogen and cools it down to the intermediate temperature T4. Then, the

cold compressed hydrogen is expanded through a Joule-Thompson valve to the storage

pressure P5. At this point, depending on the storage pressure P5 and the unexpanded

hydrogen state (T4, P4) the hydrogen is either a cold vapor or a two-phase flow. The

integrated heat exchanger HX4 inside the storage tank removes the remainder of the heat






42


to convert the hydrogen to 100% liquid that can be stored or drained from the tank at

location 6.


9 ,______

1 2 3 L
HX1 HX2




Hydrogen 14
Compressor I Helium
HX3 < urbine Compressor

S 16 15
4




JT
Valve




Turbine 2
12 LH2 13

HX4
6





Figure 3-1 Proposed Liquefaction Cycle Schematic

The closed cycle helium refrigerator in this model is a two-stage Brayton cycle

with external heat loads at HX3 and HX4. The helium is compressed from the low

pressure to an undefined high pressure P8. Heat of compression, as well as external heat

loads, is removed in HX2. The helium flow is split downstream of this heat exchanger,

and some mass flow ( th14 ) is split off to be expanded through the first (high temperature)


turbine. The remainder of the flow (rhlo) is pre-cooled in HX3 and then expanded in the








second (low temperature) turbine to a temperature required to remove the leftover heat of

the hydrogen vapors in the tank for that particular mass flow rate. Both expansion

turbines operate at the same pressure inlets and outlets and it is not a dual pressure cycle.

The two turbine flow streams recombine immediately downstream of HX3 and flow

together to pre-cool the high pressure helium stream and incoming hydrogen stream.

Some of the unique features that differentiate this cycle from other hydrogen

liquefaction cycles are now discussed. Note how the hydrogen input stream is not a

continuous cycle with cold vapors returning to the hydrogen compressor. The hydrogen

flow is in one direction only, from the compressor to the tank, and the ultimate liquid

yield is 100%. This is due to the presence of HX4, which removes the remaining heat of

vaporization from hydrogen downstream of the JT valve. In fact, in some cases the JT

expansion may not even be needed and no cooling of hydrogen comes internally from

expansion. The final pressure of the JT expansion is not fixed, but variable depending on

the mass flow rate of the hydrogen and the amount of cooling provided by the helium

refrigerator at HX4. In some cases this may be subatmospheric pressure if the desired

storage state is densified hydrogen.

The recuperative heat exchanger HX3 is a key component in this cycle. It is a

counterflow heat exchanger with two warm inlet streams and one cold inlet stream.

There is a net heat load on the helium cycle that is determined by the hydrogen mass flow

rate multiplied by the enthalpy difference between state 3 and state 4. The final hydrogen

temperature T4 prior to expansion is a variable to be optimized in the model. This

optimization is done in a later section with HX3 assumed to be a perfect heat exchanger

with no pressure drop. The advantages to using HX3 to precool the hydrogen are







obvious. The greater the amount of energy removed from the input stream at high

temperatures, the more efficient the cycle efficiency will be. This is the purpose for

many of the LN2 pre-cooled systems in use today, except this cycle does not use

consumable nitrogen as a pre-cooling source but relies on closed cycle helium

refrigeration instead. An additional feature is the incorporation of an ortho-para catalyst

in the inner passages of the hydrogen stream, which allows for the heat of conversion to

be removed continuously at every temperature in the most efficient manner possible.

The depiction of the compression step is shown for simplicity only and in most

cases multiple stages of compression will be used with interstate cooling. The helium

compressor is most probably an oil flooded screw compressor, and extra equipment will

be needed downstream of the compressor to remove oil and other contaminants prior to

flowing into the coldbox. These compressors are used successfully in large-scale helium

liquefiers at major particle accelerator facilities. The hydrogen can be compressed either

by a mechanical compressor or as a high pressure output of a hydrogen production

system, such as a steam methane reformer or an electrolysis unit. If the hydrogen is

already compressed by the production system, this will save energy by taking advantage

of the prior compression, and in these cases the work input for compression of hydrogen

will not be factored into the liquefaction work input. In some cases the hydrogen may

not even be compressed, if the JT expansion process is not needed. This is the situation

presented in the Chapter 6 experimentation section, with room temperature hydrogen

being cooled and liquefied entirely by the heat exchanger in the storage tank.

Model Development

A thermodynamic model based on the conservation of mass and conservation of

energy principles has been developed to predict cycle behavior and optimize the








operating conditions. The model uses P1, Tl, P7, T7, and rhhyd as input parameters. The

heat exchanger delta pressure and temperature can be specified as well, but in most cases

the heat exchange process was approximated as perfect. In the model, an isentropic

compression in one stage is used, but multiple stages and intercooling more closely

approximates an isothermal compression stage and would reduce the overall work input.

An isentropic expansion efficiency of 80% is used for the calculations for both the

compressors and expansion turbines. The desired liquefaction storage temperature is also

required as an input, and has a great effect on the outcome.

The compression ratios of the hydrogen and helium streams are variables to be

optimized. Work required for compression is calculated, then the heat exchange required

to reject the heat of compression is performed prior to flowing through the recuperative

heat exchanger. Knowing the desired storage pressure and the heat exchanger pressure

drops, the system pressures are known at all points in the cycle. The high temperature

turbine exit pressure is set by the low-pressure requirements of the compressor, and a

dual pressure system is not approximated. The unknown parameters at the recuperative

heat exchanger are the outlet temperatures (T4, TI 1, and T16) and the required helium

mass flow rates through both the high temperature and low temperature turbines.

Assuming an intermediate hydrogen temperature at T4, the other heat exchanger

temperatures can be calculated. The helium mass flow rates are then computed using the

energy balance on the tee and the energy balance across the whole heat exchanger by the

relations

m1h3 + i15 h5 = h16h6 = (h13 + 15)hl6 3-1

rh3 (h4 h+ ( h0) = m16 h,) 3-2







From there, an isenthalpic expansion is calculated across the JT valve to the desired

storage pressure. The heat required to fully liquefy the JT product stream is calculated,

and that determines the sizing of the helium at heat exchanger 4. If the hydrogen is not

saturated at the exit of the JT valve (a condition that can occur if T4 is not low enough or

P2 is not high enough), then the helium in HX4 must remove the remaining sensible heat

prior to hydrogen liquefaction. The low temperature expansion turbine pressure ratio is

already determined by the cycle parameters, so the turbine exit temperature is known.

The required mass flow rate is calculated using an energy balance across HX4. The

model optimizes the cycle in terms of minimum mass flow rate required for the desired

cooling in HX3 and HX4. Several constraints are placed on the optimization subroutine.

A minimum temperature at the outlet of the low temperature turbine is set at 14K to

eliminate the potential for freezing hydrogen in the vessel. The mass flow rates for all

points on the helium cycle must be positive or zero. The low-pressure helium stream into

the recuperator is constrained to be lower than the hydrogen exit intennrmediate

temperature and the high-pressure helium exit temperature.

