2.3.2 Miscellaneous The Critical State Joule-Thomson Coefficient Joule-Thomson Effect of a Vapor Gas Mixture...

Transcription

1 Contents Part 1 1 Cryocoolers: The Common Principle The Generalized Model of Cryocoolers The Interchanging Process The Conceptual Model of Cryocoolers The Essential Constituents The Elementary Cooling Mechanism The Interchanger The Coolant A Media that Undergoes a Thermodynamic Transition... 6 A Convective Fluid Ideal Gas Coolants Versus Real Gas Properties The Cooldown Process of Cryocoolers Comments... 6 DT IN IN Versus DT H... 6 Isothermal Absorption of Heat Load The Magnification Index of the Interchanger, I M Definition Hot Stream with Minimum Capacity Rate Cold Stream with Minimum Capacity Rate The Unified Expression Example The Ideal Case with e! 1 and DT! Implementation of Interchangers Recuperators and Regenerators DC and AC Cryocoolers Characteristics of Interchangers The Temperature Domain The Longitudinal Domain The Dimensionless Longitude, NTU The Curvature of the Temperature Profiles Dependence of I M on the Size of the Interchanger Formulation The Extreme Behavior The Case of Balanced Capacity Rates Remarks ix

2 x Contents Entropy Generation Formulation Ideal Gas Counter-Flow Heat Exchanger Cryocooolers Interchanging Process Optimization Under Finite Size Constraint Regenerative Versus Recuperative Interchanging Enhanced Interchanging A Preferred Condition Sub-optimum Interchanging The Most Common Factor Interchanging in Liquefiers Where _n L _n H Low Temperature Degradation Factors That Enhance Interchanging Precooling Split Flow Isentropic Expansion Serial Isentropic Expansion Hybrid Interchanging Real Cryocoolers in View of the Generalized Model From Siemens to Linde and Hampson The Elementary Cooling Mechanisms and Their Characteristics, dt(t) Continuous Isentropic Expansion Series of Isentropic Expansions with Work Extraction Series of Blow Down (Isentropic) Expansions The Joule-Thomson Expansion Valve The Injector Adiabatic Demagnetization Phase Separation of 3 He- 4 He Mixtures Mixing Two Separate Streams of 3 He and 4 He A Vortex Tube Thermoacoustic Expanders The Lowest Attainable Stable Temperature of Cryocooling Formulation Monotonically Decreasing dt An Increasing Value of dt The Minimum Value of dt When _C H > _C L Other Limits to the Lowest Attainable Temperature Thermal Losses The Second Law A Pinch Point The Shape of Cooldown Curves The Relationship Between I M and dt for Various Cryocoolers The Joule-Thomson Cryocooler with Pure Coolants (Except He and H 2 ) Joule-Thomson Cryocoolers with Mixed Coolants (discussed in Chap. 8) Joule-Thomson Cryocoolers of He and H Satellite Cryocoolers That Liquefy Helium (see also Sects and ) Stirling, Giffird-McMahon, Pulse Tube and Reverse Brayton Cryocoolers

3 Contents xi The Active Magnetic Regenerative Refrigerator (AMRR) The Dilution Refrigerator The Mixing Refrigerator A Non-viable Cryocooler Due to Inherently Poor Interchanging Special Examples of Interchangers Continuous Flow Interchanging Using Two Opposing Regenerators Combining a Periodic Expander with a Recuperative Interchanger Pulse Tube Expander Interchanged by a Recuperator Interchanger Combined with Convective Cooling A Gifford-McMahon (GM) or Stirling Cryocooler A Mixed Coolant Closed Cycle Joule-Thomson Cryocooler The Thermoelectric Elements Interchanging Mass Transfer Separation of Isotopes Counter Current Exchange: A Principle of Biology Refrigerator Versus Cryocooler Second Law Considerations Performance of Cryocoolers The Thermodynamic Presentation of Cryocoolers The Sites of Entropy Generation The Coefficient of Performance, COP The Figure of Merit, FOM The Real Gas Properties Group of Cryocoolers Description The First Law The Second Law The COP and FOM The Ideal Gas Group of Cryocoolers Description The COP and FOM The Lowest Attainable Temperature Defined by the Second Law The Finite Lowest Attainable Temperature A Comparison of Joule-Thomson with Other Coolers Introduction Characteristics Cryocooling Via a Boiling Bath of Cryogen High Heat Flux High Temperature Stability Cooling Large and Irregularly Shaped Objects Compact and Light Weight Cold Finger The Open Cycle Mode of Operation No Moving Parts in the Entire Cooling System Reliable Operation After a Long Storage Period No Heat Rejection at Ambient Temperature A System That Becomes More Compact as the Cooling Duration Shortens

