APPLICATIONSOF TURBULENTAND MULTIPHASECOMBUSTION

APPLICATIONSOF TURBULENTAND MULTIPHASECOMBUSTION

KENNETH K. KUO

RAGINI ACHARYA

JOHN WILEY & SONS, INC.

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Library of Congress Cataloging-in-Publication Data:Kuo, Kenneth K.KuApplications of turbulent and multiphase combustion / Kenneth K. Kuo,Ragini Acharya.Ragini p. cm.RaIncludes bibliographical references and index.RagiISBN 978-1-118-12756-8 (hardback); 978-1-118-12757-5 (ebk.); 978-1-118-12758-2 (ebk.);978-1-118-12759-9 (ebk.); 978-1-118-13068-1 (ebk.); 978-1-118-13069-8 (ebk.);978-1-118-13070-4 (ebk.)R1. Combustion engineering. 2. Turbulence. 3. Multiphase flow—Mathematical models.4. Combustion—Mathematical models. I. Acharya, Ragini. II. Title.RaTJ254.5.K847 2012Ra621.402′3—dc23

2011051086

ISBN: 978-1-118-12756-8

Printed in the United States of America10 9 8 7 6 5 4 3 2 1

http://www.copyright.comhttp://www.wiley.com/go/permissionshttp://booksupport.wiley.comhttp://www.wiley.com

Ken Kuo would like to dedicate this book to his wife, Olivia (Jeon-lin), and theirdaughters, Phyllis and Angela, for their love, understanding, patience, and

support, and to his mother, Mrs. Wen-Chen Kuo, for her love andencouragement.

Ragini Acharya would like to dedicate this book to her parents, Meenakshi andKrishnama Acharya, for their love, patience, and support and for having endless

faith in her.

CONTENTS

Preface xvii

1 Solid Propellants and Their Combustion Characteristics 1

1.1 Background of Solid Propellant Combustion, 41.1.1 Definition of Solid Propellants, 41.1.2 Desirable Characteristics of Solid

Propellants, 41.1.3 Calculation of Oxygen Balance, 51.1.4 Homogeneous Propellants, 6

1.1.4.1 Decomposition Characteristicsof NC, 6

1.1.5 Heterogeneous Propellants (or CompositePropellants), 7

1.1.6 Major Types of Ingredients in SolidPropellants, 8

1.1.6.1 Description of Oxidizer Ingredients, 101.1.6.2 Description of Fuel Binders, 121.1.6.3 Curing and Cross-Linking Agents, 141.1.6.4 Aging, 15

1.1.7 Applications of Solid Propellants, 161.1.7.1 Hazard Classifications of Solid

Propellants, 16

vii

viii CONTENTS

1.1.8 Material Characterization of Propellants, 161.1.8.1 Propellant Density Calculation, 161.1.8.2 Propellant Mass Fraction, �, 171.1.8.3 Viscoelastic Behavior of Solid

Propellants, 171.1.9 Thermal Profile in a Burning Solid Propellant, 18

1.1.9.1 Surface and Subsurface TemperatureMeasurements of Solid Propellants, 18

1.1.9.2 Interfacial Energy Flux Balance at theSolid Propellant Surface, 20

1.1.9.3 Energy Equation for the Gas Phase, 211.1.9.4 Burning Rate of Solid Propellants, 231.1.9.5 Temperature Sensitivity of Burning

Rate, 251.1.9.6 Measurement of Propellant Burning Rate

by Using a Strand Burner, 261.1.9.7 Measurement of Propellant Burning Rate

by Using a Small-Scale Motor, 371.1.9.8 Burning Rate Temperature Sensitivity of

Neat Ingredients, 411.2 Solid-Propellant Rocket and Gun Performance

Parameters, 431.2.1 Performance Parameters of a Solid Rocket

Motor, 441.2.1.1 Thrust of a Solid Rocket Motor, 441.2.1.2 Specific Impulse of a Solid Rocket

Motor, 481.2.1.3 Density-Specific Impulse, 561.2.1.4 Effective Vacuum Exhaust Velocity, 581.2.1.5 Characteristic Velocity C∗, 581.2.1.6 Pressure Sensitivity of Burning Rate, 591.2.1.7 Thrust Coefficient Efficiency, 601.2.1.8 Effect of Pressure Exponent on