Analysis

From the development of the model, it becomes apparent the independent variables

to be used in the optimization process are the hydrogen compression pressure P2, the

intennrmediate temperature downstream of the recuperative heat exchanger T4, and the

helium compression pressure P8. The combined work of the hydrogen and helium

compressors are the dependent variables to be minimized. This process can be repeated

for a range of inlet conditions and final storage pressures for hydrogen, variations in

compressor and turbine efficiencies, and inefficiencies in the recuperative heat exchange

process.








For a given pair of hydrogen and helium high pressures, there is a range of

intermediate temperatures that can be used to give a satisfactory solution to the equations

3-1 and 3-2. The family of curves shown in Figure 3.2 displays this relation. For this

figure, the hydrogen cycle was assumed to have no hydrogen compression and the stream

is isobaric at 120 kPa. This means no isenthalpic cooling of the hydrogen and the

liquefaction is completely performed by the heat exchange with the helium in HX3 and

HX4. Using a range of different helium pressures (ranging from 360 kPa to 7200 kPa),

the temperatures that give a non-trivial solution are plotted. If the intermediate

temperature is colder than the left hand curve in the figure, the system will not work

because the high temperature turbine will be limited to the temperatures it can achieve,

and T16 will not be less than T4. Similarly, using T4 higher than the right hand curve

requires a greater amount of cooling has to be performed at the low temperature turbine,

and the turbine exit temperature decreases. In order to get the required cooling inside the

storage tank, the mass flow rate increases. The recuperative heat exchanger becomes

unbalanced and eventually the required mass flow rate through the high temperature

turbine becomes zero. Notice the range of temperatures increase as the helium

compression ratio increases, which allows for greater cycle flexibility during operation.

Similar behavior was observed in the cycle when the hydrogen was compressed and

expanded in the JT valve. The dependence of the cycle feasibility on a small range of

acceptable intermediate temperatures places many constraints on the actual system, and

care must be taken to ensure the cycle does not operate outside these limits. It is also

shown later that the overall work increases as the intermediate temperature increases, so

operating on the left hand side of the curve is desired.






48



8000
P2 =120 kPa
P7 = 120 kPa
7000 P5 = 101 kPa
% = 0.80
rt = 0.80
6000 AP, = 10 kPa
AT,= 0
5000


"! 4000


3000-


2000

1000

0 -
20 25 30 35 40 45 50
T4 (K)


Figure 3-2 Acceptable Intermediate Temperatures as a Function of Helium Compression

The figure above gives no information on the work input requirements, only


operating conditions that are acceptable for the cycle at those temperatures and pressures.


Since the cost of liquefaction is directly related to the energy input rate, regards for the


dependence of work input on the system operating points should be considered. Below,


Figure 3-3 plots the work input for liquefaction of 1 gram per second of gaseous


hydrogen against the intermediate cycle temperature, for a range of compression ratios in


the helium cycle. All other cycle parameters are constant and defined below. No work


input was done on the incoming hydrogen gas stream and all cooling was done through a


heat exchange process in HX3 and HX4. Notice there is a range of acceptable solutions


for certain intermediate temperatures, and points past the endpoints of the isobaric lines


do not have solutions that converge in the model. For a given helium compression ratio,


the work input is reduced as the intermediate temperature is decreased. This dependence


is more pronounced as the helium compression is reduced, as small increases in T4 lead










too much larger increases in work input. In addition, the required work actually increases


for these smaller pressure ratios, due to the increase in required mass flow rate.


Subsequent analysis therefore concentrates on helium compression ratios of 10 or greater.


205000
P2 =120 kPa
195000 P7 = 120 kPa
P5 = 101 kPa
185000 7, =0.80

175000 = 0.80
AP, = 10 kPa P
165000 P8 (kPa)
A = 0 --1200
155000 -U-2400
3600
g 145000 4600
1 06000
135000 -*-7200
-+-I840
125000 600
360
115000

105000

95000 /

85000
75000
25 30 35 40 45 50
T4 (K)


Figure 3-3 Compression Work vs Intermediate Temperature (P2=120 kPa)


Figure 3.4 shows a similar plot of work vs T4 for a cycle that has some


compression work in the hydrogen side. The hydrogen compression ratio is 10, and some


isenthalpic cooling is occurring at the JT valve. Note the lower helium compression ratios


are not included in the figure. The plots look very similar to the case where there is no


hydrogen compression (Figure 3-3), but there are some slight differences in values of


total work. These differences will be explored a little later in Figure 3.8, when the work


is plotted as a function of the hydrogen compression ratio. Again, for the low helium


pressures, there is a steep increase in work for very small increases in intermediate


temperature, and these cycles should be avoided if possible. The higher helium


compression cycles also exhibit greatly increased work input requirements.

















ATH = 0 P8 (kPa)
155000 -.-1200
2400
3600
4800
135000-000
--7200

115000


95000 -



30 32 34 36 38 40 42 44 46 48 50
T4 (K)


Figure 3-4 Compression Work vs Intermediate Temperature (P2=1200 kPa)

Meanwhile, it is informative to look at some of the cycle parameters in this case to


see how the cycle functions. Figure 3-5 plots the required helium mass flow rate through

each turbine as a function of intermediate temperature for a cycle with both the hydrogen


and helium compression ratios set at 10 to 1. Note how the overall mass flow rate

increases as the intermediate temperature increases, and the high temperature turbine

flow rate decreases from approximately 10% of the flow at the lower T4 to zero at the


upper end of the T4 curve. The secondary y-axis plots the work input for both the

hydrogen and helium. The hydrogen work is constant since the compression ratio and


mass flow rate are fixed. The helium work input increases due to the increase in requires

mass flow rate, even though the compression ratio is fixed.

Another way to evaluate the efficiency of each cycle is to look at the heat rejected


by the hydrogen in each heat exchanger. Figure 3-6 shows the heat rejection in HX3 and

HX4 for a range of intermediate temperatures and helium compression ratios, with the













P2 = 1200 kPa
P8 = 1200 kPa
45 P7 = 120 kPa
P5 = 101 kPa 120000
r = 0.80
40 = 0.80

35 AP = 10 kPa 100000


30.1
3 8 00 --Ti flow

2 t -U-T2 flow
25 o Hydrogen work
Helium work
60000
2 20

15 40000

10
20000
5 -

0 0
33 5 34 34 5 35 35 5 36 36 5 37 37 5 38
T4 (K)



Figure 3-5 Turbine Mass Flow Rates and Cycle Work


hydrogen pressure fixed at 1200 kPa. The upper curve shows the majority of the heat


being rejected in HX3, which is the higher temperature heat exchange. However, for


warmer intermediate temperatures, the amount of heat rejected is decreased in HX3 and


increased in HX4. This fact does not change with increases in helium cycle pressure, as


is evidenced by the different P8 curves plotting on top of each other. Another way of


looking at this plot is to think the cycle that rejects the greatest amount of heat at the


highest temperatures will be the most efficient, and the work curves plotted in Figures 3-


3 and 3-4 provide more evidence of this.