4 xii Contents Rapid Cooldown: The Ultimate Advantage A Very Low Level of Vibrations at the Cold End Cryocooling of a Gimbaled Payload Ease of Integration Ease of Distributing the Cooling Power Closed Cycle Joule-Thomson Cryocoolers Drawbacks Requirement for High Purity Gas Inferior Thermodynamic Efficiency A Requirement of High Pressure for Open Cycle Operation A Higher Compression Ratio References Part II Theoretical Aspects 2 The Joule-Thomson Effect, Its Inversion and Other Expansions Introduction The Joule-Thomson Coefficient The Differential Coefficients The Single Phase Domain The Two Phase Domain of a Pure Substance The Integral Effect Derivatives Through the Equations of State In Terms of Volume Derivatives In Terms of Pressure Derivatives In Terms of Compressibility, Z In Terms of the Product Pv In Terms of the Residual Volume In Terms of Heat Capacities In Terms of the Virial Coefficients In Terms of the Intermolecular Forces The van der Waals Gas The Principle of Corresponding States The Zero Pressure Joule-Thomson Coefficient Speed of Sound and the Joule-Thomson Coefficient The Joule-Thomson Coefficient of Mixtures Miscellaneous Thermal Expansivity and the Joule-Thomson Coefficient Entropy and the Joule-Thomson Coefficient Minimum of the Isothermal Joule-Thomson Coefficients The Volumetric Joule-Thomson Coefficient The Joule-Thomson Effect and Magnetism Measurements of the Joule-Thomson Effect Experiments The Adiabatic Expansion The Isothermal Expansion Measurement of Compressibility The Integral Adiabatic Joule-Thomson Effect

5 Contents xiii Miscellaneous The Critical State Joule-Thomson Coefficient Joule-Thomson Effect of a Vapor Gas Mixture A Liquid-Liquid Phase Change The Joule-Thomson Effect of a Solid-Gas Aerosol Differential Inversion States Introduction Definition The Extended Inversion States On the Microscopic Level Basic Features of the Differential Inversion Curve in the (P, T) Plane The Inversion States and the Principle of Corresponding States Dependence on Acentricity Factor The Quantum Gases The Pseudo-Critical Parameters of the Quantum Gases Differential Inversion Curve Extension Below the Critical Temperature The Differential Inversion Curve (D.I.C.) in Various Coordinate Planes The P-h Plane The T-s Plane The h-s Plane Inversion States of Mixtures The Speed of Sound at the Inversion States The van der Waals Equation of State The (T, P) Plane The Density The Extended Saturation Line The Integral Joule-Thomson Effect The Quantity c P c V Equation of State Dependence The Differential Inversion States in the Plane of (v,t) The Compressibility Plane of Z(P) The Envelope of Isotherms in the (Z, P) Plane Intersections of Adjacent Isotherms in the (Z, P) Plane The Isotherms at Zero Pressure and Z=1Vicinity Boyle Temperature and the Maximum Inversion Temperature Z as a Function of the Inversion Pressure for a van der Waals Gas The Compressibility Plane of Z (Y) The Differential Inversion States Z as a Function of the Inversion Temperature The Intersection of the Inversion Curve with the Unit Compressibility Line Empirical Correlations for the Differential Inversion Curve The Correlation of Jacob and the Principle of Corresponding State The Generalized Correlations for Low Acentricity Gases

6 xiv Contents 2.6 The Integral Inversion States Formulation Characteristics of the Integral Inversion Curve (I.I.C.) The Principle of Corresponding States and the Quantum Gases The van der Waals Equation of State and the Integral Inversion Curve The Plane of (P,T) The Reduced Density Compressibility, Z The Relationship Between the Differential and Integral Inversion Curves The Differential Joule-Thomson Effect The Values of c P c V Chronological Notes on Inversion States Witkowski, 1898: The Discovery of the Differential Inversion States van der Waals and Olshewski, 1900: Focusing on Integral Inversion States Porter, 1906: Shifting the Attention to the Differential Inversion States The Differential Inversion Curve by the EOS Molecular Simulation of the Inversion States Miscellaneous Joule Expansion The Joule Coefficient by Pressure The Joule Coefficient by Volume The Inversion of the Joule s Effect Isentropic Expansion The Coefficient of Isentropic Expansion The Real and the Ideal Gas In Terms of the Thermal Expansivity In Terms of Heat Capacities In Terms of the Speed of Sound Derivatives Through the Equations of State For the van der Waals Gas The Isentropic Expansion Coefficient by Density The Relationship Between the Isentropic and Isenthalpic Expansion The Relationship Between m s and m The Role of the Differential Inversion Curve The Integral Effect The Isentropic Expansion and Cryocoolers Preserving the Stagnation Enthalpy of Flow References The Linde-Hampson Cryocooling Process General Perspective The Fundamental Elements of the Linde-Hampson Cycle Throttling Recuperation Sub-critical Expanded Pressure A Supply Pressure that Is Above the Critical Point A Phase Transition