Stable/Unstable Burning in Solid RocketMotor, 60

1.2.2 Performance Parameters of Solid-Propellant GunSystems, 61

1.2.2.1 Energy Balance Equation, 641.2.2.2 Efficiencies of Gun Propulsion

Systems, 67

CONTENTS ix

1.2.2.3 Heat of Explosion (�Hoex), 691.2.2.4 Relative Quickness, Relative Force,

and Deviations in MuzzleVelocity, 70

1.2.2.5 Dynamic Vivacity, 71

2 Thermal Decomposition and Combustion of Nitramines 72

2.1 Thermophysical Properties of Selected Nitramines, 762.2 Polymorphic Forms of Nitramines, 78

2.2.1 Polymorphic Forms of HMX, 802.2.2 Polymorphic Forms of RDX, 82

2.3 Thermal Decomposition of RDX, 882.3.1 Explanation of Opposite Trends on α-

and β-RDX Decomposition with IncreasingPressure, 90

2.3.2 Thermal Decomposition Mechanismsof RDX, 92

2.3.2.1 Homolytic N–N Bond Cleavage, 922.3.2.2 Concerted Ring Opening Mechanism of

RDX, 942.3.2.3 Successive HONO Elimination

Mechanism of RDX, 962.3.2.4 Analysis of Three Decomposition

Mechanisms, 1042.3.3 Formation of Foam Layer Near RDX Burning

Surface, 1062.4 Gas-Phase Reactions of RDX, 109

2.4.1 Development of Gas-Phase Reaction Mechanism forRDX Combustion, 111

2.5 Modeling of RDX Monopropellant Combustion withSurface Reactions, 125

2.5.1 Processes in Foam-Layer Region, 1262.5.2 Reactions Considered in the Foam Layer, 1282.5.3 Evaporation and Condensation Consideration for

RDX, 1282.5.4 Boundary Conditions, 1302.5.5 Numerical Methods Used for RDX Combustion

Model with Foam Layer, 1312.5.6 Predicted Flame Structure, 132

x CONTENTS

3 Burning Behavior of Homogeneous Solid Propellants 143

3.1 Common Ingredients in Homogeneous Propellants, 1473.2 Combustion Wave Structure of a Double-Base

Propellant, 1483.3 Burning Rate Behavior of a Double-Base Propellant, 1493.4 Burning Rate Behavior of Catalyzed Nitrate-Ester

Propellants, 1553.5 Thermal Wave Structure and Pyrolysis Law of

Homogeneous Propellants, 1583.5.1 Dark Zone Residence Time Correlation, 166

3.6 Modeling and Prediction of Homogeneous PropellantCombustion Behavior, 167

3.6.1 Multi-Ingredient Model of Miller andAnderson, 171

3.6.1.1 NC: A Special Case Ingredient, 1723.6.1.2 Comparison of Calculated Propellant

Burning Rates with the ExperimentalData, 175

3.7 Transient Burning Characterization of Homogeneous SolidPropellant, 187

3.7.1 What is Dynamic Burning?, 1883.7.2 Theoretical Models for Dynamic Burning, 190

3.7.2.1 dp/dt Approach, 1933.7.2.2 Flame Description Approach, 1943.7.2.3 Zel’dovich Approach, 1943.7.2.4 Characterization of Dynamic Burning of

JA2 Propellant Using the Zel’dovichApproach, 196

3.7.2.5 Experimental Measurement of DynamicBurning Rate of JA2 Propellant, 201

3.7.2.6 Novozhilov Stability Parameters, 2023.7.2.7 Novozhilov Stability Parameters for JA2

Propellant, 2033.7.2.8 Some Problems Associated with Dynamic

Burning Characterization, 2053.7.2.9 Factors Influencing Dynamic

Burning, 207Chapter Problems, 208

CONTENTS xi

4 Chemically Reacting Boundary-Layer Flows 209

4.1 Introduction, 2104.1.1 Applications of Reacting Boundary-Layer

Flows, 2114.1.2 High-Temperature Experimental Facilities Used in

Investigation, 2114.1.3 Theoretical Approaches and Boundary-Layer Flow

Classifications, 2124.1.4 Historical Survey, 212

4.2 Governing Equations for Two-Dimensional ReactingBoundary-Layer Flows, 216

4.3 Boundary Conditions, 2214.4 Chemical Kinetics, 224

4.4.1 Homogeneous Chemical Reactions, 2244.4.2 Heterogeneous Chemical Reactions, 226

4.5 Laminar Boundary-Layer Flows with SurfaceReactions, 229

4.5.1 Governing Equations and Boundary Conditions, 2294.5.2 Transformation to (ξ, η) Coordinates, 2294.5.3 Conditions for Decoupling of Governing Equations

and Self-Similar Solutions, 2324.5.4 Damköhler Number for Surface Reactions, 2334.5.5 Surface Combustion of Graphite Near the

Stagnation Region, 2344.6 Laminar Boundary-Layer Flows With Gas-Phase

Reactions, 2394.6.1 Governing Equations and Coordinate

Transformation, 2394.6.2 Damköhler Number for Gas-Phase Reactions, 2404.6.3 Extension to Axisymmetric Cases, 242

4.7 Turbulent Boundary-Layer Flows with ChemicalReactions, 243

4.7.1 Introduction, 2434.7.2 Boundary-Layer Integral Matrix Procedure of

Evans, 2434.7.2.1 General Conservation Equations, 2434.7.2.2 Molecular Transport Properties, 2474.7.2.3 Turbulent Transport Properties, 251

xii CONTENTS

4.7.2.4 Equation of State, 2564.7.2.5 Integral Matrix Solution Procedure, 2564.7.2.6 Limitations of the BLIMP Analysis, 257

4.7.3 Marching-Integration Procedure of Patankar andSpalding, 257

4.7.3.1 Description of the Physical Model, 2584.7.3.2 Conservation Equations for the Viscous

Region, 2584.7.3.3 Modeling of the Gas-Phase Chemical

Reactions, 2594.7.3.4 Governing Equations for the Inviscid

Region, 2604.7.3.5 Boundary Conditions, 2614.7.3.6 Near-Wall Treatment of k̃ and ε̃, 2624.7.3.7 Coordinate Transformation and Solution

