Combustion Processes 9781400877027

Table of contents :
CONTENTS
PART 1. THERMODYNAMICS OF COMBUSTION
A. High Temperature Equilibrium
1. Problems in Combustion
2. Determination of Equilibrium Composition and Thermodynamic Properties
3. Determination of Heat Release and Flame Temperature
4. Gas Imperfection
5. Failure to Maintain Equilibrium in Combustion
6. Cited References and Bibliography
B. Expansion Processes
1. Classification of Flow Processes
2. Thermodynamic Relations for Flow Processes
3. Determination of Performance Parameters for Isentropic Flow
4. Nonequilibrium Effects
5. Two-Phase Flow
6. Cited References
C. Computational Methods in Combustion Calculations
1. Introduction
2. Calculation of the Equilibrium Composition
3. Calculation of the Thermodynamic Properties at Equilibrium
4. Evaluation of Performance Factors of Fuel-Oxidant Systems
5. Cited References
PART 2. CHEMICAL KINETICS OF COMBUSTION
D. Fundamentals of Chemical Kinetics
1. Introduction
2. General Considerations
3. The Half Life of a Reaction
4. The Order of Simultaneous Reactions
5. Temperature and the Velocity of Chemical Reaction
6. The Potential Energies of 2-, 3-, and 4-Atom Systems
7. Potential Energy and Activation Energy
8. Statistical Treatment of the Activated Complex
9. Absolute Rate Theory and Collision Theory. A Comparison
10. The Theory of First Order Processes
11. The Theory of Third Order Processes
12. The Reaction of Molecules with Atoms or Radicals
13. Chain Mechanisms
14. Branching Chains and Explosions
15. Wall Reactions
16. Gas Reactions at Surfaces. General Principles
17. Adsorption
18. Adsorption Equilibrium. The Adsorption Isotherm
19. Desorption Phenomena
20. Kinetics of Chemical Reactions at Surfaces
21. Adsorption and Desorption as Rate-Determining Processes
22. Transport to and from the Surface as Rate-Determining Steps
23. Kinetics of Reactions in Solid and Solid-Gas Systems
24. Fast Reactions: Introduction
25. Rates of Fast Reactions
26. Experimental Methods
27. Nonequilibrium and Nonequipartition Systems in Fast Reactions
28. The Persistence of Nonequilibrium Conditions
29. Cited References
E. Kinetics of Several Oxidation Reactions
1. The Hydrogen-Oxygen Reaction
2. The Carbon Monoxide-Oxygen Reaction
3. The Oxidation of Paraffin Hydrocarbons
4. Some Other Exothermic Reactions
5. Cited References and Bibliography
PART 3. FLAME PROPAGATION IN GASES
F. Mechanics of Reaction Continua
1. Fundamental Equations
2. Application of the Phenomenological Theory of Irreversible Processes
3. Cited References and Bibliography
G. Combustion Waves in Nonturbulent Explosive Gases
Chapter 1. Theory of Combustion Waves
1. Description and General Equations
2. Special Solutions for One-Dimensional Steady State Propagation
3. WaveNear a Heat Sink. Dead Space and QuenchingDistance
4. Curved Waves
5. Principles of Stabilization of Combustion Waves in Gas Streams
6. Calculation of Wave Shape and Gas Flow Pattern
7. Momentum Change and Thrust Pressure
8. Propagation in Channels
9. Thermal Model of Combustion Wave. Excess Enthalpy
10. Principles of Ignition
11. Simplified Equations for Calculations Involving Heat Transport Across the Combustion Wave
Chapter 2. Experimental Phenomena of Combustion Waves
12. Ignition: Experiments and Comparison with Theory
13. Observations on the Propagation of Combustion Waves
14. Stability and Quenching Limits, and Structure of Burner Flames
Chapter 8. Combustion Waves in Closed Vessels
15. Dependence of Pressure Rise and Temperature Distribution on Fraction of Gas Burned
16. Correlation of Rate of Pressure Rise with Burning Velocity
17. Cited References
H. Combustion Waves in Turbulent Gases
1. Phenomenological Description of Turbulent Flames
2. The Work of Damkohler
3. The Work of Shelkin
4. Turbulent Burning Velocity Measurements of the National Advisory Committee for Aeronautics
5. Turbulent Flames Confined in Channels
6. Turbulent Flame Measurements at California Institute of Technology
7. Other Experimental Studies of Turbulent Flames
8. Turbulence
9. Turbulent Diffusion
10. Theory of Flame Propagation by Large Scale Turbulence
11. Experimental Measurement of the Turbulent Burning Velocity
12. Turbulence Generation by the Turbulent Flame
13. Pressure Drop Across the Flame, Diffusion of Turbulence, Thickness of the Turbulent Flame
14. Propagation of Flames in Turbulent Explosive Mixtures
15. Stability of Turbulent Flames
16. Numerical Data of Turbulent Flames
17. The Status of Turbulent Flame Research
18. Cited References
I. Diffusion Flames
1. Introduction
2. Laminar Diffusion Flames
3. Transition Region Between Laminar and Turbulent Diffusion Flames
4. Turbulent Flames
5. Cited References
PART 4• COMBUSTION OP LIQUIDS AND SOLIDS
J. Combustion of Liquid Fuels
1. Atomization
2. Mixing and Precipitation of Fuel Sprays
3. Evaporation of Fuel Drops
4. Combustion of Fuel Drops
5. Cited References
K. Combustion of Solid Fuels
1. Introduction
2. Properties of Solid Fuels and Combustion Products
3. Fuel and Air Contact
4. Oxidation Mechanisms
5. Ignition
6. Combustion Processes
7. Exhaust
8. Concluding Remarks
9. Cited References
L. Combustion of Liquid Propellants
Chapter 1. Ignition Phenomena in Bipropellant and Monopropellant Systems
1. Introduction
2. Experimental Methods Used for Measuring Ignition Delay in Bipropellant Systems
3. Representative Ignition Delay Measurements on Spontaneous Bipropellant Systems
4. Ignition of Representative Nonspontaneous Bipropellants
5. Ignition of MonopropelIants
Chapter 2. Motor Performance of Selected Monopropellants
6. General Characteristics of Monopropellants
7. Classification of Monopropellants
8. Performance Characteristics of Monopropellants
Chapter 3. Combustion of Selected Bipropellant Systems
9. Classification of Oxidizers and Fuels
10. Combustion of Bipropellants in Rocket Engines
11. Performance Characteristics of Several Bipropellant Combinations
12. Modern Trends in Combustion Research on Liquid-Fuel Rocket Engines
13. Cited References
M. Combustion of Solid PropelIants
1. General Characteristics of Solid Propellants
2. Thermal Decomposition of Propellant Components
3. The Burning of Double-Base Propellants
4. The Burning Rate of Propellants
5. Theories of the Burning of Propellants
6. The Mechanism of Burning of Composite Propellants
7. The Ignition of Solid Propellants
8. Cited References
PART 5. DETONATION PROCESSES IN GASES, LIQUIDS, AND SOLIDS
N. Detonation Processes in Gases, Liquids, and Solids
Chapter 1. Experimental Methods for Observing Detonation
1. Introduction
2. Measurement of Detonation Velocities
3. Detonation Temperatures
4. Flow Velocities
5. Other Experiments
Chapter 2. The Physical Chemistry of Detonation Processes in Gases, Liquids, and Solids
6. Some Characteristic Differences Between Detonation and Explosion
7. Equations of State for Detonation
8. A Finite Time of Energy Release in Detonation
9. The Finite Time of Energy Release in Relation to Lateral Venting
10. Data on Energy Release in Stable Regimes
11. Mechanisms of Activation in the Propagation of Detonation
Chapter 3. Limiting Conditions for Stable Detonation
12. The Decay and Failure of Detonation
13. Macroinitiation of Detonation. Graded Detonative Impulses
14. The Transition from Macrocombustion to Detonation
15. Mieroinitiation of Detonation. The Sensitiveness of Explosives
Chapter 4. The Development of Research in the Physical Chemistry of Detonative Processes
16. Basic Detonation Parameters
17. Studies on the Marginal Propagation of Detonation
18. Direct Microinitiation
19. Cited References
PART 6. ENERGY PRODUCTION BY NUCLEAR REACTIONS
O. Energy Production by Nuclear Reactions
1. Introduction
2. Nuclei
3. Nuclear Energies
4. Nuclear Reactions
5. Summary and Conclusions
6. Cited References and Bibliography
Index

