Jet, Rocket, Nuclear, Ion and Electric Propulsion - Springer LINK

Volume 7

APPLIED PHYSICS AND ENGINEERING

An International Series

Jet, Rocket, Nuclear, Ion and Electric

Propulsion: Theory and Design

Jet, Rocket, Nuclear, Ion and Electric

Propulsion: Theory and Design

Edited and authored by W H. T. Loh NORTH AMERICAN ROCKWELL CORPORATION

DOWNEY, CALIFORNIA

ISBN-13: 978-3-642-46111-8 001: 10.1007/978-3-642-46109-5

All rights reserved.

e-ISBN-13: 978-3-642-46109-5

No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag.

© 1968 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1968 Library of Congress Card Number 68-26005

Title No. 3897

Preface

During the last decade, rapid growth of knowledge in the field of jet, rocket, nuclear, ion and electric propulsion has resulted in many advances useful to the student, engineer and scientist. The purpose for offering this course is to make available to them these recent advances in theory and design.

Accordingly, this course is organized into seven parts: Part 1 Introduction; Part 2 Jet Propulsion; Part 3 Rocket Propulsion; Part 4 Nuclear Propulsion; Part 5 Electric and Ion Propulsion; Part 6 Theory on Combustion, Detonation and Fluid Injection; Part 7 Advanced Concepts and Mission Applications. It is written in such a way that it may easily be adopted by other universities as a textbook for a one semester senior or graduate course on the subject. In addition to the undersigned who served as the course instructor and wrote Chapter I, 2 and 3, guest lecturers included: DR. G. L. DUGGER who wrote Chapter 4 "Ram-jets and Air-Aug­mented Rockets," DR. GEORGE P. SUTTON who wrote Chapter 5 "Rockets and Cooling Methods," DR .. MARTIN SUMMERFIELD who wrote Chapter 6 "Solid Propellant Rockets," DR. HOWARD S. SEIFERT who wrote Chapter 7 "Hybrid Rockets," DR. CHANDLER C. Ross who wrote Chapter 8 "Advanced Nuclear Rocket Design," MR. GEORGE H. McLAFFERTY who wrote Chapter 9 "Gaseous Nuclear Rockets," DR. S. G. FORBES who wrote Chapter 10 "Electric and Ion Propul­sion," DR. R. H. BODEN who wrote Chapter 11 "Ion Propulsion," DR. ANDREW CHARWAT who wrote Chapter 12 "Interaction Flows Due to Steps, Notches and Secondary Jets," DR. A. K. OPPENHEIM who wrote Chapter 13 "Theory of Explosions and Its Relevance to Propulsion," DR. ANTONIO FERRI who wrote Chapter 14 "Super­sonic Combustion Theory," DR. SIN-I CHENG who wrote Chapter 15 "Combustion Instability Theory," and Chapter 16 "Advanced Space Compulsion Techniques," DR. JOHN F. MCCARTHY, JR. who wrote Chapter 17 "Zero 'G' Propulsion Problems," and DR. KRAFFT A. EHRICKE who wrote Chapter 18 "Propulsion Systems and Com­parison for Space Missions."

w. H. T. LOH, Course Instructor

Los Angeles, California

v

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . v

PART ONE - INTRODUCTION

Chapter 1. Fundamentals of Thermodynamics and Aerodynamics

[1-1] Introduction .......... 3 [1-2] Equation of State ........ 3

[1-2.1] Equation of State of Real Gases 4 [ 1-3] First Law of Thermodynamics 5

[ 1-3.1] Specific Heats . . . . . . . 6 [ 1-3.2] Internal Energy ...... 6 ( 1-3.3] Relationship Between Specific Heats cp and Cv 7

[ 1-3.4] Enthalpy . . . . . . 7 [1-3.5] Entropy ...... 8

[1-3.5.1] Reversible Process 9 [1-3.5.2] Adiabatic Process 9 [1-3.5.3] Isentropic Process 9 [1-3.5.4] Polytropic Process 10