Procedure of Patankar and Spalding, 2634.7.3.8 Comparison of Theoretical Results with

Experimental Data, 2664.7.4 Metal Erosion by Hot Reactive Gases, 2724.7.5 Thermochemical Erosion of Graphite Nozzles of

Solid Rocket Motors, 2814.7.5.1 Graphite Nozzle Erosion Minimization

Model and Code, 2834.7.5.2 Governing Equations, 2864.7.5.3 Heterogeneous Reaction Kinetics, 2904.7.5.4 Results from the GNEM Code, 2934.7.5.5 Nozzle Erosion Rate by Other Metallized

Propellant Products, 3124.7.6 Turbulent Wall Fires, 316

4.7.6.1 Development of the Ahmad-FaethCorrelation, 321

5 Ignition and Combustion of Single Energetic Solid Particles 330

5.1 Why Energetic Particles Are Attractive for CombustionEnhancement in Propulsion, 335

5.2 Metal Combustion Classification, 3365.3 Metal Particle Combustion Regimes, 3415.4 Ignition of Boron Particles, 344

CONTENTS xiii

5.5 Experimental Studies, 3515.5.1 Gasification of Boron Oxides, 3525.5.2 Chemical Kinetics Measurement, 3535.5.3 Boron Ignition Combustion in a Controlled Hot Gas

Environment, 3545.6 Theoretical Studies of Boron Ignition and Combustion, 362

5.6.1 First-Stage Combustion Models, 3625.6.2 Second-Stage Combustion Models, 3655.6.3 Chemical Kinetic Mechanisms, 3655.6.4 Methods for Enhancement of Boron Ignition, 3675.6.5 Verification of Diffusion Mechanism of Boron

Particle Combustion, 3695.6.6 Chemical Identification of the Boron Oxide

Layer, 3715.7 Theoretical Model Development of Boron Particle

Combustion, 3725.7.1 First-Stage Combustion Model, 3725.7.2 Second-Stage Combustion Model, 3775.7.3 Comparison of Predicted and Measured Combustion

Times, 3815.8 Ignition and Combustion of Boron Particles in

Fluorine-Containing Environments, 3845.8.1 Multidiffusion Flat-Flame Burner, 3855.8.2 Test Conditions, 3875.8.3 Experimental Results and Discussions, 3885.8.4 Surface Reaction of (BO)n with HF(g), 3935.8.5 Surface Reaction of (BO)n with F(g), 3945.8.6 Governing Equations During the First-Stage

Combustion of Boron Particles, 3955.8.7 Model for the “Clean” Boron Consumption Process

(Second-Stage Combustion), 3965.8.7.1 Chemical Kinetics During Second-Stage

Combustion, 3975.8.7.2 Consideration of Both Kinetics- and

Diffusion-Controlled Second-StageCombustion, 402

5.8.7.3 Governing Equations During theSecond-Stage Combustion of BoronParticles, 403

xiv CONTENTS

5.8.8 Numerical Solution, 4035.8.8.1 Comparison with Experimental Data in

Oxygen-Containing (Nonfluorine)Environments, 404

5.8.8.2 Comparison with Experimental Data andModel Predictions in Fluorine-ContainingEnvironments, 405

5.9 Combustion of a Single Aluminum Particle, 4105.9.1 Background, 4135.9.2 Physical Model, 4145.9.3 Aluminum-Combustion Mechanism, 4175.9.4 Condensation Aspect of Model of Beckstead et al.

(2005), 4195.9.5 General Mathematical Model, 4225.9.6 Boundary Conditions, 4245.9.7 Dn Law in Aluminum Combustion, 429

5.10 Ignition of Aluminum Particle in a Controlled PostflameZone, 437

5.11 Physical Concepts of Aluminum AgglomerateFormation, 4395.11.1 Evolution Process of Condensed-Phase Combustion

Products, 4405.12 Combustion Behavior for Fine and Ultrafine Aluminum

Particles, 4435.12.1 10 μm Aluminum Particle—Early Transitional

Structure, 4445.12.2 100 nm Aluminum Particle—Late Transitional

Structure, 4465.13 Potential Use of Energetic Nanosize Powders for

Combustion and Rocket Propulsion, 447Chapter Problems, 452Project No. 1, 452Project No. 2, 454

6 Combustion of Solid Particles in Multiphase Flows 456

6.1 Void Fraction and Specific Particle Surface Area, 4626.2 Mathematical Formulation, 463

6.2.1 Formulation of the Heat Equation for a SingleParticle, 469

CONTENTS xv

6.3 Method of Characteristics Formulation, 4726.3.1 Linearization of the Characteristic Equations, 476

6.4 Ignition Cartridge Results, 4776.5 Governing Equations for the Mortar Tube, 484

6.5.1 Initial Conditions, 4886.5.1.1 Initial Condition for Velocity, 4886.5.1.2 Initial Condition for Porosity, 4886.5.1.3 Initial Condition for Temperature and