7 Contents xv Classification by Flow Rate Balance The Cooler The Liquefier The Satellite Cooler Remarks Classification by Phase Transition Vapor Liquid Phase Transition Vapor Solid Phase Transition Normal (He-I) to Superfluid Helium (He-II) Transition Closely Related Recuperative Cycles Ejector The Cold Air Cycle Combining the Use of a Recuperator with the Extraction of External Work The Reverse Brayton Cycle The Claude Cycle The Superfluid Joule Thomson Refrigerator The Ideal Linde-Hampson Cryocooling Cycle The P-h Plane The High Pressure Isobar The Isenthalpic Expansion Isothermal Phase Change The Low Pressure Isobar Isothermal Compression The Cool Down Temperature, T CD Remarks The h-t Plane The T-s Plane The Maximum Specific Cooling Capacity Real Linde-Hampson Cooler Cycles Introduction The Temperature Difference at the Warm End of the Recuperator, DT Operation with Excess Flow Rate as a Source of DT The Largest DT The Dependence of DT on the Amount of Flow Excess, Dh T _Q = _n Recuperator s Lack of Thermal Conductance as a Source of DT The Extent of Recuperation Definition The Nominal Extent of Recuperation Under and Over Recuperated Cycles The Extent of Recuperation (dh) and the Magnification Index (I M ) Cycles Of Nominal Recuperation Performance of Nominal Recuperators Introduction The Effectiveness, e Definition The Degraded Specific Cooling Power The Minimum Effectiveness, e MIN The Relationship Between DT and e... 87

8 xvi Contents The Efficiency, The Definition of Efficiency The Relationship Between and e Relationship Between and DT The Linde-Hampson Liquefier Cycles The Ideal Cycle of the Liquefier Liquefiers with Nominal Recuperation The Misbalance of Flow Rates The Yield of Liquefaction The Span of Specific Enthalpies The Real Cycle of the Liquefier Sizing of Nominal Recuperators Size Versus Performance Lack of NTU as a Source of Ineffectiveness Excess Flow Operation as a Source of Ineffectiveness The Average Ratio of Capacity Rates Minimum Number of Heat Transfer Units, NTU MIN Flow Rate Dependence of Recuperator s Size Size Versus Duty Scaling a Recuperators Size Yield of Liquefaction The Cryocooler The Ideal Operation Operation with Excess Flow The Liquefier The Ideal Liquefier Versus Cryocooler The Finite Size Recuperator The Splitting Ratio, SP Sizing a Liquefier s Recuperator Maximizing Production Rates The Highest Specific Cooling Rate, _Q = _n, Versus the Highest Cooling Rate, _Q Cryocoolers with Fixed Recuperating Area Cryocoolers with Fixed Flow Rate Liquefiers with Fixed Recuperating Area Nozzle Inlet Temperature Temperature Differences Between the Recuperating Streams The Coolers The Ideal Cooler Cryocoolers Operating with Excess Flow as a Function of NTU for Nominal Cryocoolers The Liquefier Dependence on Specific Heat Capacities The Operating Line The Cooler The Liquefier Helium and Hydrogen JT Cryocooling Longitudinal Temperature Distribution The Mechanisms of Throttling Introduction The Laminar Regime

9 Contents xvii The Turbulent Regime Shock Waves Second Law of Thermodynamics Considerations Coefficient of Performance, COP Formulation The Dependence of COP on the Inlet Pressure The Pressure of the Optimum COP Remarks of Consistency The Global Optimum of COP; the Cold Air Cycle The Cost of Refrigeration Figure of Merit, FOM Availability Analysis References Thermodynamic Characterization of Coolants Introduction Temperatures of Phase Transition Liquefaction Solidification The Integral Isothermal Joule-Thomson Effect, Dh T Residual Enthalpy, h R, and Dh T Pressure Dependence of Dh T Examples of the Pressure Dependence of Dh T The Super Critical Temperature Range, T>T C Dh T in the Low Pressure Range The Pressure Dependence of Dh T for the Quantum Gases The Sub Critical Temperature Range, T<T C Deriving Dh T by the Equations of State General Expressions The Van der Waals Equation of State The Peng-Robinson Equation of State The Virial Equation of State Expended by Pressure The Virial Equation of State Expended by Density The Critical State, Dh T (T C ; P C ) Temperature Dependence of Dh T The Role of the Residual Specific Heat Capacity, c R P Helium and Hydrogen Expansion into the Two Phase Zone Temperature Dependence of Dh MAX T The Low Temperature Range, 1:2 < Q < The Entire Inversion Curve Range, T>T C The Sub Critical Temperature Range, T<_T C The Dh MAX T (T C ) Mapping the Integral Effect, Dh T The Absolute Mapping The Relative Mapping The Space of Coolants: Normal Boiling Point Dependence of Dh MAX T (T) Temperature Dependence of Dh T at a Constant Specific Density Process