[1-3.5.4.1] Work Done 10 [1-3.5.4.1.1] Special Case for Isentropic Case

where n = k 11 [1-3.5.4.1.2] Heat Added 11

[1-3.6] Mixture of Gases . . . . . . . 12 [1-3.7] Entropy-Enthalpy Diagram 14

[1-3.7.1] Remarks on Entropy-Enthalpy Diagram 17 [1-3.8] The Ideal (Reversible) Cycles .. . . . . . 17 [1-3.9] Cycle Work, Cycle Heat Added, and Cycle Efficiency 17

[ 1-4] Steady Flow Energy Equation ......... 18 [ 1-4.1] Stagnation Enthalpy or Total Enthalpy, H 19 [1-4.2] Application of Steady Flow Energy Equation to

Compressor and Turbine Analysis 20 [1-5] One-Dimensional Steady Flow Analysis . . 20

[1-5.1] One-Dimensional Energy Equation 20 [1-5.2] One-Dimensional Continuity Equation 21

vii

viii Jet, Rocket, Nuclear, Ion and Electric Propulsion

[ 1-5.3 J One-Dimensional Momentum Equation without Fluid Shearing or Friction Losses . . . . . . 21

[ 1-5.3.1 J One-Dimensional Momentum Equation with Fluid Shearing or Friction Losses 22

[1-5.4J Speed of Sound ....... 22 [1-5.5J Mach Number . . . . . . . . 23 [1-5.6J Another Form of Energy Equation 23 [1-5.7J Isentropic Flow Equations 24

[1-6J Normal Shock Waves and Rayleigh and Fanno Lines 29 [1-7J Oblique Shock Waves . . . . . . . . . . . . 33 [1-8J One-Dimensional Convergent - Divergent Nozzle Flow 38

[ 1-8.1 J Nozzle Efficiency 46 [1-8.2J Nozzle Thrust . . . . . . . . . 47

[1-9J Supersonic Inlet . . . . . . . . . . . 47 [ 1-9.1 J Constant Geometry Supersonic Inlet 49 [1-9.2J Variable-Geometry Supersonic Inlet 50 [1-9.3J Inlet Diffuser Efficiency . . . . . 50

[1-10J One-Dimensional Flow Analysis with Area Change, Friction and Heat Addition . . . . . . . . . . . . . . . 52

[ 1-10.1 J One-Dimensional Flow Analysis with Area Change, Friction and Heat Addition (Additional Analysis) 58

[1-10.2J Mixing of Two Flows in a Non-Constant Area Duct 67 [1-11 J Thermodynamic Cycle Analysis . . . . . . . . . 75

[ 1-11.1 J Ram Corn pression and Ram Pressure Recovery 75 [l-11.2J Compressor Compression and CompressOI Work 77 [1-11.3J Combustion and Burner Efficiency . 80

[ 1-11.3.1 J Combustion . . . . . . . . 80 [l-11.4J Turbine Expansion and Turbine Work . 83 [1-11.5J Nozzle Expansion and Nozz1eEfficiency '86

[ 1-12 J Variations of Basic Gas Turbine or Jet Engine Cycles 89 [ 1-12.1 J Intercoo1ing . 89 [1-12.2J Reheat . . . 94 [1-12.3 J Regeneration 97 [ 1-12.4 J After-burning 98 [l-12.5J Water Injection 99 [1-12.6] Pressure Loss in Various Components 102

[1-13.1 J Output, Input and Thermal Efficiency 103 [1-13.2J Jet Thrust ...... 103 [1-13.3J Propeller Thrust . . . . . . . . 104 [l-13.4J Specific Fuel Consumption . . . . 105

[ 1-14 J Variations of Gas Turbine Cycle and Turbojet Cycle by Gas Table Method . . . . . . . . . 105

[1-14.1 J Gas Table . . . . . . . . . . 105 [ 1-14.2 J Example 1: Gas Turbine Analysis 107 [ 1-14.3 J Example 2: Turbojet Analysis 112