In the proceeding paragraphs, it is demonstrated that the optimum intermediate


temperature to have in the cycle is the lowest temperature allowed for the given hydrogen


and helium pressures. The next step is determining the work required as a function of


hydrogen pressure. The total amount of hydrogen work is much less than the helium










4500

4000 P2 = 1200kPa
P7 = 1ZO kPa
P5 = 101 kPa
3500
q = 0.80
S= 0.80
3000- AP =10 ka
AT = -*-HX3 (P8= 1200)
2500- --HX4 (P8=1200)
g HX3 (P8=2400)
g HX4 (P8=2400)
2000 -,e-HX3 (PB=3600)
-*-HX4 (PB=3600)
1500

1000




0
30 32 34 36 38 40 42 44 46
T4 (K)


Figure 3-6 Heat Rejection at HX3 and HX4


work due to the flowrates involve, but an overall advantage can occur if some level of


cooling can be achieved by hydrogen expansion. Again, work input may not matter if the


work is from the hydrogen production process. Figure 3-7 shows the work required as a


function of T4 for a range of hydrogen pressures. The helium cycle is working at a


pressure of 2400 kPa. There is little movement in the curves for the pressure ratios less


than 10 to 1, then gradually the curve shifts to the higher temperature areas. Then the


curves start clustering again above P2=3000 and no further advantage can be gained by


higher compression.


Choosing the lowest temperature point in the curves in Figure 3-7 obtains a plot


of lowest allowed work input for each specific helium compression ratio as a function of


hydrogen pressure. Figure 3-8 shows there is an initial small spike in compression work,


followed by a decrease to a local minimum, followed by a gradual increase as systems


reach very high hydrogen pressures. This shows there exists an optimum hydrogen


















AP3X = 10 kPa P2 (kPa)
130000 ATX = 0 -o-120

120000 30
->-1200
110000 -*-2400
-+-4800
-*6000
100000 7200

80000

80000

70000
34 36 38 40 42 44 46
T4 (K)


Figure 3-7 Cycle Work vs Temperature for a Range of Hydrogen Pressures

pressure, for each helium pressure and intermediate temperature, for which the


liquefaction cycle operates at maximum thermodynamic efficiency. This hydrogen


pressure occurs at 2400 kPa. Similarly, Figure 3-9 shows the cycle work for a range of


helium pressure ratios. It is evident there exists a helium pressure that leads to a


minimization of work for each set of hydrogen pressures, and this pressure is below 1200


kPa. This figure also shows the curve with a hydrogen pressure of 2400 kPa provides the


lowest work total.


Based on the above analysis, it is concluded that the proposed combined hydrogen


and helium liquefaction cycle is feasible, and a range of operating conditions exist. There


is a minimum and a maximum intermediate temperature that can be used downstream of


the recuperative heat exchanger. Temperatures higher than this range will not work due to


HX3 becoming unbalanced as the mass flow rate through the high temperature turbine













goes to zero. Temperatures lower than the acceptable range will not work due to the high



temperature turbine not being able to provide a low enough temperature to


90000


P7 = 120kPa
P5 = 101 kPa
S=0.80
r = 0.80
APHr = 10 kPa
AT2r = 0


85000





80000





75000


0 1000 2000 3000 4000 5000
Hydrogen pressure (kPa)



Figure 3-8 Cycle Work vs Hydrogen Pressure


80000





85000





80000





75000


P7 = 120 kPa
P5 = 101 kPa
71 = 0.80
7, =0.80
AP, = 10 kPa
A7-,a=O


P8 (kPa)
-a-2400
-U-1200
3B00


6000 7000 8000


P2 (kPa)
-+-120
-m-480
1200
2400
--4800


0 500 1000 1500 2000
Helium pressure (kPa)


2500 3000 3500 4000


Figure 3-9 Cycle Work vs Helium Pressure


70000







ensure T16 is less than T4. The most efficient intermediate temperature to use for a

given set of hydrogen and helium pressures is the lowest temperature possible. This

maximized the amount of heat rejected at higher temperatures. The analysis in this

section also shows the functional relationship between hydrogen and helium pressures

and work. It is shown the most efficient cycle will operate with the hydrogen pressure at

2400 kPa, and a helium pressure at 1200 kPa. The efficiency of the liquefaction system

is 17%, which is respectable for a small scale LH2 system with only 1 intermediate stage.

Thermodynamic Analysis of Storage System

An effort will now be made to model the thermodynamic behavior of the liquid

hydrogen in the storage tank for a variety of operating conditions. In many practical

applications, simplifications to the full conservation equations can be made to provide

great insight into the physical characteristics of a system without sacrificing too much

accuracy. Such simplifications allow for closed form analytical solutions that do not

require sophisticated numerical techniques to solve. This section will focus on applying

these simplifications over a control volume to obtain general expressions for the mass

and energy balance of the system. These control volume mass and energy balances will

then be tailored for the specific operational constraints found during the zero boil off,

liquefaction, and densification processes, and these specific expressions will be compared

to results of the experimental testing discussed in Chapter 6.

Definitions and Assumptions

The control volume to be analyzed is presented in Figure 3-10. A cylindrical

double walled tank of volume 150 liters, with a diameter of 50.8 cm and length of 74 cm,

is initially partially full of liquid hydrogen in the saturated condition. The temperature of

the tank is well below the ambient temperature and there is a flow of heat into the tank








from the surroundings through the insulation into the system. This heat transfer can be

assumed to be of two forms, the radiation heat transfer from the outer vessel to the inner

vessel, and conduction heat transfer down the length of the neck of the vessel and other

solid supports. In addition, there is a cold heat exchanger integrated into the vessel that

can remove heat from the liquid. There are three ports connecting the inner vessel to the

surroundings. The liquid fill and withdraw port is present to allow for the flow of the

hydrogen from the storage vessel to the use point, in this case the flight tank of a rocket.

The vent port is designed to vent vapor from the top of the tank to the ambient pressure

surroundings, either in a controlled vent or as an emergency relief when the system

pressure reaches the maximum operating pressure. The gas supply port is necessary to

allow for pressurization of the fluid as well as to introduce hydrogen gas for liquefaction

operations. The inner tank holds only hydrogen in gaseous or liquid form. The system

thus defined constitutes an open, transient, homogeneous, multiphase system with heat

and work interactions.

Despite the apparent complexity of the system as defined above, numerous

simplifications can be made to allow for fairly accurate analysis. First, it can be assumed

that the time constant associated with defining an equilibrium state between the liquid

and vapor phases is much less than the time constant associated with any system

interactions with the surroundings. This assumption is valid as long as the heat transfer

into or out of the system is low, as it typically is in well insulated cryogenic vessels, or

the mass flow rate into and out of the system is small compared to the total system

mass. 37) This defines the system as being in thermodynamic equilibrium with respect to

the liquid and vapor phases, and requires the liquid and vapor phases to have equal













VGas Supply Port (gsp)


Figure 3-10 Simplified system representation

temperature and pressure. It is important to keep in mind that the definition of

thermodynamic equilibrium does not imply there is no time dependence in the system,

and in this case the model is a still a transient system.

A second assumption is the liquid and vapor phase have a defined, impenetrable

boundary. It is assumed there are no bubbles in the liquid and no mist in the vapor. This

allows for modeling the system as a combination of two separate single-phase control


Vent Port (vp)









volumes, with heat and mass transfer between them at the liquid to vapor interface. The

overall volume of these control volumes will vary with time, depending on the level of

evaporation or condensation at the interface as well as the temperature and pressure of the

liquid and vapor.