10 xviii Contents 4.4 Cooldown Temperature, T CD Definition Pressure Dependence of T CD Evaluation of TCD MAX Formulation The Space of Gases The Smallest Cooldown Range, DTCD MIN The Integral Isenthalpic Joule-Thomson Effect, DT h Introduction Definition The Two Domains of DT h The Domain of T > T CD (P) The Domain of T < T CD (P) The Driving Potential of the Cooling Process, DT h Examples of Various Gases and States Chronological Note DT h in the Domain of T >_ T CD (P) The Relationship Between DT h and Dh T Remarks Demonstrating the Relationship Between DT h and Dh T DT h in the Domain of T<T CD (P) The Dependence of DT h on Molecular Structure, T>T CD (P) Different DT h for Identical Dh T Gases with Similar Values of T C But with Different Molecular Structures Remarks The State Dependent DT h Variation, T > T CD (P) Pressure Dependence Temperature Dependence State Derivatives of DT h and m Mapping of DT h The Highest Attainable DT h, the DT h (MAX) A Given Gas The Space of Gases Evaluation of DT h (P; P OUT ) Through the Equation of State DT h for Mixtures Evaluating a Mixture s Dh T and c PO Mixing of Components DT h Values Direct Blow Down Yield of Liquefaction Compressibility of Coolants The Cooling Potential of a Pressure Vessel The Isothermal Discharge of a Pressure Vessel The Cooling Capacity Per Unit Volume of the Vessel The Loss of Cooling Potential Due to Void Volume The Cooling Capacity Per Unit Weight of the Vessel The Isothermal Discharge Pattern The Adiabatic Discharge of a Pressure Vessel

11 Contents xix 4.9 Monatomic and Other Coolants: Closing Remarks Characteristics of the Monatomic Gas Family Particular Identity of Each Noble Gas Helium Neon Argon Krypton Xenon Other Gases Nitrogen Oxygen Air R Methane Nitrous Oxide Carbon Dioxide Hydrogen The Role of the Differential Inversion Curve The Quantum Gases: 3 He, 4 He, H 2,D 2 andne References Part III Practical Aspects 5 Principal Modes of Operation Introduction Pressurizing Alternatives The Open System The Layout The Pressure Source The Closed Cycle Configuration The Potential Advantages Two Versions The Pressure Generator The Mechanical Compressor The Sorption Compressor The Electrochemical Compressors The Open Cycle Continuous Operation Cryocoolers Introduction Characteristics Pressurization A Highly Evacuated Dewar A Long Heat Exchanger Small Heat Capacity Cooldown Periods Coolants High Purity Gases Flow Regulation by Adjusting the Throttle Size Performance Criteria Operating Conditions The Ideal Run Actual Gas Consumption

12 xx Contents Argon Versus Nitrogen Flow Rates Temperature Stability Temperature of Operation Precooling Technology of Heat Exchangers The Cut Off Pressure Constant Flow Rate Discharge The Cooling Capacity The Optimal Regulated Pressure Comparison with Non-regulated Discharge The Cooldown Periodic Flow Rate and a Thermal Storage Device Multi-stage Cryocoolers Introduction Chronological Note The Regions of Precooling Categories of Staging Joule-Thomson Cryocoolers T PRE < T AMB < T INV ; Operational Benefits T PRE < T INV < T AMB ; Reaching Lower Temperatures T PRE < T CD < T AMB ; No Recuperator at the Final Stage Remarks Steady State Analysis The Schematic Layout The Energy Balance Comments COP Considerations of Staging The Serial and Parallel Staging Configurations of Closed Cycle Cryocoolers The Serial Configuration with Stages Having the Same FOM The Serial Configuration with Stages of the Same Relative Entropy Generation, ð_s T H = _Q L Þ i The Influence of the Number of Stages in the Serial Configuration Staging of Closed Cycle Joule-Thomson Cryocoolers Staged Cooling of a Stream Miscellaneous Reduction of System Weight and Volume Liquefaction of Quantum Gases: 3 He, 4 He, H 2,D 2 andne Candidate Precoolants Example Cryocoolers Miniature Laboratory Liquefiers Free Jet Release Motivation The Model Common Inlet Conditions for Both Stages The General Case Cold End Benefits Reducing the Size of the Cold End Reducing Back Pressure Modularity Staging by Pressure with Double Expansion: The Ball Aerospace Joule-Thomson Cryocooler