Citation preview

COMBUSTION PROCESSES

BOARD OF EDITORS THEODORE VON KARMAN, Chairman HUGH L. DKYDEN HUGH S. TAYLOR JOSEPH V. CHARYK, General Editor, 1952Associate Editor, 1949-1952 MARTIN SUMMERFIELD, General Editor, 1949-1952 COLEMAN DUP. DONALDSON AND RICHARD S. SNEDEKER,

Associate Editors, 1955-

I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII.

Thermodynamics and Physics of Matter. Editor: F. D. Rossini Combustion Processes. Editors: B. Lewis, R. N. Pease, Η. S. Taylor Fundamentals of Gas Dynamics. Editor: H. W. Emmons Laminar Flows and Transition to Turbulence. Editor: C. C. Lin Turbulent Flows and Heat Transfer. Editor: C. C. Lin General Theory of High Speed Aerodynamics. Editor: W. R. Sears Aerodynamic Components of Aircraft at High Speeds. Editors: A. F. Donovan, H. R. Lawrence High Speed Problems of Aircraft and Experimental Methods. Editors: A. F. Donovan, H. R. Lawrence, F. Goddard, R. R. Gilruth Physical Measurements in Gas Dynamics and Combustion. Edi­ tors: R. W. Ladenburg, B. Lewis, R. N. Pease, H. S. Taylor Aerodynamics of Turbines and Compressors. Editor: W. R. Hawthorne Design and Performance of Gas Turbine Power Plants. Editors: W. R. Hawthorne, W. T. Olson Jet Propulsion Engines. Editor: 0. E. Lancaster

VOLUME I I HIGH S P E E D AERODYNAMICS AND J E T PROPULSION

COMBUSTION PROCESSES

EDITORS

B. LEWIS • R. N. PEASE H. S. TAYLOR

PRINCETON, N E W J E R S E Y PRINCETON UNIVERSITY PRESS 1956

COPYRIGHT , 1956, by PRINCETON UNIVERSITY PRESS

London: GEOFFREY CUMBERLEGE, OXFORD UNIVERSITY PRESS L. c. CARD 55-8070

Reproduction, translation, publication, use, and dis­ posal by and for the United States Government and its officers, agents, and employees acting within the scope of their official duties, for Government use only, is per­ mitted. At the expiration of ten years from the date of publication all rights in material contained herein first produced under contract Nonr-03201 shall be in the public domain.

PRINTED IN THE UNITED STATES OF AMERICA BY THE MAPLE PRESS COMPANY, INC., YORK, PENNA.

FOREWORD On behalf of the Editorial Board, I would like to make an acknowledgement to those branches of our military establishment whose interest and whose financial sup­ port were instrumental in the initiation of this publi­ cation program. It is noteworthy that this assistance has included all three branches of our Services. The Department of the Air Force through the Air Re­ search and Development Command, the Department of the Army through the Office of the Chief of Ord­ nance, and the Department of the Navy through the Bureau of Aeronautics, Bureau of Ships, Bureau of Ordnance, and the Office of Naval Research made significant contributions. In particular, the Power Branch of the Office of Naval Research has carried the burden of responsibilities of the contractual ad­ ministration and processing of all manuscripts from a security standpoint. The administration, operation, and editorial functions of the program have been centered at Princeton University. In addition, the University has contributed financially to the support of the undertaking. It is appropriate that special ap­ preciation be expressed to Princeton University for its important over-all role in this effort. The Editorial Board is confident that the present series which this support has made possible will have far-reaching beneficial effects on the further develop­ ment of the aeronautical sciences. Theodore von Kdrmdn