Pressure, 4886.5.2 Boundary Conditions, 488

6.5.2.1 On the Surface of Ignition Cartridge inVent-Hole Region, 489

6.5.2.2 In the Fin Region, 4896.5.2.3 The z -direction Boundary

Conditions, 4896.5.3 Numerical Methods for Mortar Region Model, 490

6.6 Predictions of Mortar Performance and ModelValidation, 491

6.7 Approximate Riemann Solver: Roe-Pike Method, 4966.8 Roe’s Method, 4996.9 Roe-Pike Method, 501

6.10 Entropy Condition and Entropy Fix, 5026.11 Flux Limiter, 5036.12 Higher Order Correction, 5046.13 Three-Dimensional Wave Propagation, 504

Appendix A: Useful Vector and Tensor Operations 507

Appendix B: Constants and Conversion Factors Often Usedin Combustion 534

Appendix C: Naming of Hydrocarbons 538

Appendix D: Particle Size–U.S. Sieve Size and Tyler Screen MeshEquivalents 541

Bibliography 544

Index 571

PREFACE

There is an ever-increasing need to understand turbulent and multiphase combus-tion due to their broad application in energy, environment, propulsion, transporta-tion, industrial safety, and nanotechnology. More engineers and scientists withskills in these areas are needed to solve many multifaceted problems. Turbulenceitself is one of the most complex problems the scientific community faces. Itscomplexity increases with chemical reactions and even more in the presence ofmultiphase flows.

A number of useful books have been published recently in the areas of theoryof turbulence, multiphase fluid dynamics, turbulent combustion, and combustionof propellants. These include Theoretical and Numerical Combustion by Poinsotand Veynante; Turbulent Flows by Pope; Introduction to Turbulent Flow byMathieu and Scott; Turbulent Combustion by Peters; Multiphase Flow Dynamicsby Kolev; Combustion Physics by Law; Fluid Dynamics and Transport of Dropletand Sprays by Sirignano; Compressible, Turbulence, and High-Speed Flow byGatski and Bonnet; Combustion by Glassman and Yetter, among others.

Kenneth Kuo, the first author of this book, previously published Principles ofCombustion . The second edition, published in 2005, contains comprehensivematerial on laminar flames, chemical thermodynamics, reaction kinetics, andtransport properties for multicomponent mixtures. As the research in laminarflames was overwhelming, he decided to develop two separate books dedicatedentirely to turbulent and multiphase combustion.

Turbulence, turbulent combustion, and multiphase reacting flows have beenmajor research topics for many decades, and research in these areas is expectedto continue at even a greater pace. Usually the research has focused on experi-mental studies with phenomenological approaches, resulting in the developmentof empirical correlations. Theoretical approaches have achieved some degreeof success. However, in the past 20 years, advances in computational capability

xvii

xviii PREFACE

have enabled significant progress to be made toward comprehensive theoreticalmodeling and numerical simulation. Experimental diagnostics, especiallynonintrusive laser-based measurement techniques, have been developed and usedto obtain accurate data, which have been used for model validation. There is agreater synergy between the experimental and theoretical/numerical approaches.Due to these ongoing developments and advancements, theoretical modeling andnumerical simulation hold great potential for future solutions of problems. Inthese two new books, we have attempted to integrate the fundamental theories ofturbulence, combustion, and multiphase phenomena as well as experimental tech-niques, so that readers can acquire a firm background in both contemporary andclassical approaches. The first book volume is called Fundamentals of Turbulentand Multiphase Combustion; the second is called Applications of Turbulent andMultiphase Combustion. The first volume can serve as a graduate-level textbookthat covers the area of turbulent combustion and multiphase reacting flows aswell as material that builds on these fundamentals. This volume also can beuseful for research purpose. It is oriented toward the theories of combustion,turbulence, multiphase flows, and turbulent jets. Whenever appropriate,experimental setups and results are provided. The first volume addresses eightbasic topical areas in combustion and multiphase flows, including laminarpremixed and nonpremixed flames; theory of turbulence; turbulent premixed andnonpremixed flames; background of multiphase flows; and spray atomization andcombustion. A deep understanding of these topics is necessary for researchersin the field of combustion.

The six chapters in the second volume build on the ground covered in thefirst volume. Its chapters include: solid propellant combustion, thermal decom-position and combustion of nitramines burning behavior of homogeneous solidpropellants, chemically reacting boundary-layer flows, ignition and combustion ofcombustion of single energetic solid particles, and combustion of solid particlesin multiphase flows. The major reason for including solid-propellant combus-tion here is to provide concepts for condensed-phase combustion modeling asan example. Nitramines are explosive or propellant ingredients; their decompo-sition and reaction mechanisms are also good examples for combustion behaviorof condensed-phase materials. Chapters in Volume 2 focus on the applicationaspect of fundamental concepts and can form the framework for an advancedgraduate-level course in combustion of condensed-phase materials. However, theselection of materials for instruction depends extirely on the interests of instruc-tors and students. Although several chapters address solid propellant combustion,this volume is not a textbook for solid propellant combustion; many topics inthis area are not included due to space limitations.

VOLUME 1, FUNDAMENTALS OF TURBULENTAND MULTIPHASE COMBUSTION

Chapter 1 introduces and stresses the importance of combustion and multiphaseflows in research. It also provides a succinct review of major conservation

PREFACE xix

equations. Appendix A provides the vector and tensor operations frequently usedin the formulation and manipulation of these equations.