13 Contents xxi 5.5 Fast Cooldown Cryocooling Introduction Characteristics Cooldown A short run time A small pressure vessel High flow rates Non evacuated encapsulation Constant area orifice Short heat exchanger The cutoff pressure Integrated assembly Clogging Temperature of operation System level considerations Coolants: Argon Versus Nitrogen and Their Mixtures Passive Techniques Materials The Recuperator Non-evacuated Encapsulation Thermal Interface to Payload Active Techniques Higher Flow Rates Incorporating an Additional Higher Boiling Point Coolant Precoolants Direct Precooling of Payload; Sequential Precooling Indirect Precooling of a Payload Simon s Cooling Effect System Approach Optimized Cryocoolers Fixed Length Cryocoolers Special Examples Staged, Porous and Flow Regulated Fast Cryocooler Staged Wire Screen Compact Heat Exchanger Photolithographic Precooled Fast Cooler Fast Cooldown System with High Shock Resistance The Inverse Cryocooler A Single Non-recuperative Expansion Thermal Isolation Between the Cooler and Its Encapsulation Faster Cooldown of the Cold Shield of an Infrared Detector Xenon or Krypton in a Non-evacuated Encapsulation Hybrid Joule-Thomson Cryocoolers Introduction Thermoelectric Precooling Gifford-McMahon (GM) and Joule-Thomson (JT) Hybrids The Combined Helium Cycle of GM and JT Cryocoolers Miscellaneous The Stirling and Joule-Thomson Hybrids The Final Joule-Thomson Helium Stage Enhancements

14 xxii Contents An Ejector Expander for the Final Joule-Thomson Stage Cooling with 3 He Serial Double Throttling Special Examples of Hybrid Cryocoolers Subcritical (P U < P C ) Methane JT Cycle Precooled by a Stirling Cooler A JT Cryocooler with an Additional Ejector Supplying a DC Flow to a JT Cooler by Rectifying an Oscillating Flow A Brayton-JT Hybrid Cryocooler A Sequence of an Open Cycle JT Cooler and an Expander Precooling Helium Sorption Compressor Stage A Radiant Refrigeration Stage References Construction and Configuration Joule-Thomson Expansion Valves The Model of a Joule-Thomson Valve Shock and Expansion Waves: The Ultimate Throttling Mechanism The Choked (Molar) Mass Flux Ideal Gas Real Gases Subsonic Expansion The Passageway Area of a Joule-Thomson Valve Remarks The Short Duct: The Highest Mass Flux The Circular Long Duct: The Capillary Tube Adiabatic Compressible Flow with Turbulent Friction Practical Examples The Open Tube Cryocooler The Long Duct with Laminar Friction Porous Media Valve The Vortex Throttle The Annular Duct A Cylindrical Insert A Conical Annular Valve Flow Adjustment Introduction Classification Characteristics of Flow Adjustment Sensing the Heat Load and Temperature Flow Regulators for Rapid Cooldown Cryocoolers Charged Bellows Flow Regulator Cold End Bellows Warm End Bellows Principle of Operation The Balance of Forces on the Bellows Two Phase Versus Single Phase Bellows Content Solid Thermal Expansion Flow Regulators

15 Contents xxiii Classification Metal Expanding Elements Plastic and Other Non-metallic Expanding Elements Operation of a Plastic Expander Versus a Charged Belows Regulator Bimetal Flow Regulators Dual Joule-Thomson Valve Temperature Dependent Shape Memory Alloys Active Feedback (Servo) Systems Description Motivation A Bang Bang Pressure Supply Piezoelectric Actuation Shape Memory Alloy Based Transducer A Reactive-Thermo Elastic Transducer Miscellaneous Flow Adjustment of Different Coolants A Self-Adjusting Effect for a Porous Plug Flow Regulation Induced by Pressure of the Vessel A Floating Needle in a Needle Valve Flow Regulation by Liquid Solid Transition A Manually Adjustable Flow Regulator A Mechanism to Squeeze the Tube The Pressure Dependence of Flow Rates Heat Exchangers Introduction Classification Parameters of Construction Finned Tube Heat Exchangers Finned High-Pressure Tube Pressure Tubes Fins Coating Active Fin Configuration of Finned Tube Heat Exchanger Cylindrical Shape A Stepped Shape Heat Exchanger A Conical Shaped Heat Exchanger Flat Shape Heat Exchanger Pressure Tube Arrangement: The Single Stage Single Layer, Double Thread Multi-Layering for High Flow Multi-Layer Short Cryocooler Multi-Layer Effectiveness Pressure Tube Arrangements for Two Stages Heat Leaks and Stiffness Matrix Heat Exchangers Introduction Wire Mesh Matrix Porous Sintered Matrix Perforated Plate Heat Exchanger Parkinson s Heat Exchanger