Contents ix

PART TWO - JET PROPULSION

Chapter 2. Thermodynamic Cycle Analysis of Gas Turbines and Air·breathing Propulsion Systems

[2-1] Introduction .................. 119 [2-2] Symbols and Sketches of Air-breathing Propulsion Systems 119 [2-3] Gas Turbine Cycles . . . . . . . . . . . . . . . 121 [2-4] Air-breathing Propulsion Systems: Turbojet, Turboprop,

Ducted Fan, Ram Jet and Ducted Rocket 133 [2-4.1] Turbojet Cycles 147 [2-4.2] Turboprop Cycles 150 [2-4.3] Ducted Fan Cycles 153 [2-4.4] Off-Design Point Engines 160

[2-4.4.1] Compression Rate Variation with Altitude and Air Speed (Variation with Compressor Inlet Temperature) at Constant Compressor Speed. 161

[2-4.4.2] Air Flow Variation with Altitude and Airplane Speed at Constant Compressor Speed 162

[2-5] Rotary Matrix Regenerator for Turboprop Applications 165 [2-5.1] Discussion 165 [2-5.2] Operating Principles . . . . . . . . . . . 168 [ 2-5.3] Theory and Design ......... . . 172

[2-6] Analytical Solutions for Rotary Matrix, Wire Screen Heat Exchangers . . . . . . . . . . . . 173

[2-7] Pulse Jet . . . . . . . . . . . . . . 191 [2-7.1] Discharging from Point c to Point a . 192

[2-7.1.1] Supercritical Discharging When (Pip ~ [(k + 1)/2]k/(k . 11 193

[2-7.1.2] Subcritical Discharging When (Pip ~ [(k + l)/2]k/(k • 1) 195

[2-7.2] Combustion from Point b to Point c 197 [2-7.3] Charging Process from Point a to Point b 200

[2-7.3.1] Supercritical Charging and Subcritical Discharg-ing . . . . . . . . . . . . . . . .. 202

[2-7.3.2] Subcritical Charging and Subcritical Discharging 204 [2-7.3.3] Sub critical Chargiqg and Supercritical Discharg-

ing . . . . . . . . . . . . . . . .. 204

Chapter 3. Aerodynamic Design of Axial Flow Compressors and Turbines

[3-1] Introduction ..... . [3-2] Compressible Flow Analysis

[3-2.1] Radial Equilibrium [3-2.2] Continuity Equation [3-2.3] Density Relationship [3-2.4] Method of Calculation

207 208 211 214 214 215

x Jet, Rocket, Nuclear, Ion and Electric Propulsion

[3-3] Turbine Analysis . . . . . . . . . . . . . . . . 218 [3-4] Appendix: Two Dimensional Incompressible Compressor

Design . . . . . . . . . . . . . . . . . . . . 224 [3-4.1] Turning Angle () asf(CL ) and Derivation of Blade

Efficiency l1b •...........•. 232

Chapter 4. Ramjets and Air-Augmented Rockets

[4-1] Preliminary Performance Calculations . . . . . . . . 237 [4-2] Diffuser Design ................ 242

[4-2.1] Inviscid Design of External-Compression Diffusers 244 [4-2.2] Off-Design Operation, Boundary Layer Problems, and

Instabilities . . . . 248 [4-2.3] Hypersonic Inlets . . . . . . . . . . . . . 251

[4-3] Combustor and Nozzle Design . . . . . . . . . . . 254 [ 4-4] Considerations for Preliminary Design of Ramjet Vehicles 257 [4-5] Air-Augmented Rockets . . . . . 264 [4-6] Engines with Supersonic Combustion 265 [4-7] Concluding Remarks 268 [4-8] Acknowledgments 268 [4-9] Nomenclature . . . 269

PART THREE - ROCKET PROPULSION

Chapter 5. Rocket Classifications, Liquid Propellant Rockets, Engine Selection, and Heat Transfer

[5-1] Definitions and Classification of Rocket Propulsion Engines. 277 [5-2] Liquid Propellant Rockets . . . . . . . 283 [5-3] Selection Criteria .......... 293 [5-4] Heat Transfer (based largely on Reference 7) 296