Chapter 2 covers the basic structure of laminar premixed flames, conservationequations, various models for diffusion velocities in a multicomponent gas systemwith increasing complexities, laminar flame thickness, asymptotic analyses, andflame speeds. Effect of flame stretch on laminar flame speed, Karlovitz number,and Markstein lengths are also discussed in detail along with soot formation inlaminar premixed flames.

Chapter 3 discusses the basic structure of laminar nonpremixed flames andprovides detailed descriptions of mixture fraction definition, balance equationsfor mixture fraction, temperature-mixture fraction relationship, and examples,since mixture fraction is a very important parameter in the study of nonpremixedflames. The chapter also discusses laminar flamelet structure and equations, crit-ical scalar dissipation rate, steady-state combustion, and examples of laminardiffusion flames with equations and solutions. Since pollution, specifically sootformation, has become a major topic of interest, it is also covered in this chapterwith respect to laminar diffusion flames. Appendix D provides a detailed soot for-mation mechanism and rate constants that was proposed by Wang and Frenklach.

Chapter 4 is devoted entirely to turbulent flows. It covers the fundamentalunderstanding of turbulence from a statistical point of view; homogeneous and/orisotropic turbulence, averaging procedures, statistical moments, and correlationfunctions; Kolmogorov hypotheses; turbulent scales; filtering and large-eddysimulation (LES) concepts along with various subgrid scale models; and basicdefinitions to prepare readers for the probability density function (pdf) approachin later chapters. This chapter also includes the governing equations for com-pressible flows. A short introduction of the direct numerical simulation (DNS)approach is also provided at the end of the chapter.

Chapters 5 and 6 focus on the turbulent premixed and nonpremixed flames,respectively. Chapter 5 consists of physical interpretation; studies for turbulentflame-speed correlation development; Borghi diagram and physical interpretationof various regimes; eddy breakup models; measurements in premixed turbulentflames; flame-turbulence interaction (effects of turbulence on flame as well aseffect of flame on turbulence); turbulence combustion modeling approaches;Bray-Moss-Libby model (gradient and counter-gradient transport); level setapproach and G-equation for flame surfaces; and the pdf approach and closureof chemical reaction source term. In Chapter 6, the discussion focuses on majorproblems in nonpremixed turbulent combustion; turbulent Damköhler numberand Reynolds number; scales in nonpremixed turbulent flames; regime diagrams;target flames; turbulence-chemistry interaction; pdf approach; flamelet models;flame-vortex interaction; flame instability; partially premixed flames; and edgeflames.

The fundamentals of multiphase flows are covered in Chapter 7, which hassections on classification of multiphase flows; homogeneous versus multiphasemixtures; averaging methods; local instant formulation; Eulerian-Eulerian mod-eling; Eulerian-Lagrangian modeling; interface transport (tracking and capturing)

xx PREFACE

methods (volume of fluid, surface fitted method, markers on interface); and dis-crete particle methods. This chapter also provides many contemporary approachesfor modeling two-phase flows.

Spray combustion is an extremely important topic for combustion, and Chapter8 provides a comprehensive account of various modeling approaches to spraycombustion associated with single drop behavior, drop breakup mechanisms, jetbreakup models, group combustion models, droplet-droplet collisions, and densesprays. Experimental approaches and results are also presented in this chapter.

VOLUME 2, APPLICATIONS OF TURBULENTAND MULTIPHASE COMBUSTION

Chapter 1 provides a background in solid propellants and their combustionbehavior, including desirable characteristics; oxygen balance; homogeneous andheterogeneous propellants; fuel binders, oxidizer ingredients, curing and cross-linking agents, and aging; hazard classifications; material characterization of solidpropellants; and gun performance parameters including thrust, specific impulse,and stable/unstable burning behavior.

Chapter 2 focuses on nitramine decomposition and combustion; phase trans-formation; and three different approaches for thermal decomposition of royaldemolition explosive (RDX) as well as gas-phase reactions. This chapter alsodescribes a modeling approach for RDX combustion.

Chapter 3 covers the burning behavior of homogeneous (e.g., double-base) pro-pellants, describing both the experimental and modeling approaches to study andpredict the burning rate and temperature sensitivities of common solid propellants.The transient burning characteristics of a typical homogeneous propellant is alsopresented in detail, including the Zel’dovich map technique and the Novozhilovstability parameters.

Chapter 4 covers reacting turbulent boundary-layer flows, a topic of researchfor the last six decades. The chapter discusses the modeling approaches from1940s to the current date. Graphite nozzle erosion process by high-temperaturecombustion product gases through heterogeneous chemical reactions is coveredin detail. Turbulent wall fires are also covered.

Chapter 5 contains the ignition and combustion studies of single energeticparticles (such as micron-size boron and aluminum particles) including mul-tistage combustion models for cases with and without the presence of oxidelayers, kinetic mechanisms, criterion for diffusion-controlled combustion versus,kinetic controlled combustion, effect of oxidizers (such as oxygen- and fluorine-containing species), combustion of nano-size energetic particles, and their strongdependency on kinetic rates.