Next, assumptions about the properties of the fluids must be made. The fluid

velocities are considered small. Effects of heat addition or removal and mass addition or

removal are considered over the entire control volume instantaneously, and there are no

boundary layer effects. The fluid can therefore be assumed inviscid. Since interactions

with the surroundings are assumed to act instantaneously, the fluid properties are

assumed to be constant with respect to spatial dimensions in the control volume.

Conservation of Mass

The general form of the conservation of mass equation for a fixed control volume

can be expressed in integral form as(38)


8 pdV = p7* dS 3-3
v S

For the system described in Figure 3-10, with uniform, one-dimensional flow

across one inlet and two outlet locations, the conservation of mass reduces to


pdV g = p u gAg pf uiAf.Af p uP AP 3-4


While the total control volume is fixed, there are actually two volumes of interest

inside the tank that are variable, the total liquid volume and the total gas volume.

Breaking these up into separate volumes, and assuming the density is constant in that

particular volume, the conservation of mass equation becomes










-aPiV +y-PgVgs = Pgspu Agsp PwuoAlf" PvpU A 3-5

For this model, it is assumed that the thermodynamic state and the total mass flow

rate of the gas entering the gas supply port is known. The density of the vapor venting out

of the tank is assumed to be equal to the density of the vapor in the ullage, and the density

of the liquid leaving the tank out the liquid withdraw port is assumed to be equal to the

density of the bulk liquid in the control volume. Using the assumption that the system

can be treated as a bulk fluid, the mass addition is immediately distributed over the entire

control volume and the effects of the fluid velocity at the inlets are outlets are neglected.

Breaking up the system into two control volumes at the liquid to vapor interface the

following expressions for the conservation of mass are obtained

Pg2 V2 PglVg = (mggp hvp + fg )At 3-6

Pi12V PiVl = (-mlh f )At 3-7

Conservation of Energy

The general form of the conservation of energy equation for a fixed control volume,

assuming inviscid flow and neglecting gravitational potential energy and assuming there

are no internal reactions that are exothermic or endothermic, can be expressed in integral

form as(38)



J4pdV- PV dS+f p(F* V)dV= 3-8
v S v


aL[p(u + V2 +2
u-)]dV+fjp(u -)V dS









where the first term is the rate of heat added to the fluid inside the control volume from

the surroundings,38) the second term is the rate of work done on the fluid by surface

(pressure) forces, the third term is the rate of work done on the control volume by body

forces, the fourth term is the time rate of change of energy inside the control volume due

to transient effects, and the fifth term is the net rate of flow of energy across the control

surface.

Breaking down the first term, 4 is defined as the rate of heat added per unit mass.

Physically accurate modeling of this heat transfer would account for the heat flux across a

narrow thermal boundary layer near the surface of the tank, however this control volume

model assumes bulk fluid properties and no boundary layer effects. Furthermore, the

nature of the integrated refrigeration and storage system includes two heat transfer

mechanisms, the heat leak into the tank from the ambient surroundings as well as the heat

removed from the system from the refrigerator. Integrating the first term over the entire

volume therefore gives the following simplified expression for heat transfer to the system

as

4cpdV = QHL QREF 3-9


Body forces, namely the gravitational effects required for natural convection, are an

important physical effect that must be taken into account to accurately predict the heat

transfer rates across the system boundaries. However, for this simple control volume

mass and energy balance where bulk fluid properties and inviscid flow are assumed, the

work done by body forces can be neglected, and the third term in Equation 3-8 can be

dropped.








Assuming the fluid velocities are negligible, the effect of kinetic energy of the fluid

can be neglected. Again assuming bulk fluid properties, the density and internal energy

of the fluid are constant in the control volume and can be taken out of the volume integral

in the fourth term. After integrating over the control volume, the transient term the right

hand side becomes


P( -)]dV mu 3-10
at 2 at

The two surface integrals can be evaluated together. This integral is evaluated only

over the inlet and outlet locations since V dS equals zero at all other locations.

Assuming bulk fluid properties, the evaluation of these integrals yields

Pi7 dS + pu7 dS= 3-11
S S

(P, + pPuX )V1Aj (P2 + p2u2 )A2 + (P3 + p3u)V3A,

Rearranging Equations 3-9, 3-10, and 3-11, substituting in the definitions for mass

flow rate and enthalpy, breaking up this expression for separate control volumes in the

liquid and vapor space, and integrating over time reduces the general conservation of

energy equation to(39,40))

PgzVgzhg2 glglh l= hg9phggsp At thvphv+At + fg hghAt 3-12

P12Ivh2 P 1vlh11= QHL -QREF lfwh At h fghg At 3-13

where the mass flow rate between the liquid and vapor phases is found by assuming all

heat leak into the tank enters the liquid control volume and creates an equivalent amount

of boil off to the vapor control volume. The heat leak term is the summation of the

individual heat transfer components of conduction down the solid supports and








convection and radiation thru the MLI. The selection of the vapor enthalpy as the amount

of energy leaving the liquid control volume is somewhat arbitrary, and reflects the true

control volume boundary as being drawn macroscopically in the vapor space above the

liquid level.

Equation of State

At these low temperatures, the ideal gas model cannot be assumed. To relate the

thermodynamic properties of pressure, temperature, and specific volume, the National

Institute of Standards and Technology (NIST) Thermophysical Properties Database

RefProp was used. This database incorporates the Modified Benedict-Webb-Rubin

(MBWR) equation of state for hydrogen, using eight empirical constants derived from

testing at the NIST laboratory. 41) Once the state of the fluid is determined, Maxwell's

relations can be used to find the other thermodynamic variables.

Operational Simplifications

Although the above equations can be used for analysis of operations with multiple

simultaneous mass influx and outflows, such scenarios are rare. In the vast majority of

operations, there will be mass influx or outflow through only one of the ports at a time, if

any at all. The operations can be classified depending on whether the system is open or

closed to mass transfer from the surroundings, and the direction of heat transfer in the

system. Table 3-1 shows the different operating characteristics of the system. If the

refrigerator is operating and greater the capacity is greater than the heat leak, the heat

transfer is out of the system, and if the refrigeration capacity is less than the heat leak the

net heat transfer is into the system. This leads to the following simplifications of the

conservation equations, depending on the operational scenario.








Table 3-1 Operational scenarios
HEAT IN ADIABATIC HEAT OUT

MASS IN Gas Pressurization Liquefaction


CLOSED Self Pressurization ZBO Densification


MASS OUT Boil Off or Liquid Transfer Liquid Transfer
Transfer

Closed Storage With Heat Transfer To the System (Self Pressurization)

Current storage systems often have periods of time where they are vented and then

closed from the surroundings. During these periods, the valves remain closed and the

heat leak into the tank creates an evaporation of liquid that causes a pressurization of the

system. The pressure will rise until the maximum operating pressure is reached and the

relief valve opens. During this time, the mass inside the entire tank is constant, but the

relative amounts of liquid mass and vapor mass will change. The conservation of mass

equations for the vapor and liquid space can be expressed as

Pg2Vg2 PgiVgi = h fg At 3-14

Pl2V2 lVl = -fg At 3-15

During this period it is assumed the refrigerator is off and the only heat transfer in

the model is the heat leak. The conservation of energy equations for the vapor and liquid

space can be written as

Pg2Vg2hg2 Pg Vglh l= h fg hg At 3-16

P1z2V2h12 pJIlhn= HL- fghg At 3-17

The above equations have seven unknowns (Pg2, Vg2 h g2, 12 V 2 ,h12, and_ rhnf ).