PREFACE Rapid advances made during the past decade on problems associated with high speed flight have brought into ever sharper focus the need for a comprehensive and competent treatment of the fundamental aspects of the aerodynamic and propulsion problems of high speed flight, together with a survey of those aspects of the underlying basic sciences cognate to such problems. The need for a treatment of this type has been long felt in research institutions, universities, and private industry and its potential reflected importance in the advanced training of nascent aeronautical scientists has also been an important motivation in this undertaking. The entire program is the cumulative work of over one hundred scientists and engineers, representing many different branches of engineer­ ing and fields of science both in this country and abroad. The work consists of twelve volumes treating in sequence elements of the properties of gases, liquids, and solids; combustion processes and chemical kinetics; fundamentals of gas dynamics; viscous phenomena; turbulence; heat transfer; theoretical methods in high speed aero­ dynamics; applications to wings, bodies and complete aircraft; nonsteady aerodynamics; principles of physical measurements; experimental methods in high speed aerodynamics and combustion; aerodynamic problems of turbo machines; the combination of aerodynamic and com­ bustion principles in combustor design; and finally, problems of complete power plants. The intent has been to emphasize the fundamental aspects of jet propulsion and high speed aerodynamics, to develop the theoretical tools for attack on these problems, and to seek to highlight the directions in which research may be potentially most fruitful. Preliminary discussions, which ultimately led to the foundation of the present program, were held in 1947 and 1948 and, in large measure, by virtue of the enthusiasm, inspiration, and encouragement of Dr. Theodore von Kdrmdn and later the invaluable assistance of Dr. Hugh L. Dryden and Dean Hugh Taylor as members of the Editorial Board, these dis­ cussions ultimately saw their fruition in the formal establishment of the Aeronautics Publication Program at Princeton University in the fall of 1949. The contributing authors and, in particular, the volume editors, have sacrificed generously of their spare time under present-day emergency conditions where continuing demands on their energies have beep great. The program is also indebted to the work of Dr. Martin Summerfield who guided the planning work as General Editor from 1949-1952. The cooper­ ation and assistance of the personnel of Princeton University Press and of the staff of this office has been noteworthy. In particular, Mr. H. S.

PREFACE

Bailey, Jr., the Director of the Press, and Mr. R. S. Snedeker, who has supervised the project at the Press and drawn all the figures, have been of great help. Special mention is also due Mrs. Η. Ε. H. Lewis and Mrs. E. W. Wetterau of this office who have handled the bulk of the detailed editorial work for the program from its inception. Joseph V. Charyk General Editor

PREFACE TO VOLUME II This volume is concerned with combustion processes in their various aspects, encompassing chemical kinetics, the kinetics of transport processes, fluid dynamics, and thermodynamics. It deals, therefore, with rate processes in chemical reactions, with the propagation of chemical reaction by the mechanisms of combustion waves and detonation waves, with the effect of turbulence on combustion waves, with processes of simultaneous mixing and combustion of fuels and oxidants, and with chemical equilibria. These subjects are basic for an understanding of the role of combustion in propulsion processes. After a survey of basic principles the presentation continues with oxidation and flame propaga­ tion in gaseous systems, and the combustion of liquid and solid fuels and propellants. Final sections of the book are devoted to detonation processes and the principles of energy production by nuclear reaction. The volume editors express their appreciation of the cooperation re­ ceived from the authors. The bulk of the first drafts of the several sections were received in 1951, and revised copy late in 1952 and early 1953. Delays unfortunately occurred in securing the necessary permission to publish certain manuscripts. This delayed the publication date and the position of this volume in the publication sequence. The volume editors believe that the difficulties arising from these delays have been minimized as far as is possible, but emphasize these aspects in defining the book as a presentation of current science. The duties of General Editor of the present volume have largely been discharged by Professor Irvin Glassman of Princeton University. His assistance to us is deeply appreciated. Mr. R. S. Snedeker has continued to render his conspicuous service in the preparation of all the figures and in the supervision at Princeton University Press. The volume will reveal the same high quality of typography and arrangement that have been observed in the earlier volumes. To all, authors and collaborators, we extend our sincere thanks. B. Lewis R. N. Pease H. S. Taylor

CONTENTS PART 1. THERMODYNAMICS OF COMBUSTION EDITOR: B. LEWIS

A. High Temperature Equilibrium

1. 2. 3. 4. 5. 6.

James M. Carter, Aerojet Engineering Corporation, Azusa, California David Altman, Jet Propulsion Laboratory, California Insti­ tute of Technology, Pasadena, California Problems in Combustion Determination of Equilibrium Composition and Thermo­ dynamic Properties Determination of Heat Release and Flame Temperature Gas Imperfection Failure to Maintain Equilibrium in Combustion Cited References and Bibliography

B. Expansion Processes

1. 2. 3. 4. 5. 6.

David Altman, Jet Propulsion Laboratory, California Insti­ tute of Technology, Pasadena, California James M. Carter, Aerojet Engineering Corporation, Azusa, California Classification of Flow Processes Thermodynamic Relations for Flow Processes Determination of Performance Parameters for Isentropic Flow Nonequilibrium Effects Two-Phase Flow Cited References

C. Computational Methods in Combustion Calculations

1. 2. 3. 4. 5.

Stuart R. Brinkley, Jr., Combustion and Explosives Research, Inc., Pittsburgh, Pennsylvania Introduction Calculation of the Equilibrium Composition Calculation of the Thermodynamic Properties at Equilibrium Evaluation of Performance Factors of Fuel-Oxidant Systems Cited References

3

3 4 15 17 22 24 26

26 28 40 45 52 62 64

64 65 84 97 97

CONTENTS P A R T 2. CHEMICAL K I N E T I C S OF COMBUSTION EDITORS: H. S . T A Y L O R A N D R. N . P E A S E

D. Fundamentals of Chemical Kinetics

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

Hugh S. Taylor, Department of Chemistry, Princeton Univer­ sity, Princeton, New Jersey Introduction General Considerations The Half Life of a Reaction The Order of Simultaneous Reactions Temperature and the Velocity of Chemical Reaction The Potential Energies of 2-, 3-, and 4-Atom Systems Potential Energy and Activation Energy Statistical Treatment of the Activated Complex Absolute Rate Theory and Collision Theory. A Comparison The Theory of First Order Processes The Theory of Third Order Processes The Reaction of Molecules with Atoms or Radicals Chain Mechanisms Branching Chains and Explosions Wall Reactions Gas Reactions at Surfaces. General Principles Adsorption Adsorption Equilibrium. The Adsorption Isotherm Desorption Phenomena Kinetics of Chemical Reactions at Surfaces Adsorption and Desorption as Rate-Determining Processes Transport to and from the Surface as Rate-Determining Steps Kinetics of Reactions in Solid and Solid-Gas Systems Fast Reactions: Introduction Rates of Fast Reactions Experimental Methods Nonequilibrium and Nonequipartition Systems in Fast Re­ actions The Persistence of Nonequilibrium Conditions Cited References