Chapter 6 addresses the two-phase reacting flow simulation and focuses ongranular bed combustion with different solution techniques for the governingequations. It also includes experimental validation of the calculated results.

We would like to acknowledge the contributions of many of our combustionand turbulence colleagues for reviewing and providing a critical assessment

PREFACE xxi

of multiple chapters of these volumes includes Professor Forman A. Williamsof the University of California-San Diego; Professor Stephen B. Pope, CornellUniversity; Dr. Richard Behrens, Jr. of Sandia National Laboratory; Dr.William R. Anderson of the U.S. Army Research Laboratory; Professor LuigiT. DeLuca of Politecnico di Milano, Italy; and Professors James G. Brasseur,Daniel C. Haworth, and Michael M. Micci of Pennsylvania State University.They spent their valuable time reading chapters and helped us to improve thematerial covered in Volume 1 and Volume 2. We also want to thank ProfessorMichael Frenklach of University of California-Berkeley for providing us thedetailed information on soot formation kinetics used in Appendix D of Volume1. We also like to thank Professor William A. Sirignano of University ofCalifornia-Irvine for his valuable input on evaporation and combustion ofdroplet arrays. Professor Norbert Peters of the Institut für Technische Mechanikof Aachen, Germany, was very geneous to provide his book draft to KennethKuo while he was visiting the Pennsylvania State University. His notes werevery helpful in explaining turbulent combustion topics.

During the sabbatical leave of the first author at the U.S. Army Research Lab(ARL), Dr. Brad E. Forch of ARL and Dr. Ralph A. Anthenien Jr. of the ArmyResearch Office (ARO) hosted and supported a series of his lectures. The lecturematerials, which we prepared jointly, were used in the development of severalchapters of Volume 2. We greatly appreciate the encouragement and support ofDr. Forch and Dr. Anthenien.

Kenneth Kuo would like to take this opportunity to thank his many researchproject sponsors, since his in-depth understanding of many topics in turbulent andmultiphase combustion has been acquired through multi-year research. Thesesponsors include: Drs. Richard S. Miller, Judah Goldwasser, and Clifford D.Bedford of ONR of the U.S. Navy; Drs. David M. Mann, Robert W. Shaw, RalphA. Anthenien, Jr. of ARO; Dr. Martin S. Miller of ARL; Mr. Carl Gotzmer ofNSWC-Indian Head; Dr. Rich Bowen of NAVSEA of the US Navy, Drs. WilliamH. Wilson and Suhithi Peiris of the Defense Threat Reduction Agency (DTRA);and Drs. Jeff Rybak, Claudia Meyer, and Matthew Cross of NASA. The authorswould like to thank Mr. Henry T. Rand of ARDEC and Mr. Jack Sacco of SavitCorporation for sponsoring our project on granular propellant combustion.

Ragini Acharya would like to thank several professors at The PennsylvaniaState University for developing the framework and knowledge base to aid her inwriting the book manuscript, including Professors André L. Boehman, James G.Brasseur, John H. Mahaffy, Daniel C. Haworth, and Richard A. Yetter.

We both would like to acknowledge the generosity of Professor Peyman Giviof the University of Pittsburgh for granting us full permission to use some of hisnumerical simulation results of RANS, LES, and DNS of a turbulent jet flameon the jacket of Volume 1. For the cover of Volume 2, we would like to thankDr. Larry P. Goss of Innovative Scientific Solutions, Inc and Dr. J. Eric Boyerof the High Pressure Combustion Lab of PSU for the photograph of metalizedpropellant combustion. Also, Professor Luigi De Luca and his colleagues Dr.Filippo Maggi at the Polytechnic Institute of Milan for granting the permission to

xxii PREFACE

use their close-up photographs of the burning surface region of metallized solidpropellants, showing the dynamic motion of the burning of aluminum/Al2O3particles.

We would also like to thank Ms. Petek Jinkins and Ms. Aqsa Ahmed fortyping references, preliminary proofreading, and miscellaneous help with thepreparation of the manuscript. We also want to thank John Wiley & Sons fortheir patience and cooperation. Last but not least, we also would like to thankour family members for their sacrifice during the long and difficult process ofmanuscript preparation.

Kenneth K. Kuo and Ragini AcharyaUniversity Park, Pennsylvania

1SOLID PROPELLANTS AND THEIRCOMBUSTION CHARACTERISTICS

SYMBOLS

Symbol Description Dimension

Ae Exit area of a rocket nozzle L2

As Arrhenius factor in Equation 1.27 (L/t)/(T)β

At Throat area of the rocket nozzle L2

a Coefficient used in Saint-Robert’s burning rate law(or Vieille’s Law)

(L/t)/(F/L2)n

CD Mass flow factor defined in Equation 1.50 t/LCF Dimensionless thrust coefficient —Cp Constant-pressure specific heat Q/(MT)C* Characteristic velocity, defined in Equation 1.62 L/tDIsp Density impulse defined in Equation 1.60 Mt/L

3

Ea Activation energy in the Arrhenius law ofEquation 1.24

Q/N

F Thrust force of a solid propellant rocket FFe Net force acting on the exterior surface of a rocket

motorF

Fi Net force acting on the interior surface of a rocketmotor

F

If Radiative energy flux Q/(L2t)