[5-4.1] Radiation Cooling ....... 296 [5-4.2] Heat-Sink Cooling ....... 301 [5-4.3] Low Flame Temperature Metal Chamber 301 [5-4.4] Turbine Exhaust Gas Cooling 301 [5-4.5] Insulation Cooling 302 [5-4.6] Dump Cooling . . . 302 [5-4.7] Ablative Cooling 303 [5-4.8] Regenerative Cooling 304 [5-4.9] Film Cooling 304

[5-4.10] Transpiration Cooling 305 [5-4.11] Combined Methods . 305

Chapter 6. Solid Propellant Rockets

[6-1] Composition of a Solid Propellant 308

Contents xi

[6-2] Processability Criteria . . . . . . 312 [6-3] Performance of Typical Propellants 312 [6-4] Burning Rate - Pressure Relationships 314 [6-5] Propellant Area Ratio . . . . . . 316 [6-6] Temperature Sensitivity of Burning Equations 317 [ 6-7] Erosive Burning . . . . . . . . . . . . 318 [6-8] Effect of Spin on Burning Rate . . . . . . 318 [6-9] Mechanism of Homogeneous Propellant Burning 318

[6-10] Mechanism of Composite Propellant Burning . 320 [6-11] Correlation of Burning Rates with Oxidizer Activation

Energy ............ 321 [6-12] Effect of Composition on Burning Rate 321 [6-13] Catalysts . . . . . . . . 323 [6-14] Mechanical Properties . . . 323

[6-14.1] Uniaxial Tensile Test 323 [6-14.2] Uniaxial Shear Test 326 [6-14.3] Bulk Dilution Test 326 [6-14.4] Poisson's Ratio 326 [6-14.5] Glass Transition 327

[6-15] Nomenclature . . . . 329

Chapter 7. Hybrid Rocket Theory and Design

[7-1] Introduction . . . . . . . . . . . 332 [7-2] Hybrid Combustion with Negligible Radiation 334

[7-2.1] The Physical Process . . . . . 334 [7-2.2] Convective Heat Transfer . . . . . . 335 [7-2.3] The Role of Nonvolatile Particles 338

[7-3] Operating Characteristics of Hybrid Rockets with Negligible Radiation . . . . . . . . . . . . . . . . . . 340

[7-3.1] Regression Rate Insensitivity to Thermochemical Parameters . . . . . . . . . . . . 340

[7-3.2] Regression Rate Dependence Upon Grain Configuration . . . . . . . . . . . 340

[7-3.3] Throttling and Off-Design Point Operation 340 [7-3.4] Combustion Efficiency . . . . . . . . 341 [7-3.5] Regression Rate Dependence Upon Pressure 342

[7-4] Hybrid Combustion in Radiative Motors . . . . 342 [7-4.1] Regression Rate Dependence Upon Radiant Energy Flux 342 [7-4.2] Evaluation of Convective Heat Transfer Qc 344 [7-4.3] Evaluation of Radiative Heat Transfer Qr 345

[7-5] Transient Operation of Hybrid Rockets 346 [7-5.1] Penetration of Temperature Prome 346 [7-5.2] Critical Regression Rate . . . . . 348

xii Jet, Rocket, Nuclear, Ion and Electric Propulsion

[7-6] Design of Hybrid Rockets . . . . [7-6.1] Specification of Mission [7-6.2] Prelirilinary Design Procedure [7-6.3] Example Configurations

PART FOUR - NUCLEAR PROPULSION

Chapter 8. Nuclear Rocket Prqpulsion

[8-1] Nuclear Rocket Engine Design and Perfonnance [8-1.1] Types of Nuclear Rockets [ 8-1.2] Overall Engine Design . . . [8-1.3] Nuclear Rocket Perfonnance

[8-2] Component Design . . . . . . . [8-2.1] Nuclear Rocket Reactors . .