E. Kinetics of Several Oxidation Reactions Robert N. Pease, Department of Chemistry, Princeton Uni­ versity, Princeton, New Jersey 1. The Hydrogen-Oxygen Reaction 2. The Carbon Monoxide-Oxygen Reaction

101

101 102 105 105 110 113 116 118 120 124 126 127 130 132 135 137 138 139 139 140 142 143 144 147 147 148 153 156 156 160

160 175

CONTENTS

3. The Oxidation of Paraffin Hydrocarbons 4. Some Other Exothermic Reactions 5. Cited References and Bibliography

179 191 197

P A R T 8. FLAME PROPAGATION I N GASES EDITOR: B. LEWIS

F. Mechanics of Reaction Continua John M. Richardson, The Ramo-Wooldridge Corporation, Los Angeles, California Stuart R. Brinkley, Jr., Combustion and Explosives Research, Inc., Pittsburgh, Pennsylvania 1. Fundamental Equations 2. Application of the Phenomenological Theory of Irreversible Processes 3. Cited References and Bibliography G. Combustion Waves in Nonturbulent Explosive Gases

203

203 211 214 216

Bernard Lewis and Guenther von Elbe, Combustion and Ex­ plosives Research, Inc., Pittsburgh, Pennsylvania Chapter 1.

Theory of Combustion Waves

1. Description and General Equations 2. Special Solutions for One-Dimensional Steady State Propa­ gation 3. WaveNear a Heat Sink. Dead Space and QuenchingDistance 4. Curved Waves 5. Principles of Stabilization of Combustion Waves in Gas Streams 6. Calculation of Wave Shape and Gas Flow Pattern 7. Momentum Change and Thrust Pressure 8. Propagation in Channels 9. Thermal Model of Combustion Wave. Excess Enthalpy 10. Principles of Ignition 11. Simplified Equations for Calculations Involving Heat Trans­ port Across the Combustion Wave Chapter 2.

216 223 227 231 233 238 244 245 249 251 271

Experimental Phenomena of Combustion Waves

12. Ignition: Experiments and Comparison with Theory 13. Observations on the Propagation of Combustion Waves 14. Stability and Quenching Limits, and Structure of Burner Flames

287 296 298

CONTENTS

Chapter 8.

Combustion Waves in Closed Vessels

15. Dependence of Pressure Rise and Temperature Distribution on Fraction of Gas Burned 16. Correlation of Rate of Pressure Rise with Burning Velocity 17. Cited References H. Combustion Waves in Turbulent Gases

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

B61a Karlovitz, Combustion and Explosives Research, Inc., Pittsburgh, Pennsylvania Phenomenological Description of Turbulent Flames The Work of Damkohler The Work of Shelkin Turbulent Burning Velocity Measurements of the National Advisory Committee for Aeronautics Turbulent Flames Confined in Channels Turbulent Flame Measurements at California Institute of Technology Other Experimental Studies of Turbulent Flames Turbulence Turbulent Diffusion Theory of Flame Propagation by Large Scale Turbulence Experimental Measurement of the Turbulent Burning Velocity Turbulence Generation by the Turbulent Flame Pressure Drop Across the Flame, Diffusion of Turbulence, Thickness of the Turbulent Flame Propagation of Flames in Turbulent Explosive Mixtures Stability of Turbulent Flames Numerical Data of Turbulent Flames The Status of Turbulent Flame Research Cited References

I. Diffusion Flames

1. 2. 3. 4. 5.

K. Wohl and C. W. Shipman, Department of Chemical Engineering, University of Delaware, Newark, Delaware Introduction Laminar Diffusion Flames Transition Region Between Laminar and Turbulent Diffusion Flames Turbulent Flames Cited References

305 306 310 312

312 314 317 320 324 331 333 334 337 339 342 346 351 353 359 360 362 363 365

365 367 381 386 404

CONTENTS PART 4• COMBUSTION OP LIQUIDS AND SOLIDS EDITOR: R. N. PEASE

J. Combustion of Liquid Fuels

1. 2. 3. 4. 5.

J. P. Longwell, Esso Eesearch and Engineering Company, Linden, New Jersey Atomization Mixing and Precipitation of Fuel Sprays Evaporation of Fuel Drops Combustion of Fuel Drops Cited References

K. Combustion of Solid Fuels

1. 2. 3. 4. 5. 6. 7. 8. 9.

Melvin Gerstein and Kenneth P. Coffin, Lewis Flight Propul­ sion Laboratory, National Advisory Committee for Aero­ nautics, Cleveland, Ohio Introduction Properties of Solid Fuels and Combustion Products Fuel and Air Contact Oxidation Mechanisms Ignition Combustion Processes Exhaust Concluding Remarks Cited References

L. Combustion of Liquid Propellants

407

407 415 425 438 443 444

444 444 446 448 451 458 466 467 468 470

David Altman and S. S. Penner, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California Chapter 1.

Ignition Phenomena in Bipropellant and Monopropellant Systems

1. Introduction 2. Experimental Methods Used for Measuring Ignition Delay in Bipropellant Systems 3. Representative Ignition Delay Measurements on Spon­ taneous Bipropellant Systems 4. Ignition of Representative Nonspontaneous Bipropellants 5. Ignition of MonopropelIants Chapter 2.

470 474 481 487 488

Motor Performance of Selected Monopropellants

6. General Characteristics of Monopropellants 7. Classification of Monopropellants 8. Performance Characteristics of Monopropellants

489 490 492

CONTENTS

Chapter 3.

Combustion of Selected Bipropellant Systems

9. Classification of Oxidizers and Fuels 503 10. Combustion of Bipropellants in Rocket Engines 504 11. Performance Characteristics of Several Bipropellant Com­ binations 507 12. Modern Trends in Combustion Research on Liquid-Fuel Rocket Engines 511 13. Cited References 512 M. Combustion of Solid PropelIants

1. 2. 3. 4. 5. 6. 7. 8.