The initial temperature and pressure in the tank are known giving the rest of the initial








thermodynamic state variables, and the heat leak is assumed known by either design data

on the insulation system effectiveness or by experimentation. However the liquid and

vapor volume are related by the following expression,

V =V +V 3-18

and the mass flow between the liquid and vapor depends on the heat transfer by

QHL = th g hfg 3-19

Combing equations 3-14 thru 3-19 with the equation of state, the system of seven

equations and seven unknowns can then be solved.

A Microsoft Excel based program has been written to model this behavior. First,

the heat leak into the system is estimated for the given initial conditions. This heat leak

model includes the effects of radiation and convection thru the multi layer insulation as

well as the effect of conduction down the solid wall of the neck and various interface

tubing. The radiation and convection across the tank surface area follows the modified

Lockheed correlation for multi layer insulation.(42) This takes into account the number of

layers of insulation, the density of the layers, and the boundary conditions of temperature.

This also assumes a vacuum in the annulus of less than 10-3 Torr. The conduction heat

leak down the length of the neck or tube can be found by the Fourier equation, except the

thermal conductivity will not be constant over that wide range of temperatures. The

thermal conductivity can be integrated over a range of temperatures if the governing

equation is known, and the thermal conductivity integral has been calculated for a range

of materials and temperatures by McMordie.(43) These relations are then added into the

model to create an estimate for heat leak into the tank as a function of geometry and

thermal boundary conditions. For this model, it is assumed the upper boundary









temperature is constant at 300K, while the lower boundary temperature is variable and

equal to the fluid temperature at that instant.

Once the heat leak is known, the total interactions with the surroundings are known

since this is a closed system. Next, the initial temperature, pressure, and mass are set, and

the rest of the initial conditions are determined. Then, the equation of state is used to find

the liquid and vapor densities. Then the total volume of liquid and gas are found using the

conservation of mass and the volume relation expressed in Equation 3-18. The liquid and

vapor specific enthalpies are found using the RefProp program, and the total liquid and

vapor enthalpy is then computed. At this point all state properties of the liquid and vapor

phases are known for the initial condition. The total amount of energy transferred into the

system is then calculated by multiplying the heat leak rate by the chosen timestep.

Ideally, knowing the new enthalpy in the tank, RefProp should be able to calculate the

new pressure since the specific enthalpy and the density of the system are known.

Unfortunately, there are some thermodynamic states for certain fluids where convergence

of the enthalpy/density specifications cannot be met by the RefProp program, and this

proved to be the case in this situation. An alternate procedure was developed, where a

new pressure is assumed, then new liquid and vapor enthalpies and total quality are

calculated, and the total system enthalpy is compared to the previous timestep plus the

known heat leak. The Excel add in Solver was used to eliminate the differences in these

system enthalpies by varying the pressure, and a new system pressure was determined.

This model was used to predict system pressure and temperature increases over a

period of time for a liquid hydrogen system with a known heat leak. Figure 3-11 shows









the temperature and pressure for a 150-liter hydrogen dewar initially filled with liquid

hydrogen at the 50% mark. Notice the system temperature rate


450 30

400 V=50% (5412 g) --29
Q-f(T) 28
350 -
--27
300 26 26
S-- P (kPa)
S250 25
2- --T(K)
0 24 E
200- --240
-23
150
-22
100 -21

50 20
0 240 480 720 960
Time (min)

Figure 3-11 Self pressurization temperature and pressure vs. time

of increase begins to fall while the pressurization rate of increase gets larger as time

progresses. As the time continues, the system temperature increases so the heat of

vaporization decreases, and more of the heat leak is contributing to latent heating of the

hydrogen as opposed to sensible heating.

Although liquid hydrogen is being converted into a vapor, the overall liquid level

continues to rise over time. Figure 3-12 shows the system quality and the liquid and

vapor volumes respectively. Notice the fraction of the vapor in the system increases in a

similar manner to the pressure, again this is due to the decrease in the heat of

vaporization. But due to a decrease in density in the warmer liquid, the overall liquid

volume is increasing. The corresponding decrease in vapor volume also plays a role in

the pressurization rate increase, although the vapor density is also increasing. This

increase in liquid volume is critical to the design of dewars especially when they are near
































Figure 3-12 Self pressurization tank quality and phase volume vs. time

their 100% full level, since further increases in temperature will lead to thermal

expansion of the incompressible liquid, and a rapid overpressurization may occur.

A comparison of system pressurization rates is shown in Figure 3-13 for three

different liquid levels. It seems intuitive that the system that is most full will pressurize

more quickly since there is less vapor space to fill. However, this proves not to be the

case. This is explained by the fact that the greater the liquid quantity in the tank, the

more of the heat leak is absorbed by sensible heat of the liquid and less goes to

vaporization. For example, the liquid absorbed 97% of the heat leak into the system as

sensible energy for the tank that was 75% full, but only 78% of the heat leak for the 25%

full case.

Figure 3-14 shows the behavior of the system as predicted by the model compared

to the experimental data. The data is from a zero boil off test conducted overnight with

the cryocooler turned off, after liquefaction operations introduced 1.25 kg of hydrogen

into the tank. The initial pressure was measured at 33 kPa. As is evident in the graph,


82000 0.10
P1=101 kPa
T1=20.2 K
80000-
Liquid Volume 0.08
78000 -

0.06
E 76000 0.06

3 74000- Quality 0.04

72000
0.02
70000
Vapor Volume
68000 0.00
0 200 400 600 800 1000
Time (min)




































Figure 3-13


Self pressurization rates for variable liquid level


300

T1=17.6K
250 Liquid volume =16 L


200
I-
50- --Model
50 --Experiment

a.
100 -


50-


0
0 150 300 450
Time (min)



Figure 3-14 Self pressurization (model vs. data)


the predicted system pressurization rate is within 15% of the actual test data. This


discrepancy is explained by the assumptions that the tank is modeled as an isothermal


system, with the temperature at the top of the tank being equal to the temperature at the


bottom (liquid temperature). The heat leak estimate assumes the tank is nearly full, so it


450

400 -

350 -

300 -

` 250 25% full
50% full
S200- 75% full
a.
150-

100-

50 T1=20.3 K
Q=f(T)
0 1
0 200 400 600 800 1000 1200 1400
Time (min)










gives the heat leak rate for tanks in this condition. In this instance, 1.25 kg of hydrogen

only had a liquid level of 16 liters, and there was a large temperature gradient down the

length of the tank, reducing the heat leak compared to the model prediction. Corrections

to this model will be made in later sections to account for variable liquid levels.

Open Storage With Heat Transfer To The System (Boil off)

There may be periods of time when the heat leak into the tank created a pressure

rise that causes the tank relief valve to open, creating a boil off loss. During these times,

it is assumed the system is closed to gaseous mass input or from liquid mass output.