[8-2.1.1] General Design Considerations [8-2.1.2] Reactor Core Materials [8-2.1.3] Thennal Design . [8-2.1.4] Mechanical Design [8-2.1.5] Nuclear Design . [8-2.1.6] Shielding

18-2.2] Nuclear Rocket Nozzles [8-2.2.1] General Design Considerations [8-2.2.2] Heat-Transfer Analysis .

[8-2.2.2.1] Over-all Problem . [8-2.2.2.2] Hot-Gas Boundary [8-2.2.2.3] Cold-Gas Boundary

[8-2.3] Propellant Feed Systems . . . [8-2.3.1] General Design Considerations [8-2.3.2] Turbopump Power Cycle [8-2.3.3] Turbopump

[8-2.3.3.1] Pumps .... [8-2.3.3.2] Turbines . . . . [ 8-2.3.3.3] Power Transmission [8-2.3.3.4] Critical Speeds

[8-2.3.4] Valves ....... . [8-2.4] Nuclear Rocket Engine Control

[8-2.4.1] General Design Considerations [8-2.4.2] Power Level Control . . [8-2.4.3] Chamber-Pressure Control . .

[8-2.5] Thrust-Vector-Control Systems [8-2.5.1] General Design Considerations [8-2.5.2] Types of Systems . . . . .

[8-2.5.2.1] Auxiliary Thrusters [8-2.5.2.2] Jet-Deflection Systems

349 349 350 351

359 359 359 361 362 362 362 364 365 365 367 369 370 370 371 371 371 373 375 375 375 376 376 381 381 382 382 383 383 384 386 387 387 387 388 389

Contents xiii

[8-2.5.2.2.1] Fluid-Injection Systems 389 [8-2.5.2.2.2] Jetevators and Jet Vanes 390

[8-2.5.2.3] Gimbal Systems ...... 390

Chapter 9. Radioisotope Propulsion

[9-1] Alternative Approaches . . 395 [9-1.1] Direct Recoil Method 395 [9-1.2] Thermal Heating Method 397

[9-2] Basic Thruster Configurations 398 [9-3] Propulsion System and Upper Stage 400 [9-4] Relative Mission Capabilities 402

[9-4.1] Primary Propulsion . 402 [9-4.2] Auxiliary Propulsion 404

[9-5] Thruster Technology . . 405 [9-5.1] Design Criteria 405

[9-5.1.1] Performance 405 [9-5.1.2] Safety . . 406 [9-5.1.3] Design Criteria Summary 409

[9-5.2] Heat Source Development 409 [9-5.2.1] Radioisotope Fuel 409 [9-5.2.2] Capsule Technology 410

[9-5.2.2.1] General Considerations 410 [9-5.2.3] Thermal Design ..... 412 [9-5.2.4] Fabrication and Non-Destructive Testing

Techniques . . . . 414 [9-5.2.5] Pressure Containment . 414 [9-5.2.6] Impact . . . . . . . 415 [9-5.2.7] Heat Source Simulation 418 [9-5.2.8] Oxidation and Corrosion of Encapsulating

Materials . . 418 [9-5.3] Nozzle Performance 419

[9-6] Summary . . . . . . . 422

PART FIVE - ELECTRIC AND ION PROPULSION

Chapter 10. Electric and Ion Propulsion

[ 10-1] Basic Concepts . . . . . . . [ 10-1.1] Energy Sources [ 10-1.2] The Separately Powered Rocket [10-1.3] Effects of Variable Mass ... [ 10-1.4] Power Requirements and Rocket Efficiency [10-1.5] Effects of Gravitational Fields .....