Clayton Huggett, Rohm and Haas Company, Philadelphia, Pennsylvania General Characteristics of Solid Propellants Thermal Decomposition of Propellant Components The Burning of Double-Base Propellants The Burning Rate of Propellants Theories of the Burning of Propellants The Mechanism of Burning of Composite Propellants The Ignition of Solid Propellants Cited References

514

514 518 532 541 554 564 568 572

PART 5. DETONATION PROCESSES IN GASES, LIQUIDS, AND SOLIDS EDITOR: R. N. PEASE

N. Detonation Processes in Gases, Liquids, and Solids

577

A. R. Ubbelohde, Department of Chemistry, Queen's Univer­ sity, Belfast, Ireland John Copp, Department of Chemistry, University College, Dundee, Scotland Chapter 1.

1. 2. 3. 4. 5.

Experimental Methods for Observing Detonation

Introduction Measurement of Detonation Velocities Detonation Temperatures Flow Velocities Other Experiments Chapter 2.

577 578 582 582 583

The Physical Chemistry of Detonation Processes in Gases, Liquids, and Solids

6. Some Characteristic Differences Between Detonation and Explosion 583 7. Equations of State for Detonation 585 8. A Finite Time of Energy Release in Detonation 586

CONTENTS

9. The Finite Time of Energy Release in Relation to Lateral Venting 587 10. Data on Energy Release in Stable Regimes 591 11. Mechanisms of Activation in the Propagation of Detonation 594 Chapter 3.

12. 13. 14. 15.

Chapter 4.

16. 17. 18. 19.

Limiting Conditions for Stable Detonation

The Decay and Failure of Detonation Macroinitiation of Detonation. Graded Detonative Impulses The Transition from Macrocombustion to Detonation Mieroinitiation of Detonation. The Sensitiveness of Explosives

596 598 600 603

The Development of Research in the Physical Chemistry of Detonative Processes

Basic Detonation Parameters Studies on the Marginal Propagation of Detonation Direct Microinitiation Cited References

606 606 607 607

PART 6. ENERGY PRODUCTION BY NUCLEAR REACTIONS EDITOR: R. N. PEASE

0. Energy Production by Nuclear Reactions

1. 2. 3. 4. 5. 6. Index

H. Soodak, Department of Physics, The College of the City of New York, New York Introduction Nuclei Nuclear Energies Nuclear Reactions Summary and Conclusions Cited References and Bibliography

613

613 614 617 623 645 652 653

PART ONE

THERMODYNAMICS OF COMBUSTION

SECTION A

HIGH TEMPERATURE EQUILIBRIUM JAMES M. CARTER DAVID ALTMAN A,l. Problems in Combustion. There are two principal problems in determining the nature of high temperature combustion. The first is the determination of the nature and amount of the combustion products which may exist and also the thermodynamic properties of the mixture at one or more sets of combustion conditions. These combustion conditions are always idealized for purposes of calculation. Thus in a rocket or jet motor, steady state conditions are assumed; combustion during starting or stopping is considered separately by approximate methods from a knowledge of steady state conditions. In order for thermochemistry and thermodynamics to apply to com­ bustion, either certain other simplified conditions must be assumed, or much more detailed information is required than is usually available. Thus, in effect, calculations on combustion in rocket and jet motors are made on the assumption that the combustion process occurs in a small mass element which is injected into a motor near the center of an infinite stream of identical elements and which then travels through the motor with negligible velocity and at constant pressure. The combustion chamber of the motor is assumed long enough to permit equilibrium to be attained, and the walls are assumed far enough removed to exert no effect since the element in question is surrounded by identical elements. Similarly in explosions such as may occur in guns, or in intermittent devices, calculations are actually made for a mass element of given density, surrounded by identical elements of the same density, all in a container large enough to have no effect on the element being considered, except to keep its density constant. It is obvious that in most cases these conditions are far from fulfilled, and that effects due to combustion speed, mixing, loss of heat to walls, and other phenomena must be considered. However, the simplified condi­ tions assumed make calculation much simpler and do provide an upper limit for the efficiency of combustion processes. When these conditions are met, the reaction equilibria among the substances present, as dis­ cussed in I,A and C, do determine the combustion products and their thermodynamic properties.

A · HIGH T E M P E R A T U R E EQUILIBRIUM

Further simplification is obtained by assuming that combustion products are perfect gases, which is nearly true for most processes treated in rockets or jet motors. Deviations which may occur at high pressures, or in ultrafast processes, are considered in I,A and C and in other texts on thermodynamics [1,2,8], The second problem is the determination of the heat which may be released by the combustion, the maximum combustion temperature which can be reached, or the work which may be extracted, subject to the possible compositions as determined above and to the conditions under which the combustion occurs. The usual conditions assumed are those for adiabatic combustion at constant pressure or at constant volume. Other conditions (those involving heat transfer or external work) are considerably more complicated. Discussion of these conditions has been given by Lewis and von Elbe [4] and by Hirschfelder [5], The combustion process may be represented by combustibles (pi, V i , T 1 ) = combustion products (p2, V i , T i ) + Q

kilocalories (1-1)

with Q determined by the expression Ey t ,T t - Ey l l T i

=

- Q - [""J'pdV J Pi,Vi

In the above, the composition of the combustibles and the initial state are known; the composition of the products and their state, together with Q, are to be determined. This problem may conveniently be divided into two parts: the deter­ mination of equilibrium composition and thermodynamic properties; and the determination of flame temperatures and heat released or work done for various final states of the combustion products. A,2. Determination of Equilibrium Composition and Thermo­ dynamic Properties. The composition and thermodynamic properties of the equilibrium products of combustion are uniquely determined by the atomic composition, the temperature, and the pressure (or volume of the system), as is shown in I,A and C. In particular, at a specified tempera­ ture and pressure they do not depend on the heats of formation of the combusting materials or on their heat of reaction. (However, these quan­ tities will determine the temperature range over which the composition and thermodynamic properties are of interest, since they determine the initial energy of the system.) For example, the equilibrium composition and thermodynamic properties of the combustion products of the combustible mixtures repre­ sented by 6C -(- 3H2 + 402, 3C2H2 + 402, and CeH6 + 402 are iden­ tical at any chosen temperature and pressure. Flame temperatures, heat