Im Impetus of a gun propellant Q/MIst Specific impulse t

1

2 SOLID PROPELLANTS AND THEIR COMBUSTION CHARACTERISTICS

Symbol Description Dimension

It Total impulse of a rocket FtKn Ratio of propellant burning surface area to throat area —kf Specific reaction-rate constant (for a forward reaction

of order of m)(N/L3)1-m/t

kg Thermal conductivity of gas Q/(LTt)kp Thermal conductivity of propellant Q/(LTt)L Dynamic vivacity, defined in Equation 1.96 L2/(Ft)Lw Web thickness LM Mass MMi The i

th molecular species —Mw Molecular weight of the combustion products M/Nṁp Propellant mass burning rate per unit area M/(L

2t)N Total number of chemical species —n Pressure exponent of Saint-Robert’s law (or Vieille’s

law)—

P or p Pressure F/L2

Pc Pressure in the rocket motor combustor F/L2

Qg Heat of reaction per unit mass Q/MQs Heat release per unit mass at burning propellant

surfaceQ/M

q̇r Radiative heat flux Q/(L2t)

rb Burning rate of solid propellant L/tR Gas constant Q/(MT)RF Relative force, defined in Equation 1.93 —RQ Relative quickness, defined in Equation 1.92 —Ru Universal gas constant Q/(NT)T Temperature TTi Initial temperature TTs Surface temperature of a burning propellant Tt Time tU Internal energy QUg Gas velocity L/tV or V Volume L3

Ve Exhaust jet velocity from a rocket motor, or muzzlevelocity

L/t

Ve,vac Effective vacuum exhaust jet velocity of a rocketmotor

L/t

W Work QXk Mole fraction of the k

th species —x Distance measured away from burning propellant

surfaceL

SYMBOLS 3

Symbol Description Dimension

Yi Mass fraction of ith species, defined in Equation 2.59 —

y Subsurface distance normal to the burning surface ofa propellant

L

Greek Symbolsαd Divergence angle of the nozzle exit station measured

from centerline

◦

αp Thermal diffusivity of solid propellant L2/t

β Dimensionless temperature exponent, defined inEquation 1.27

—

� Dimensionless parameter defined in Equation 1.44 —δth Thermal wave thickness L

�Hoex Heat of explosion per unit mass, defined inEquation 1.91

Q/M

ε Strain —ςe Characteristic coefficient of a gun system —ηb Ballistic efficiency, defined in Equation 1.85 —ηC

FThrust coefficient efficiency, defined in Equation 1.71 —

ηp Piezometric efficiency, defined in Equation 1.83 —ηth Thermal efficiency of a gun system, defined in

Equation 1.88—

θ Dimensionless temperature defined in Equation 1.5 —� Ratio of propellant mass to rocket motor mass —l Paremeter associated with the divergence angle of the

nozzle exit section, defined in Equation 1.40—

ν ′i Stoichiometric coefficient of the ith reactant — or N

ν ′′i Stoichiometric coefficient of the ith product — or N

πk Pressure insensitivity of the rocket motor, defined inEquation 1.66

1/T

ρ Density M/L3

σp Temperature sensitivity of a propellant 1/Tτ Stress F/L2

ω̇′′′g Gas-phase reaction rate per unit volume M/(L3t)

Subscriptsf Forward reactiong Gasi Initial or ith speciesp Propellants Surface

4 SOLID PROPELLANTS AND THEIR COMBUSTION CHARACTERISTICS

Many books are specifically devoted to solid propellants. Readers interested inextensive discussions of solid propellant combustion can read the books editedby Kuo and Summerfield (1984), De Luca, Price, Summerfield (1992), Yang,Brill, and Ren (2000), and Kubota (2007). This chapter provides the backgroundinformation for readers to understand certain basic materials related to the solidpropellants and their combustion characteristics.

The chapter includes performance parameter considerations for solid propel-lant rocket motors and gun propulsion systems. Definitions and significance ofmany important parameters for rocket motors are covered at the beginning ofthe chapter, including specific impulse, characteristic velocity, thrust coefficient,density Isp, pressure sensitivity parameter, thrust-coefficient efficiency, and oth-ers. Various performance parameters for solid-propellant gun systems are alsocovered, including muzzle velocity, pressure-travel curve, maximum pressure,velocity-travel curves, piezometeric efficiency, ballistic efficiency, gun-propellantimpetus, thermal efficiency, characteristic coefficient, relative quickness, relativeforce, and dynamic vivacity. Many of these parameters have been consideredin the formulation and development of modern solid propellants for both rocketand gun propulsion systems for space propulsion and military applications. Thechapter also addresses the relationship between propellant burning rate behaviorand these performance parameters.

1.1 BACKGROUND OF SOLID PROPELLANT COMBUSTION

1.1.1 Definition of Solid Propellants

A solid propellant is a solid state substance that contains both oxidizer andfuel and is able to burn in the absence of ambient air. Solid propellants usu-ally generate a large number of gaseous molecules at high temperatures (Tf =2,300–3,800 K) during combustion. Condensed phase species are produced, espe-cially from metallized solid propellants. High-temperature combustion productsare used mainly for propulsion and gas generation purposes. There are two typesof solid propellants, which are differentiated by the condition in which theiringredients are connected:

1. In homogeneous propellants , the oxidizer and fuel are chemically linkedand form a single chemical structure. These propellants are physicallyhomogeneous.