Typically during boil off situations, the tank pressure will remain constant, at the set

pressure of the relief valve. Some systems with no backpressure vent directly to

atmospheric pressure. This implies the liquid temperature inside the tank will also remain

constant, at the saturation temperature corresponding to the tank pressure, and so the

liquid density is also constant. Likewise, the vapor temperature and density can assume to

be constant, although there will be some small increase in density as the liquid boil off

creates a forced convection current that cools the upper part of the vapor volume. The

conservation of mass equations then reduce to

Pg (Vg2 Vg ) = (- hp +fg)At 3-20

P (V2 Vl)= -f At 3-21

and the conservation of energy equations reduce to

Phg (Vg2 Vg) = h, At + m hghAt 3-22

Pih (V Q V L) = Q mfghg At 3-23









The above equations have four unknowns and can be solved easily. Note the

equation of state is not necessary since the state of the fluid is assumed constant with the

isobaric venting process.

A Microsoft Excel spreadsheet has been developed to model this boil off process.

Initial conditions and system constraints are first determined. For this example, the initial

system mass must be input, and the relief valve set pressure is determined. Using these

parameters with the system volume, the initial temperature, liquid and vapor mass,

density and volumes, and heat of vaporization are calculated. The system heat leak is

calculated for this tank temperature. Then, the mass of the liquid boil off is calculated,

and the new liquid mass and volumes are found. Next, the new vapor volume is

calculated and using the constant vapor density, a new vapor mass is found. Knowing the

initial and final vapor and liquid masses, the mass of the vent loss is calculated. This

mass will always be slightly less than the mass of the liquid boil off, since some boil off

vapor must fill in the additional volume lost by the liquid.

Figure 3-15 shows the values of liquid and vapor mass in a 150 liter dewar filled

halfway with liquid hydrogen at atmospheric pressure. Notice the liquid mass drops at an

approximately linear rate, since the heat leak is a function of the constant liquid

temperature. The vapor mass increases slightly over the boil off process. Figure 3-16

compares the time it takes to completely evaporate a given volume of liquid depending

on the boil off pressure. Hydrogen storage losses occur more quickly when the vapor

pressure is elevated, mainly due to the decrease in heat of vaporization, but also partly

due to the greater mass fraction of hydrogen that is in the vapor phase initially.






71



5000

Pl=101 kPa
T1=20.3 K
4000-



3000 -
00 -- Liquid

-Vapor
2000-



1000-



0-
0 10 20 30 40 50 60 70 80
Time (hr)

Figure 3-15 Liquid and vapor mass during boil off


5000
Liquid Volume = 75 L

4000-



S3000- -P=1 atm
S-P = 3 atm
P = 5 atm
2* 2000 P = 0.05 atm
--Is.-----


1000-



0
0 10 20 30 40 50 60 70 80
Time (hr)



Figure 3-16 Boil off time dependence on pressure


The simplification made that the liquid and vapor temperature and pressure were uniform


throughout the volume makes this boil off model less precise, in actuality there will be


temperature gradients in the ullage space and down the tank walls that will decrease the


total heat transfer to the liquid as the liquid volume drops. There is no experimental data








in this work to compare this model to, since no boil off occurred during the liquid

hydrogen experimentation portion discussed in Chapter 6.

Closed Storage With Zero Net Heat Transfer (Zero Boil Off)

The ZBO operation is a closed storage system with refrigeration provided to

remove heat leak into the tank. The state of the fluid will depend on the capacity of the

refrigeration system. There exists a point on the refrigerator capacity vs. temperature

curve where the capacity is exactly equal to the heat leak into the tank. As such the

system can be modeled as steady state and the conservation equations can be reduced to

V2 = Vg 3-24


V2 = 3-25


QL = QREF 3-26

As given by Cryomech, the AL330 performance curve is plotted with the heat leak vs.

temperature curve below in Figure 3-17. After curve fitting the performance curve,


100



75
Predicted Cry ocooler
Performance(63)

50-

U ZBO Data Points
25- / Predicted Heat Leak(59)




10 15 20 25 30
Temperature (K)


Figure 3-17 Cryocooler performance and heat leak vs. temperature







the equations can be set equal to each other and solved for the intersection, which is

16.25 K. This system temperature can be considered analogous to a cryocooler no-load

temperature. The results of this closed system energy balance derived in this section

agrees very well with the experimentation value of no load system temperature, ranging

from 16.42 K to 16.85 K, obtained during several densification tests. These data points

are plotted on the cryocooler curve and are labeled below

Open System With Heat Transfer Out Of The System (Liquefaction)

During liquefaction operations it is preferable there is no mass outflow from the

tank, so there is always an increase in overall system mass. The refrigeration system

must be operating (except when stored refrigeration energy in a subcooled liquid can

temporarily liquefy a small quantity of gas) to remove the enthalpy flowing into the gas

supply port. The conservation equations can be simplified as follows;

pgVg2V PglVg = (mhgp + thfg )At 3-27

P2V2 -- PVl = -mhfg At 3-28

PgzVgzhg2 PglVhgl= mhgh ggpAt + fg h At 3-29

12V2 h12 Pl h1l= QHL -QREF fghg At 3-30

At first it is tempting to consider the liquefaction model to be equivalent to the boil

off model as they both are open systems with net heat exchange, but instead of heat

transfer into the tank and mass transfer out of the tank, the liquefaction system operates in

the opposite direction. However this is not accurate, as there are additional

simplifications in the boil off model imposed by the relief valve, namely that the pressure

in the tank is constant. Depending on the gas supply port mass flow rate and the net

amount of refrigeration, the tank pressure may increase, decrease, or remain constant. But








during operations where the ullage pressure is increasing, gas is entering the tank at a

faster rate than the cryocooler capability to remove its energy, and a non-saturated vapor

condition occurs. This phenomenon is not described accurately by this model, which

assumes thermodynamic equilibrium between the liquid and vapor phases.

The model has been modified to accept these conditions and predict the system

liquefaction rate to maintain thermal equilibrium for a given set of initial conditions. The

net heat transfer out of the system from the combination of heat leak and cryogenic

refrigeration is then calculated for that given temperature condition. To maintain

equilibrium this must match the increase in system enthalpy from the gas supply port.

Knowing the conditions of the inlet stream and the final liquid state, the change in

enthalpy required for liquefaction is calculated. The appropriate mass and vapor volumes

are then found. Figure 3-18 shows predicted liquefaction rates for a range of storage

states. This chart shows the liquefaction rate increases as expected, when the storage

pressure is higher. This is due to the saturation temperature corresponding to this

pressure being higher, which has three effects. First, the cryocooler operates more

efficiently at higher temperatures and there is greater cooling power available. Second,

the amount of enthalpy required to be removed from the incoming gas is less. Finally,

the net heat transfer from the surroundings is slightly less since there is a smaller thermal

gradient.