A,2 · EQUILIBRIUM COMPOSITIONS

released, or work available, differ widely because of different initial energies of the three systems. These energies are determined by the basic conservation-of-energy equations. EQUILIBEIUM COMPOSITION. Equilibrium conditions in the combus­ tion products can be obtained from thermodynamic data and from the total amounts of each atomic species involved. For many reactions, values of the equilibrium constants are available either from experimental measurements or as calculated values from spectroscopic data. Other equilibrium constants may be calculated from free energy data. The theory of equilibrium conditions is treated in I1A and sources of data are also included in I,A. There is always an element of arbitrariness involved in choosing the equilibria regarded as significant. For instance, a choice frequently made is to neglect all equilibria involving species present in less than 0.01 or 0.1 per cent of the total. But this is not all-conclusive; obviously an equilibrium involving 0.01 per cent of the total moles present for a reac­ tion with an energy change of 150 kilocalories per mole is more significant, in determining the state of the system, than an equilibrium involving 0.1 per cent of the moles for a reaction with an energy change of 10 kilo­ calories per mole. A rough calculation which involves the heat given off in a combustion process resulting in products stable at ambient temperature, and the specific heats of these products, serves to set an upper limit on the com­ bustion temperature. At this temperature, the equilibria which may exist among products involving all the atomic species present are examined. For example, the combustion of gasoline (taken as octane C8Hi8) with oxygen may be used. A typical reaction for rocket motors may be ap­ proximated by C8HI8 + 602 8CO + 4H20 + 5H2 (2-1) (In combustion reactions involving carbon, hydrogen, and oxygen, a useful rule in estimating reaction products is, (1) to oxidize carbon to CO, (2) to use remaining oxygen to oxidize hydrogen to water, and (3) if any oxygen remains, to oxidize CO to CO2.) If this reaction occurred at 300°K, with the products remaining at 300°K, the heat released would be about 425 kilocalories. Cooling the products to 0°K would release an additional 35 kilocalories. Thus the total heat released can be expressed as C8HI8 (1) + 602 (g, 300°K) = 8CO (g) + 4H20 (g) + 5H2 (g, 0°K) + 460 kcal Enthalpy tables for the products establish a temperature near 3000°K, if the entire heat release is employed in raising the temperature.

A · HIGH T E M P E R A T U R E E Q U I L I B R I U M

Examination of the equilibrium constants for the various reactions which might be involved shows that the water-gas reaction is such that CO 2 is present, that steam will dissociate to OH, H2, and O2; H2 and O2 will dissociate to H and O respectively, but that because of the large excess of H2, O2 and especially O will be present in very small amounts. There­ fore an initial estimate of the species present would include CO, CO2, H2, H2O, OH, H. In the calculation of equilibrium compositions, the starting point is a series of equations; these equations will equal in number,all of the un­ knowns to be determined. These equations are of two kinds: the material balance equations, U = YjUi

(2-2)

(M) = Y (nia) • Ui (2-3) (N) = Y (ms) · Ui etc., and the equilibrium equations, f c . f d

.

.

.

Kif = i: Jb . . . JA

(2-4)

JB

etc. The first equation states that the total number of moles is equal to the sum of the number of moles of the molecular components. The second set of equations expresses the fact that the total number of gram atoms of each atomic constituent, denoted by (M), (N), etc., is distributed among the molecular components Ui, with n,M atoms of M in the com­ ponent i. The third set of equations are the usual equilibrium expressions for the gas reactions c t A -f-

-}-'*·

• cC

-f- • · *

In the equilibrium equations, / is the fugacity. Conversion to the usual forms for pressure, mole fraction, etc. is made by use of appropriate multiplying factors Qp, Qx, etc. involving fugacity as a function of pressure or density. These relations are given in I,A and C. The following equi­ librium expressions are those most frequently involved in combustion involving carbonaceous fuels. The numbering used follows that given by Hirschfelder [5], and all subsequent references to equilibrium constants or reactions follow this numbering. It should be emphasized that while the expressions are given in terms of pressure, this is accurate only insofar as the perfect gas laws apply. When appreciable deviations occur, pressures must be replaced by fugacities.

A,2 • EQUILIBRIUM

COMPOSITIONS

In the simplest cases, when there are only one or two atomic species and two or three molecular species, these equations may be solved simply by algebraic means. In general, however, the number and complexity of the equations make this impossible. For the reaction given in Eq. 2-1, the equilibrium equations would be set up as follows:

and if the Derfect eras laws hold, so that

The above set of seven equations involving seven unknowns does not lend itself to easy algebraic solution. In this case, which is relatively simple, the algebraic solution can be obtained, but ordinarily, with more molecular species and more equations involved, such a method is virtually impossible. Recourse must then be had to one of a number of approximate methods. These may be classified as (1) trial and error methods, (2) iterative methods, (3) graphical methods and use of published tables, and (4) punched-card or machine methods. < 7 )

A · HIGH TEMPERATURE EQUILIBRIUM

1. Trial and error methods. The straightforward method of solving for an equilibrium composition may be accomplished by the insertion into Eq. 2-4 of trial values consistent with the material balance Eq. 2-3 until all equations are satisfied. Simple rules, such as the one given previously in the example employing octane and oxygen, may be employed to assign initial trial values. This direct method is the least efficacious and is recom­ mended only in those cases where the number of components is small and a reasonably good guess can be made of the composition. The trial and error method, however, can effectively be applied to more complicated systems if the number of working equations are first reduced by algebraic substitutions. A general method for handling C, H, 0, and N systems of up to ten components is demonstrated in the follow­ ing treatment. Let the number of moles of the components be represented by the following symbols: f = W n1

a = nHj b=

H h2 O

9 —

Wno

C =

Tlco

h =

Woh

d = Tlco1

i = U3

e = n0,

j = n0

These ten unknowns are related by means of Eq. 2-3 and 2-4 as follows: (2-5) (2-6)

(2-7) (2-8)