16 xxiv Contents Linde Type Heat Exchanger The Tube in Tube Heat Exchanger The Parallel Wrapped Tube Type Heat Exchanger Narrow Channel Heat Exchangers in Diffusion Bonded Metal Plates Hampson s Versus Linde s Heat Exchangers Hampson s: Strongly Coupled with Its Dewar Linde s: More Readily Adaptable for Hybrid Precooling Linde s: Potentially Provides a Lower Heat Leak Hampson s: Enables a Simpler Flow Adjustment Hampson s: Potentially More Compact Mems Cryocoolers New Emerging Opportunities Size Reduction, in Terms of Length and Volume Cooling Capacity Below 20 mw Flat and Rectangular Shape Advantages for Integrating Cost Reduction Fixed Orifice Glass Versus Silicon Superconducting Electronics: Stanford University, CA, USA William Little Single Stage Narrow Channel Devices Multi-Staging Common Layer Strategy Separate Layers for Each Stage Missile Application: Segmented and Isolated Silicon Layers Space Applications: Twente University, The Netherlands Concentric Glass Tube Heat Exchanger Silicon Wafer Heat Exchanger for Two Phase Streams ðp U <P C Þ Optimized Wide Channels On Chip Cooling of Terahertz Sensor: NIST/CU Program The System The Cryocooler The Compressor Miscellaneous Micro-Size Heat Pipes A Cryosurgical Probe A Radio-Frequency Coil Accessories and Special Arrangements Filtration A Filter at the Warm End A Filter at the Cold End Enhancing the Cooling Effect of a Cryogen Bath Liquid Absorbent Materials Fluid Deflection Using a Skirt Controlling the Outlet Pressure An Ejector Active Servo Control of the Expanded Pressure An Absolute Pressure Controller Collecting the Outgoing Gas

17 Contents xxv Matching a Cooled Object s Shape Cooling a Rectangle Cooling an Annular Payload Miscellaneous References Transient Behavior Introduction Regimes of Transient Behavior The Heat Load The External Heat Load The Latent Internal Heat Load Changes of Heat Load The Cooldown Process The Surplus of Cold Production De-stablizing Effects Continuous Accumulation of Liquefied Coolant Temperature Decrease at the Inlet to the Nozzle Passive Stabilizing Effects Elevation of Heat Leak Suppression of the Cooling Capacity Active Stabilizion: Reducing Excess Flow Bang-Bang Control Warming Characteristic Cooldown Behavior of the Cooled Object The Expanded Stream The Cooled Object Miscellaneous The Cooldown Behavior of a Flow Demand Cryocooler Termination of Cooldown Cooldown Behavior at Various Locations Along the Cryocooler Correlations and Similarity of Cooldown Periods Empirical Correlations The Semi Analytical Similarity Model for Rapid Cooldown Cryocoolers The Pressure Dependence for the Cooldown Period of a Given Cryocooler Formulation Similarity Results Approximate Similarity Relations Cooldown Tendency of Gases, TND The Integral Model for the Cooldown Periods Cooldown Flow Rates The Effective Heat Capacity of a Cryocooler The Average Cooling Power During Cooldown Energy Balance During Cooldown Gas Consumption for Cooldown Classifications of Rapid Cooldown Cryocoolers Optimized Cryocoolers

18 xxvi Contents Cryocoolers with a Common Efficiency and Backpressure Comparison of Cryocooler Classifications References Part IV 8 Mixed Coolant Cryocooling Introduction Classification of Mixed Refrigerant Joule-Thomson Cryocoolers The Linde-Hampson Mixed Coolant Closed Cycle Cryocooler The Auto-Cascade Closed Cycle Cryocooler The Linde-Hampson Mixed Coolant Open Cycle The Synergy of Mixed Coolants Miscellaneous Chronological Notes Interchanging with Mixed Coolants The Mixed Coolant Linde-Hampson Cycle Chronological Perspective Description of the Mixed Coolant Cycle Characteristic Features Low Pressure of Operation Suppressed Boiling Point of the Mixed Coolant Balanced Recuperation Reduced Entropy Generation The Temperature at the Entrance to the Nozzle Possible Non-choked Flow Through the Throttle Increased Thermodynamic Efficiency The Distribution of Exergy Losses A Larger Heat Transfer Area Mixed Coolant Linde-Hampson Cryocoolers Introduction Oil Free, Two-Stage and Single Stage Compression Lubricated, Single-Stage Compression Precooled Mixed-Coolant Closed Cycles Advantages Enhanced Oil Removal Eliminating the Use of an Absorbent Eliminating Higher Boiling-Point Components Precooling with a Closed Cycle Vapor Compression System Thermoelectric Precooling of a Microcryocooler Reducing the Size of the Cold End of a Two Stage Cryosurgical Probe Mixed Coolant Closed Cycle for Precooling Pure Coolants Scope Nitrogen Oxygen Quantum Gases