427 427 429 432 434 435

xiv Jet, Rocket, Nuclear, Ion and Electric Propulsion

[ 1 0-2] Thrust Devices . . . . . 436 [10-2.1] Thermal Thrusters . 437

[ 10-2.1.1] The Resistojet 437 [10-2.1.2] Arc Jets 439 [10-2.1.3] Ablative Thrusters 439

[10-2.2] Electrostatic Thrusters 440 [10-2.2.1] Ion Engines . . . 441

[10-2.2.1.1] High Pressure Arcs (Duop1asmatron) . 441 [10-2.2.1.2] Contact Thrusters . . . . 442 [10-2.2.1.3] The Bombardment Thruster 447

[10-2.2.2] Colloid Thrusters . 449 [10-2.3] Plasma Thrusters 452

[ 10-2.3.1] j x B Machines 453 [10-2.3.2] MPD Arcs 454 [10-2.3.3] Pulsed Inductive Accelerators 455

[ 10-3] State of the Art and Future Trends 456 [10-3.1] Sample Problem 1 457 [10-3.2] Sample Problem 2 460 [10-3.3] Sample Pro.b1em 3 462

Chapter 11. Ion Propulsion

[ 11-1] Introduction . . . [11-2] Fundamentals

[ 11-2.1] Performance Analysis [ 11-2.1.1] Characteristic Velocity [11-2.1.2] Payload .... [11-2.1.3] Specific Power . .

[11-2.2] Electrical Thrust Devices [11-2.2.1] Ion and Colloid

[ 11-3] Ion Rocket Engine ... . [11-3.1] Ion Sources ... . [11-3.2] Electromagnetic Fields [11-3.3] Charged Colloid Sources

463 464 465 465 467 468 470 470 471 475 480 481

PART SIX - THEORY ON COMBUSTION, DETONATION AND FLUID INJECTION

Chapter 12. Interaction Flows Due to Supersonic Secondary Jets

[ 12-1] Introduction . . . . [12-2] Jets Directed Upstream [12-3] Transverse Jets [ 12-4] Summary . . . . .

487 488 496 502

Contents xv

Chapter 13. Gasdynamics of Explosions

[ 13-1] Theoretical Aspects . . . . . . . . . . . . 508 [ 13-1.1] Fundamentals of Non-steady Gasdynamics 508

[ 13-1.1.1] Continuity Equation 509 [13-1.1.2] Equation of Motion . . 510 [ 13-1.1.3] Entropy Equation 510 [ 13-1.1.4] Characteristic Relations 512

[13-1.2] GasdynamicDiscontinuity . . 515 [13-1.2.1] Mechanical Conditions 515 [13-1.2.2] The Hugoniot Relationship 516 [13-1.2.3] Oblique Discontinuity . . 521

[13-1.3] Simple Wave . . . . . . . . 523 [13-1.3.1] Simple Wave in Non-Steady Flow 523 [13-1.3.2] Simple Wave in Steady Flow 524

[13-2] Analytical Aspects . . . . . . 527 [13-2.1] Vector Polar Method . . 527

[13-2.1.1] Wave Interactions 529 [13-2.1.2] Wave Intersections 542

[13-3] Appendix: Salient Properties of the Hugoniot Curve 555

Chapter 14. Supersonic Combustion Technology

[ 14-1] Introduction .......... 561 [14-2] Performance of Supersonic Combustion Ramjet 562

[14-2.1] Possible Air-breathing Engine Schemes . 562 [14-3] Supersonic Combustion ......... 564

[14-3.1] Qualitative Description of Supersonic Combustion Controlled by Mixing . . . . . . . . . . 564

[14-3.1.1] Supersonic Combustion Controlled by Diffusion . . . . . . . . . . . . 564

[14-3.1.2] Supersonic Combustion Controlled by Heat Convection . . . . . . . 570

[14-3.2] Analysis of the Reaction Process 574 [ 14-3.2.1] Determination of Reaction Times 575 [14-3.2.2] Numerical Results . . . . . . 578 [14-3.2.3] Discussion of Results . . . . . 581 [14-3.2.4] Tangential Injection with Chemical Reaction 582

[14-3.3] Analysis of Mixing Processes . . . . . . . 583 [14-3.3.1] Mixing of Non-Reacting Flows 584 [14-3.3.2] Discussion of Experimental Results of

Non-Reacting Gases . . . . . 586 [14-3.3.3] Mixing with Pressure Gradients 587

Chapter 15. Combustion Instability Theory

[ 15-1] Introduction . . . . . . [ 15-1.1 ] Unstable Combustion . . .