2. In heterogeneous propellants , the oxidizer and fuel are physically mixed butdo not have chemical bonds between them. These propellants are physicallyheterogeneous.

1.1.2 Desirable Characteristics of Solid Propellants

• High gas temperature and/or low molecular mass of products• High density

BACKGROUND OF SOLID PROPELLANT COMBUSTION 5

• Good mechanical and bond properties• Good aging characteristics• Desirable ignition characteristics (to be addressed later)• Low-hazard manufacturing and handling• Predictable and reproducible properties (mechanical, burning rate, etc.)• Low thermal expansion coefficient• Low temperature sensitivity• Nontoxic exhaust gases with minimum smoke• Low absorption of moisture• Minimum sensitivity of burning velocity to pressure, initial temperature, and

gas velocity (erosive burning)

1.1.3 Calculation of Oxygen Balance

The oxygen balance of a propellant is the amount of oxygen in weight percentagethat is liberated as a result of complete conversion of the energetic material intoCO2, H2O, SO2, Al2O3, and others. If the equilibrium products of a propellantcontain an excess amount of oxygen, the oxygen balance of this propellant ispositive. If oxygen is needed for the complete combustion of the energetic mate-rial (EM), the oxygen balance is negative. Usually the oxygen balance of a solidpropellant is negative. Oxygen balance is defined as:

OxygenBalance = Mass of excess oxygen in 1 mole of compoundMass of 1 mole of compound

(1.1)

The calculation of oxygen balance is performed by assuming the conversion ofthe atoms (like C, H, N, O, and Al, etc.) into fully oxidized molecules:

C → CO2 N → 0.5N2 H → 0.5H2O Al → 0.5Al2O3

EXAMPLE 1.1

RDX (C3H6O6N6); Calculate the oxygen balance of which is a propellantingredient that also can be considered a monopropellant for its oxygen balancecalculation.

3C → 3 CO2 6 O-atoms are needed6H → 3 H2O 3 O-atoms are needed6N → 3 N2 0 O-atoms are neededTotal O-atoms needed = 6 + 3 + 0 = 9For a complete combustion, 9 oxygen atoms are needed. The RDX molecule

supplies 6 atoms, which means that 3 atoms are still required. The molecularweight of 3 g-atoms of oxygen is equal to 3 × 15.9994 = 47.998 g. Themolecular weight of the RDX compound is 222.117 g, which corresponds to100%; 47.998 g ÷ 222.117 g = 0.2161. Therefore, the oxygen balance ofRDX is −21.61%.

Note: In case a compound contains Cl, consider H + Cl → HCl as the reaction.

6 SOLID PROPELLANTS AND THEIR COMBUSTION CHARACTERISTICS

1.1.4 Homogeneous Propellants

Homogeneous propellants have a uniform physical structure consisting of chemi-cally bonded fuel and oxidizer ingredients. Their major constituents are nitrocellu-lose (NC) and nitroglycerine (NG). Nitrocellulose is a typical example of single-base homogeneous propellants. Nitrocellulose is a nitrated cellulose whose chem-ical structure is represented by C6H7.55O5(NO2)2.45 and C6H7.0006N2.9994O10.9987for 12.6% and 14.14% nitrogen content, respectively. Propellants that are com-posed of NC and NG are called double-base propellants and are typical homo-geneous propellants. The molecular structures and thermochemical properties ofseveral homogeneous propellant ingredients are shown in Figures 1.1 to 1.3.

1.1.4.1 Decomposition Characteristics of NC

When nitrocellulose is decomposed thermally, two major fragments are generated.One group of fragments with a C/H and C/H/O structure acts as a fuel with theother fragment of NO2 acting as an oxidizer. Since nitrocellulose is a fibrousmaterial, it is difficult to form a specified propellant grain using it as a singleingredient (called monopropellant). Liquid materials called plasticizers usuallyare mixed with the nitrocellulose to gelatinize it and to form a specific shape for

C

C

H

C

H

CH2-O-NO2

CH2-O-NO2

O

C

H

ONO2

ONO2

ONO2

ONO2C

H

H

C

C

H

C

H

O

C

HC

H

H

O

O O

n

Nitration level 14.14%Molecular weight 297.106 g/molOxygen balance −24.24%Density 1.66 g/ccHeat of combustion 650.6 kcal/molEnthalpy offormation −155.99 kcal/mol

Physical state Solid

Figure 1.1 Molecular structure and thermochemical properties of nitrocellulose (NC).

H2C

H2C

NG

HC O

O

O

NO2

NO2

NO2

Nitration level -Molecular weight 227.087 g/molOxygen balance 3.52%Density 1.593 g/ccHeat of combustion 364.3 kcal/molEnthalpy offormation

−84.90 to −118.90kcal/mol

Physical state Liquid

Figure 1.2 Molecular structure and thermochemical properties of nitroglycerine (NG).