(2-9) (2-10)

c + d = (C)

(2-11)

= (O)

(2-12)

(H) 2/ + (/= (N)

(2-13)

b + c + 2 d + 2e + g + h + j 2a -)-

2b

h

i —

(2-14)

A,2 · EQUILIBRIUM COMPOSITIONS

where (C), (0), (H), and (N) represent the total number of gram atoms of the elements, η is the total number of moles in the equilibrium mixture, and ρ is the total pressure. The subscripts on the K's denote the specific equilibria as given in Eq. 2-4. Although η is accurately given by the equation n = a + b + c + d + e + f + g + h + i + j

the concentrations of the components are not sensitive to small variations in n. This fact permits the choice of an approximate η value in Eq. 2-6 to 2-10 with only very little loss in accuracy. The above ten equations may now be simplified to yield the following three working equations: t = (H) - 2 a - K , ( n / r ) W 2

»-

- < c > τ£τί ~h

Kio(n/p)* a* +

- 2 Κ '(ί)% (2-16)

2g a + 0 - (N ) = 0 K\(n/p)b' 2

(2-17)

Equations 2-15, 2-16, and 2-17 are the three basic equations upon which the trial and error method is applied. A likely value of a = nBi is chosen. Values of b and g are then obtained directly from Eq. 2-15 and 2-16. The values of a, b, and g so obtained are now substituted into Eq. 2-17. Non­ zero solutions of Eq. 2-17 require new trial values of a until that equation is satisfied. Once Eq. 2-17 is satisfied, all other components are obtained simply from the individual Eq. 2-5 to 2-14. The introduction of the component n N , which occurs at very high temperatures, or components containing other elements such as sulfur and fluorine can easily be made by this scheme. 2. Iterative methods. Briefly, this method consists in determining (by inspection or otherwise) which species are present in largest amounts, and of solving the reduced number of equations involving these species only. The minor species are then determined from the major ones by use of the equilibrium equations, and the concentration of the major species is corrected for the presence of minor ones by using the mass balance equations. New relations among the major species are then determined, using the corrected values, and a second set of values for the minor species is calculated. This process is continued until no further change is produced by repeating the process. Obviously, the method can be continued to give as accurate values as desired. Usually the process is terminated at some predetermined limit of accuracy, such as 0.1 or 0.01 mole per cent. In the example above, the first step would be taken by assuming that

A · HIGH T E M P E R A T U R E E Q U I L I B R I U M

H and OH are not present. Eq. 2-2, 2-3, and the water-gas equilibrium of Eq. 2-4 are then solved algebraically for the major components. This involves only a simple quadratic, since ρ and η do not enter into the equilibrium equation. H and OH are then calculated from the second and third equations in Eq. 2-4. Then second approximations to (H) and (O) are calculated from Eq. 2-3 by the relation (H)' = (H) — nH — n0u and (O)' = (O) — Ti0H. These second approximate values are used as in the first step to calculate new values for the major components, and these in turn are used again for H and OH. As a final step, equilibria which may have been neglected in setting up the equations are examined. (In the present case the dissociation of steam to hydrogen and oxygen would be most probable.) If the amount of oxygen does prove negligible, based on the equilibrium values found for steam and hydrogen above, the procedure is justified. However, if the amount of oxygen is comparable to the amounts of other minor con­ stituents, Eq. 2-2 to 2-4 must be rewritten to include this component, and the process must be gone through again. The process above is comparatively easy when the combustion mixture is relatively far from stoichiometric proportions. Fortunately this is true for most rocket propellants, which are usually underoxidized, and for fuel-air mixtures in turbojets, etc., which are overoxidized. This means that several molecular species are present in large amounts, which condi­ tion will be changed little by the presence of minor species. The iteration process therefore converges very rapidly. As stoichiometric proportions are approached in a combustion mix­ ture, however, the iteration process becomes progressively less efficient, particularly at the higher temperatures involved. Thus in hydrogenoxygen mixtures, if either excess hydrogen or excess oxygen is present, it can safely be assumed that H2O and either H2 or O2 are the two major components, and the concentrations of OH, H, 0, and either O2 or H2 can be fairly easily determined. In stoichiometric proportions the concentrations of many or all species other than H2O are roughly equal, and a change in one introduces changes in the others which are proportionately of the same magnitude. Under these conditions, the iterative process converges very slowly. For exact stoichiometric proportions as in steam, carbon dioxide, and some other important substances, the labor involved in calculation is not too serious, since only one final composition is involved. Most combustion mixtures are not in exact stoichiometric proportions and also involve more than one combustion reaction. Brinkley and others [6,7,8] have devised a number of systematized methods of iteration. Some of the more complex methods will even con­ verge fairly rapidly [9, p. 187] for highly dissociated systems near stoichi­ ometric proportions.

A,2 · EQUILIBRIUM COMPOSITIONS One method (Sachsel, et al. [10, p. 620]), which is applicable when electrical computers are available, is to transform all of the equilibrium equations, Eq. 2-4, to logarithmic form. These then become simple linear equations and amenable to machine calculations. 3. Graphical methods and tables for use within definite composition ranges for several important systems have been developed by Winternitz, Huff, Calvert, and Kassner [10, p. 620; 11; 12], These, together with (4) machine and punched-card methods of computation, are more fully described in Sec. C of this volume. From the above, it is apparent that at the combustion temperatures usually encountered, determination of equilibrium compositions is a com­ plicated and tedious process. Even if the only information required is the composition at the flame temperature, two or three such composition calculations must be made, since an initial estimate of the flame tem­ perature (for which the composition is required) will usually be in error by an appreciable amount. If compositions are required not only at flame temperatures over a range of pressures or densities, but at lower tem­ peratures and pressures in order to follow expansion processes, the number of calculations which must be made is greatly increased. Interpolation of equilibrium compositions. Frequently it is desired to know the equilibrium compositions at temperatures or pressures other than those for which calculations have been made. ^ For different tem­ peratures, the most accurate method is the use of the equilibrium con­ stants for the temperature in question. These can be interpolated quite accurately, since in general a plot of In K vs. T is nearly linear. When compositions are determined at other pressures, a new set of equilibrium calculations must be made since the pressure enters into Eq. 2-4 and these equations must, therefore, be altered for the new pressure. There is, however, a simple graphical method of obtaining equilibrium compositions at temperatures or pressures intermediate to those for which two or more calculations have been made. It can also be used for a limited amount of extrapolation. When the amounts of the various components are plotted on the logarithmic scale of semilogarithmic paper against either temperature (at one pressure) or pressure (at one temperature), it is found that nearly straight lines are obtained. Therefore the procedure is to plot the amounts of the minimum number of components (starting with the least abundant) which will completely determine the composition, on semilogarithmic paper, and to read off the amounts at intermediate temperatures or pressures. By plotting the components least abundant, the maximum accuracy is obtained, since these components undergo the greatest percentage changes with temperature or pressure. The amounts 1 There is a definite need for sets of tables or charts for the more important systems, at reasonably close intervals of composition, and all based on the same data for equi­ librium constants, equations of state, etc. Such a basis might be the Bureau of Stand­ ards Tables of Chemical Thermodynamic Quantities [1S\.