599 599

xvi Jet, Rocket, Nuclear, Ion and Electric Propulsion

[ 15-2] Review of Theoretical Developments ...... 601 [ 15-2.1] Early Developments and the Time Lag Concept 601 [15-2.2] Current Status in Liquid Propellant Rockets 602 [ 15-2.3] Current Status in Solid Propellant Rockets 603

[15-3] Formulation and Analysis . . . . . . . . . 605 [15-3.1] Low Frequency, Capacitive Type Stability 605 [15-3.2] High Frequency, Wave Type Instability 608 [15-3.3] The Energy Approach 610 [15-3.4] Non-linear Effects 612 [15-3.5] Nozzle Outflow 613

[ 15-4] Concluding Remarks . . 614

PART SEVEN - ADVANCED CONCEPTS AND MISSION APPLICATIONS

Chapter 16. An Advanced Space Propulsion Concept

[16-11 Introduction . . . . . . . . . . . . . 621 [ 16-1.1] General Consideration for Propulsion in Space 621 [16-1.2] Power Supply . . . . . . . . . . . . 622 [16-1.3J Propellant Storage and Handling Facilities . . 624 [16-1.4] Electrostatic and Electromagnetic Thrusters . 625 [16-1.5] Advanced Electric Propulsion Systems for Space

Vehicles . . . . . . . . . . . 627 [16-2] Sputtering, A Thrust Generation Mechanism . . . 628

[16-2.1] Sputtering Phenomena . . . . . . . . 628 [16-2.2] Possible Performance of Sputtering Thrusters 632 [ 16-2.3] Energy Efficiency of the Sputtering Process 633

[16-3] Analyses of an Elementary Mission with Different Electric Thrusters . . . . . . . . . . . . . . . . 635

[16-3.1] General Consideration ........ 635 [16-3.2] Performance Formula for Electric Thrusters 637 [16-3.3] Optimization with Electric Thrusters 639

[ 16-4] Summary and Concluding Remarks . . . . . . 642

Chapter 17. Zero 9 Propulsion Problems

[ 17-1] Introduction . . . 644 [17-2] Basic Definitions 645

[17-2.1] Zero Gravity 647 [17-2.2] Engineering Considerations of Zero-g Environment. 649 [17-2.3] Principle of Minimum Energy 651

[ 17-3] Hydrostatics . . . . . . . . . . . . . 651 [17-3.1] The Variational Problem ..... 651 [17-3.2] Solutions for the Variational Problem 655 [17-3.3] Conclusions from Hydrostatic Analysis 658

Contents xvii

[ 17-4] Static Configurations in Zero g . 658 [17-5] Hydrodynamics . . . . . . . 661

[17-5.1] Propellant Slosh at Zero g 662 [17-5.2] Propellant-Position Control 667 [17-5.3] Capillary Stability . . . . 673

[ 17-6] Dimensional Analysis, Modeling, and Test 677 [ 17-6.1] Gas Interface Velocity 677 [17-6.2] Propellant Accumulation 684 [ 17-6.3] Gas Ingestion . . . . . 691 [ 17-6.4] Analytical Considerations of Gas Ingestion 695

[ 17-7] Capillary Barriers 697 [ 17-7.1] Static Stability 699 [17-7.2] Dynamic Stability 701

[17-8] Zero g Propellant Gauging 712 [17-9] Summary and Conclusions. 714

[17-10] Appendix A. Derivation of Slosh Frequency 717 [ 17-11] Appendix B. Derivation of Flow Rate during Propellant

Settling . . . . . . . . . . . . . . . . . . . 721

Chapter 18. Propulsion Systems-Comparison and Evaluation for Space Missions

[ 18-1] Goals . . . . . . . . . . . . . . . . .. 728 [18-2] Propulsion-Vehicle-Mission Integration . . . . . . .. 728 [ 18-3] Elements of Integrated Transportation System Comparison

(ELV, GISV, CISV and HISC) ........... 749