19 Contents xxvii Vapor-Liquid Cycle of Higher Boiling Point Gases Nitrogen in an Open Cycle Precooling a Natural Gas Liquefier Accelerated Cool-Down Cryocoolers Enlarged Orifice at Cool-Down Mixtures with Helium and a Fixed Orifice Porous Plug Throttle Pressure Vessel Assistance The Heat Exchanger Miscellaneous Single or Double Phase Charged Refrigerant Cryocooling Temperatures Centrifugal Compressor Recuperation by Regenerators Thermal Ballast Integral Closed Cycle Cryocooler Flammable Versus Nonflammable Coolant Cryocoolers Sorption Compression for a Multi Component Gas Thermodynamic Performance of the Mixed Coolant Cycle Temperature of Operation The Temperature in the Evaporator and the Operating Line The Boiling Point Versus the Pinch Point Temperature Equivalent Specific Heat Capacities and the Pinch Point Occurrence The Cooling Capacity The Limiting Cooling Capacity, Dh T (T IN ) The Actual Cooling Capacity, Dh MIN T Operation with Excess Flow Rate Examples The Mixture of 0.40N 2, 0.30 C 2 H 6, 0.30 C 3 H The Binary Mixtures of N 2 with 20% and 40% of C 3 H Aspects of Mixed Coolant Composition The Dh T of Components and of Their Mixture The Dh T of Pure Gases at Subcritical Pressure The Linear Superposition of Enthalpies Functional Groups of Components Reducing the Operating Pressure of the Mixture Components for Suppressing a Mixture s Boiling Point Bridging Components Quantum Gases Miscellaneous Clog Free Operation and Solid Liquid-Vapor Phase Equilibria Introduction Mixtures of Soluble Additives Eutectic Composition of Insoluble Additives Additives of Transitive Solubility

20 xxviii Contents A Conservative Approach Miscellaneous Lubricants for Compressors Propane Aspects of Liquid Vapor Phase Equilibrium Condensation Inside the Compressor Condensation at Ambient Temperature The Temperature Inside the Evaporator: Miscible Additives The Temperature Inside the Evaporator: Partially Miscible Additives Miscellaneous Reported Mixtures Species and Concentration Primary Components Hydrocarbons Flammability Retardant for Hydrocarbons Halogenated Derivatives of Hydrocarbons Fluoro-Ethers Inert Gas Additives Ozone Depleting Additives Oxygen Quantum Gases Miscellaneous Optimized Mixtures The COP of a Closed Cycle Cryocooler The COP of a Precooled Cryocooler The COP for a Distributed Load Cycle Compactness of the Cold End Cooldown Aspects of Closed Cycle Operation Closed-Loop Parameters The Amount of Coolant and the Volume of the Loop The Relationship Between the Up and Down-Stream Pressures The Compressor The Displacement The Rate of Volumetric Displacement The Rate of (Molar) Mass Displacement The Volumetric Efficiency The Specific Cooling Capacity of the Coolant The Liquefied Amount, n LIQ Simplified Analysis Assumptions The Compression Ratio Mass Conservation The Absolute Values of the Pressures The Distribution Ratios of a Coolant s Mass and Pressure The Circulating Flow Rate Cooling Power

21 Contents xxix Warming Capability The Hydrodynamic Time Constant of the Closed Cycle The Hydrodynamic Behavior During Cooldown of a Closed Cycle The Self-Regulating Effect of a Substantial Liquefied Fraction Description of the Self-Regulating Effect Pure Coolant Closed Cycle The Mechanism of Self-Regulation: Adjustment of DP Cooldown Versus Steady State Cooling Capacity The Self-Regulating Response to Heat Load Variation Mixed Coolant Closed Cycle The Mechanism of Self-Regulation: Adjustment of the Composition Cooling Power at Steady State Versus Cooldown The Change of Composition During Cooldown Additional Closed Cycle Cryocoolers Compressor Output Regulation Composition Changes During Cooldown The Influence of the Orifice Operating Parameters Versus Heat Load Inlet and Outlet Temperatures of a Capillary Tube Throttle The Influence of the Charging Pressure Miscellaneous Kleemenko s Cycle and Coolers Introduction Chronological Notes Description Fuderer and Missimer Cryocoolers and Coolant Compositions Missimer s Multi-throttling Cryocoolers The Enhanced Phase Separation Reaching Low Temperatures Kleemenko Cycle Versus the Linde-Hampson Cycle with Mixed Coolants The Thermodynamic Efficiency Temperature Stability Flexibility to Include Higher Boiling and Melting Point Components Capability to Support Distributed Load Construction and Operation Closed Cycle Applications Comparison of Closed Cycle Mixed Coolant Joule-Thomson Coolers with Closed Cycle Stirling Coolers Very Low Level of Vibrations at the Cold End Large Separation Between the Compressor and the Cold End Flexible Connection Between the Cold End and the Compression Unit