Figure 3-18 also shows the experimental data for three periods where the mass flow

rate was constant and sufficient to maintain a constant pressure in the tank. This

comparison shows a general correlation in the shape of the profile, but the results vary by

as much as +/- 28%. The discrepancies between the predicted vs. actual liquefaction








rates can be partially explained by the experiment not taking into account the heat of

conversion between ortho and para hydrogen. The model assumes equilibrium hydrogen

but there is a finite time required to change the normal hydrogen to equilibrium

hydrogen. Other factors include the actual experiment was not an isothermal system and

there were temperature stratifications that the model did not include. An additional cause

of the discrepancy is the uncertainty in the measurements, since the exact state of the

incoming gas was not known and there was no experimental method to control the


10
9-
8-
7
E 6- -model
5 expedment 1
a experiment 2
o 4 experiment 3
,-.


2-

1
0
60 80 100 120 140 160
Pressure (kPa)


Figure 3-18 Comparison of predicted vs. actual liquefaction rate

pressure and mass flow rate. In these cases it can be seen that while the pressure and mass

flow rate was relatively constant, there were variations in the measurements that implied

the system was not truly in thermodynamic equilibrium. These uncertainties are plotted

as x and y error bars in the individual liquefaction experiment data points. In some cases,

variations in the "constant" mass flow rate were as high as 8.7%, and pressure

fluctuations were up to 2.2%. Clearly, more data needs to be collected, and with better

control and fidelity.









Closed Storage With Heat Transfer Out Of The System (Densification)

A closed system with heat transfer out of the system by refrigeration is similar to

the closed self-pressurization case with the exception the pressure and temperature will

decrease until the system reaches steady state and the refrigeration capacity balances out

the heat leak into the tank. In the meantime, the mass of the liquid and vapor will change

as some vapor is condensed out of the ullage space. The conservation equations can be

written as

Pg2Vg2 PglVgl = fg At 3-31

P12V 2 P =1 -fg At 3-32

Pg2Vg2hg2 PgVgh = fghg At 3-33

P,2V212 -PIjVIhjl=QHL -QREF hfg g At 3-34

Again this is a system of seven unknowns and seven equations (including the

volume relation, the mass transfer between the vapor and liquid relation, and the equation

of state), and can be solved in a similar manner. The same Excel program was used to

estimate densification rates as the self pressurization rates, with the exception that the

heat transfer rate previously given by the heat leak estimation is now the difference

between the heat leak and the refrigeration capacity of the cryocooler at the system

temperature. Results of this model are shown below.

Figure 3-19 shows the temperature and pressure of the system with a tank initially

50% full of LH2 at the normal boiling point. The pressure and temperature decrease

more rapidly at first since the cryocooler is producing more refrigeration at higher

temperatures. Eventually the pressure and temperature reach the steady state condition






77



120 25

Liquid Volume = 75 L
100-
23

80
21 21
42 605 -Pressure
S--Temperature
219 E
a. C
40

20 17
20-


0 15
0 2 4 6 8
Time (hr)



Figure 3-19 Predicted densification temperature and pressure


defined by the zero boil off model. Figure 3-20 demonstrated the predicted densification


times for three different initial liquid levels ranging from 25% to 75% full. As expected


the smaller the mass in the tank, the less time it takes for densification. Some launch


Figure 3-20 Densification rates for variable liquid levels








scenarios may depend on on-board densification, and predictive models will need to be

developed to estimate countdown hold times for densification

Figure 3-21 compares temperature data obtained during experimentation with the

simplified model. Note the predicted densification time profiles vary widely; this is

explained by two factors. First, non-equilibrium processes are occurring in the tank

where the ullage space is developing significant temperature stratifications. Some

cryocooler capacity must be used to chill this vapor back to the saturated state. Refer to

Figure 6-14 on page 149 for details on the thermal profiles in the tank during this

densification process. Second, similar to the pressurization model, heat transfer processes

are modeled using a uniform temperature in the tank and the heat leak and cryocooler

performance will vary in those conditions.


24.00
Pl=180 kPa
23.00 ML=0.98 kg

22.00-

g 21.00-
-Model
0 20.00 -
0 -Data
19.00-

18.00-

17.00

16.00
0 0.5 1 1.5 2 2.5
Time (hr)


Figure 3-21 Predicted vs. actual densification rates

Based on the above discussions, it appears the model has two major components of

error. First, the isothermal model is not entirely accurate as thermal stratification in the

tank will cause variations in heat leak. Second, there are non-equilibrium processes







happening during many operational scenarios, especially when the liquid and vapor states

are not fully saturated. An attempt to create a correction factor for these two situations

will be made in the following section.

Corrected model

Variations in the predicted heat leak will occur since the model used assumes an

isothermal tank and the physical system has temperature stratifications inside the vapor

region. These stratifications will cause warmer temperatures at the top of the tank,

minimizing the temperature gradient and reducing heat leak from the outside. A

correction to the isothermal model developed above will be proposed to account for this

variation. The correction factor will consist of two components. First, an adjustment

must be made to account for variations in the tank liquid level. The modified Lockheed

Martin correlation for MLI performance depends on the tank being at 100% full and at a

constant temperature. Actual tanks will have a temperature gradient up the vertical walls

of the tank between the liquid level and the top of the tank. This means the delta T

between the hot and cold temperatures will be less than 100% for a portion of the tank,

especially any warm supports and tubes that connect to the top of the tank. Boil off

testing at KSC has shown heat leak is approximately a linear relationship with liquid

level, so the first component of the heat leak correction will be of this form.

The second component of the correction factor must take into account transient

effects associated with the generation or destruction of thermal stratification layers inside

the system. This correction will be applied during operational models when the state of

the liquid and vapor in the tank is changing. For the cases above, this includes

pressurization and densification operations. During boil off venting, steady state zero

boil off, and steady liquefaction the thermodynamic variables exhibit no time








dependence, since there is no net heat transfer to or from the fluid at these times. During

the steady boil off or liquefaction the enthalpy flow into or out of the tank cancels the

heat leak or refrigeration, and during zero boil off the refrigerator is balanced by the heat

leak. During the pressurization case, a net heat leak into the system creates a temperature

change is the fluid, while during densification the net refrigeration power has the opposite

effect.

Looking at an energy balance in the system during this transient operation shows a

general relationship for the heat leak into the tank and a temperature change according to

the relation

Oh
p- = V-kVT 3-35
at

Integrating this equation with respect to time gives a function for heat leak that is

dependent on the time and the initial volume. To determine exact true function of this

relationship, this differential equation can be solved. The boundary conditions for this

case would be a variable temperature at z=0 (liquid level), variable temperature along the

walls of the tank and a variable temperature at the top of the tank. This would also need

to be modeled with a variable thermal conductivity and specific heat, and enthalpy would

need to be expressed in terms of the temperature and pressure in the tank. This exercise is

beyond the scope of this simplified model correction. To determine a general form of this

correction term, it is useful to examine the profiles of ullage temperatures in Figure 6-22.

Data taken during self pressurization tests that show thermal stratifications in the liquid

level give an indication a logarithmic relationship of heat leak with respect to time.

Adding a time dependent logarithmic correction in combination with the linear

dependence on liquid level gives a corrected heat leak of the form









Qcorrected = (A + (Qz2 + QcoK A) B) C Ln(D t) 3-36

where A is the heat leak in the tank as the liquid level approaches zero, QLM is the

predicted heat leak from the MLI correlation, QcoN is estimated conduction heat leak, B

is the liquid level (%), and C and D are constants used to fit the model data to the

experimental curve.