A · HIGH T E M P E R A T U R E E Q U I L I B R I U M

of the other (major) components are then determined from Eq. 2-3, and the total number of moles of gas from Eq. 2-2. Even in cases where this method does not give the accuracy desired, it can be used to eliminate all but the final steps in an exact calculation by the iterative method. THERMODYNAMIC PROPERTIES. As in the case of the compositions, the thermodynamic properties of gases are point functions of atomic com­ position, temperature, and pressure or volume. However, for energy quantities there is the requirement of a base point. The choice of this point may be entirely arbitrary, but once the choice is made all thermo­ dynamic quantities must be referred to it. Several such bases are in com­ mon use. Two bases frequently employed are the system stable at room temperature (25°C, 300°K, 70°F) and at a pressure of one atmosphere, and the system hypothetically stable at O0K and one atmosphere, with combustion products ordinarily gaseous in the perfect gas state at this temperature. Since more and more tables of enthalpies, entropies, etc., based on O0K are becoming available, this latter base has much to recom­ mend it. (See Sec. C and I,A.) For calculations involving shifts in chemical equilibrium during expansion, two other bases are more logical. The first is a base with the elements at ambient temperature, and the second, with the elements at 0°K. The latter has the advantage of corresponding more closely with theoretical considerations for absolute enthalpy, entropy, etc. It has the practical disadvantage at present that many heats of formation at 0°K are not known, and that in some cases enthalpy differences between ambient conditions and 0°K are not known. However, this situation is being remedied rapidly [18]. In the following discussion, the use of this base is assumed, as it results in the simpler formulas. If some other base is used, a constant is added to all thermodynamic quantities. Since behavior on combustion and expansion always involves differences, this constant cancels out in any computation. The determination of enthalpy and internal energy for the equilibrium compositions at various temperatures and pressures (or densities) may be divided into two parts. The first is that due to the heat or energy of reaction at the base temperature, from the standard composition at base temperatures to the equilibrium composition at the temperature T. The second is the change in enthalpy or internal energy in heating this mixture from the base temperature to the temperature T, plus the effects in going from the perfect gas state at one atmosphere to the pressure or density under consideration. These relations are expressed in the equations below.

H = Σ n * ' + Σ η ί { · Η % ~ H ° o ) i + n j * (If) d p ( 2 _ i 8 ) r E =

Y

j

Ti i • ( A E f ) i + ^ n,(E° T - E f t i + η

( | | ^ dV

(2-19)

A,2 • EQUILIBRIUM

COMPOSITIONS

Here, nt- is the number of moles of component i present at temperature T and is the heat or energy of formation of the component i at 0°K, from the elements at is the integral of the specific heat of component i from If the elements at ambient temperature are taken as a base point, Eq. 2-18 becomes

and similarly for Eq. 2-19. If a base of stable composition at ambient temperature is used, the first term on the right of Eq. 2-18a is replaced by where is the change in component i in going from the composition stable at 298°K to the equilibriumcompositionat T. (It should be noted as an advantage of the base at that and The last terms in the equations correct for the changes in enthalpy or internal energy with pressure or volume. For perfect gases these terms are zero. In the general listed by Bridgman [14] for these and other thermodynamic formulas,

The numerical values of the expressions above are determined from the equation of state for the gas mixture. Entropy values for combustible mixtures may be determined in a number of ways. For many substances entropy tables are available for the standard state at a pressure of one atmosphere [IS], The entropy of the mixture is then given by the expression

For other materials, tables of the free energy function are available [IS]. By use of the relation F = H — TS, the entropy may be determined as

In both the above equations, the term _ is the entropy of mixing all the components, each originally present at one atmosphere, to give the mixture at one atmosphere. To obtain the entropy at the desired pressure or volume, there must be added to the above values the change of entropy with pressure or < 13

)

A · HIGH T E M P E R A T U R E E Q U I L I B R I U M

volume. This is given by the equation

S - S0 = For most of the applications met with in jet and rocket propulsion, gases may be assumed to obey the perfect gas laws, so that the above equations reduce to

S - S 0 = - n R In — = nR In XPo

Va

(2-25)

Specific heats for the combustion products are obtained from the expressions (2-26) In the above, it is necessary to keep in mind that the changes in enthalpy or internal energy include not only the amounts due to change in tem­ perature for each species, but also those due to the change in equilibrium composition with temperature, according to the equations

The first two terms in the above give the heat involved in changes in composition, the third terms give the perfect gas value of the specific heat at fixed composition, and the last terms give the effect due to gas imperfections. In view of the complex nature of these equations, a convenient method of obtaining average values for the specific heats over a range of temperatures is by differences from tables of enthalpy or internal energy, if these values are determined at fairly close intervals, both in temperature and in pressure (or volume). For some purposes, y = C v /C r is required. This can be obtained from enthalpy and energy tables as above. For more accurate determinations, use is made of the thermodynamic relationship (2-29)

A,3 · HEAT RELEASE AND FLAME TEMPERATURE

This can be cast into the form := ^ = γ cP

Ί^(θρ\ (dV\ Cp \dTjy \dT/p



where μ is the gas viscosity. In principle, Eq. 5-11 and 5-12 can be solved with the aid of the energy equation, \mzu\ + \m.u\ = CP(T