22 xxx Contents Distribution of Cryocooling Potential Cryocooling of a Large Surface Magnetic Interference at the Cold End The Rejected Heat Flux at the Payload Heat Rejection at the Warm End of the Cold Finger Advantages of the Stirling Cryocooler Typical Experience Open Cycle Cryocooling by Mixed Gases Introduction The Necessity for High Pressure Preference Parameters The Composition of High Pressure Mixed Coolant High Pressure Operation and Proposals Optimized High Pressure Mixtures Mixing On-Site The Mixing Enthalpy Examples References Part V 9 Special Topics Gas Purity and Clogging The Origin of Impurities Vapor Phase Contaminants Minute Solid Particles Cleanliness of the Pressure Supply Components Parameters of Clog Formation Vapor-Solid Phase Transition Nucleation and the Rate of Deposition Viability of Clog Formation in the Heat Exchanger Water Vapor Contamination Carbon Dioxide Vapor Contamination The Level of Contamination and the Feed Pressure Flow Rate and Size Dependence Experimental Study of Clog Formation Evolution of Plug in a Sonic Expansion Valve Clog Formation in the Heat Exchanger Water Versus Carbon Dioxide Clog Formation Aspects of Impeding Clog Formation Proposed Clog Retarding JT Valves Mechanisms to Mitigate Clog Formation in Heat Exchangers Orifice Heating The Vortex Throttle Desiccants Fixed Orifice Versus Flow Demand Valves Monitoring Gas Purity Laboratory Equipment

23 Contents xxxi The Gas Chromatograph The hygrometer Gas Purity Testers Flow Rates Introduction Three Kinds of Flow Rates The Flow of a Joule-Thomson Cryocooler Is Choked The Unit of Standard Liters Per Minute Choked Flow Rates of Real Gases The Deviation from the Ideal Gases Model The Pressure Range of Significant Deviations Inlet Temperature Dependence The Principle of Corresponding States The Critical Pressure Ratio Pressure Dependence of a Cryocooler s Flow Rates The Free Flow Rate, n FR _ The Recuperated Flow Rate, _n RE The Ratio of Cryocooler Flow Rates, _n RE = _n FR Discharge of a Pressure Vessel Through a Fixed Orifice Cryocooler Discharge Pattern of a Fixed Versus Adjustable Orifice Cryocooler A Simplified Model The Instantaneous Flow Rate The Thermal Interaction of the Pressure Vessel The Optimal Orifice Size The Run Time Dt Different Coolants Discharging Through the Same Cryocooler Modeling the Joule-Thomson Cryocooler The Scope of Modeling Description of the Model Reported Modeling Experience The High Pressure Coolant Stream The Governing Equations Mass Conservation (Continuity) Energy Conservation Momentum conservation Geometric Parameters of the Model The Low Pressure Stream of Coolant Other Components of the Heat Exchanger The High Pressure Tube The Cold Finger Encapsulation The Mandrel Cryosurgical Devices Introduction Elements of Cryobiology Cold Cryosurgical Machines Cooling by a Boiling Agent Cooling by Melting Agent Cooling by a Sublimating Agent Warm Cryosurgical Machines The Joule-Thomson Effect

24 xxxii Contents The Peltier (or Thermoelectric) Effect The Blow-Down of a Pressure Reservoir Stirling and Pulse Tube Closed Cycle Cryocoolers Joule-Thomson Probes and Machines Nitrogen and Argon Devices Carbon Dioxide and Nitrous Oxide Machines Closed Cycle, Mixed Refrigerant Coolers Miscellaneous Open End Probes Multi-probe Devices Active Warm-up MRI Compatibility Krypton Accessories The Warming Joule-Thomson Cryocooler Recuperative Heating The Positive Feedback of a Temperature Increase The Thermodynamic Relations Transient Behavior The Final Steady State Temperature Thawing a Cryosurgical Probe Cryo-Cycling References A1: The British Patent No. 2064, of Dr. Charles Williams Siemens, 1857: Refrigeration Apparatus A2: Equations of State A2.1 Van der Waals Equation of State A2.2 Peng-Robinson Equation of State A2.3 Virial Equation of State (proposed by K. Onnes in 1992) A2.4 Truncated Virial Equation of State A2.5 Interrelating the Third Parameter of the Principle of Corresponding States A3: Parameters of Gases Index