The corrected model (model B) shown below uses the following values; A=5,

B=10% (based on conditions used in experiment), C=0.019, and D= 10,500. Figures 3-

22 and 3-23 below show the results of this corrected model for the densification and self-

pressurization processes as compared to the experimental data. An additional day of data

was added to each figure, and this data is compared to the model as well. The added

pressurization data has the same initial conditions as the first, and the curves plot on top

of each other very neatly. The added densification data was from testing several days

after the previous data curve, and the initial mass and temperature change. In this case,

the corrected model was run again and the curve is plotted against the data. In both the

pressurization operation and the densification operation, the corrected model is a better

prediction tool than the original isothermal model. However, in order to get a true model

of the system behavior the full conservation equations must be discretized and solved

numerically.

Storage Fluid Analysis

In order to more accurately model the behavior of the hydrogen in the system, the

full conservation of mass, momentum and energy equations must be considered. The

system described by Figure 3-24 is an unsteady, open system that will be approximated in




































Figure 3-22 Corrected model vs. densification data


Figure 3-23 Corrected model vs. pressurization data


three-dimensional space using cylindrical coordinates. Due to symmetry about the axis,


dependence in the 0 direction can be neglected. Gravitational effects must be taken into


account. The overall system boundary is set as the inside wall of the inner tank, defined


as r=R. The upper height of the tank is at the coordinate z=Z. There are three modes of


24.00

23.00-
P1=180 kPa
22.00- Mass =0.98 kg

21.00- model A (6-25)
data (6-25)
20.00- model B(6-25))
. data (7-16)
19.00- model B(7-16)

18.00- P1=78kPa
Mass=1.22kg
17.00

16.00
0 0.5 1 1.5 2 2.5
Time (hr)


250-


200-
20/ model A (7-15)

150- data (7-15)
model B(7-15)
data (7-16)
I. Mass=1.22 kg
100 ..


50 -


0
0 150 300 450
Time (min)








heat exchange between the system and the surroundings, radiation on the outer surfaces

through the MLI, conduction down the length of any pipe or tube support between the

inner and outer vessel, and refrigeration by the cold heat exchanger of the cryocooler.

There is mass transfer in and out of the tank from the gas supply line and the vent line.

The velocity profiles at the tank inlet and outlet will depend on the geometry, and for

now a fully developed laminar flow profile driven by the pressure gradient can be

assumed at the interface. There is a longitudinal and radial velocity component in both

the liquid and vapor space. The liquid velocity is driven by the free convection currents at

the heat exchange surfaces, with a circulation pattern of warm updrafts along the walls

and a cold downdraft in the center at the cold HX. This differs from conventional

cryogenic dewars that only have the warm upward velocity with a layer of warm fluid at

the top of the liquid. Therefore the liquid velocity will have a superimposed freestream

velocity from the circulation currents as well as the free convection velocity. One

important result of a full numeric analysis is to determine whether this freestream

velocity will drive the heat transfer coefficient higher than otherwise, and hence increase

the amount of heat transfer from the surroundings. If so, anti convection baffles may be

added. The vapor velocity will be driven by warm convection currents as well as the

velocity in and out of the supply and vent line. The thermodynamic state of the liquid

and gas is variable, dependent on both time and location inside the tank. The total mass of

the liquid and vapor will depend on the initial conditions as well as mass flow into and

out of the tank and evaporation or condensation at the liquid to vapor interface. The

liquid to vapor interface is assumed to be a free liquid surface, with homogenous phases

above and below, and the location of the interface in the z direction and the profile will







84




p sp

TP T
Sgsp
u gsp
Vent Port -^ ___ Gas Supply Port






FREE CONVECTION
CURRENTS



Mass=f(t)
S/\ Temp=f(r,z,t)
qAC Press=f(r,z,t)

A4, GH2

LH2
FREE CONVECTIC N
fCURREN;S

Volume=f(t)
Mass=f(t)
Temp=f(r,z,t)
Press=f(r,z,t) h






TEMPERATURF-- z
VELOCITY
BOUNDARY LAYE






MM. Liquid Fill and Withdrawl






Figure 3-24 Proposed system representation


vary. This location will be denoted as z=h. More details on this interface will be given


when the boundary conditions are discussed.


To understand the fluid behavior in order to model it, a consideration of the flow


regime must be taken into account. While the exact flow velocity is unknown, order of


magnitude estimates can be made to find a representative Reynolds number. A potential








and kinetic energy balance of the fluid gives a velocity of the magnitude(44)


V {gL Ar}/ 3-37
P

The velocity depends on the characteristic length of the system and the relative change in

density, which depends on the temperature gradient. An energy balance between the heat

leak thru the insulation compared to the heat transfer to the liquid allows for a rough

calculation of the temperature difference between the wall and the bulk fluid. Using the

heat transfer coefficient found in Chapter 6, for steady state conditions this delta T will be

between .01 and .04 K. This estimate compares well to the experimental data found

during boil off tests conducted with liquid nitrogen at KSC.(45) During some transient

operations this temperature gradient will be greater. Varying the length scale of the heat

transfer and the delta T, the liquid vertical velocity ranges between 2.5 and 35 cm/sec.

The vapor velocities are slightly higher. The dependency of the characteristic velocity as

a function of temperature difference is shown in Figure 3-25. The liquid velocities are

plotted for cooling of the hydrogen by the cold heat exchanger, while the vapor velocities

are for the warming of the vapor by the tank walls. The length scale is 35 cm, which is

approximately with the tank half full. At first, this free convective velocity seems very

high, but an examination of the fluid properties shows this is feasible. The volumetric

coefficient of thermal expansion, 8 ,for liquid hydrogen at 20 K is 0.0164 K-1. This is

two orders of magnitude higher than f of water, which is 2.15 x 10-4 K-1 Similarly, the

bulk coefficient of gaseous hydrogen is 17 times greater than that of steam. Small

temperature differences in hydrogen systems cause large displacements and hence, high

velocities.











90
P1=101 kPa
80 T1=20.3 K

70 L=35 cm

60 -

S50 -- Liquid
40 -Vapor
0 -4
30

20

10


0 0.5 1 1.5 2 2.5 3
Delta T (K)


Figure 3-25 Predicted Free Convection Velocity

Using the density and viscosity of both triple point and NBP liquid hydrogen, a

range of estimates for Re can be computed. The characteristic length used is the height

of the liquid and for the figure below is set at 50% full. Figure 3-26 plots this estimate of

Reynolds number for a range of temperature gradients. From this figure, it appears the

Reynolds numbers may be quite high at times, like when the temperature gradients are

higher during transient operations. After the system has had time to approach steady state

conditions, the delta T will be less and the liquid and vapor Reynolds number will

approach 8x104 and 4x104, respectively. In this case the flow inertia is more moderate,

and viscous forces play a greater factor in the flow. However the Reynolds number is

still high enough that the flow can be modeled with a viscous boundary layer and an

inviscid core. This premise will be revisited in a few sections when an order of

magnitude analysis on the conservation of momentum equation is addressed.