Table of Contents

Title Page




Volume 1, Fundamentals of Turbulent and Multiphase Combustion

Volume 2, Applications of Turbulent and Multiphase Combustion

Chapter 1: Solid Propellants and Their Combustion Characteristics

1.1 Background of Solid Propellant Combustion

1.2 Solid-Propellant Rocket and Gun Performance Parameters

Chapter Problems

Chapter 2: Thermal Decomposition and Combustion of Nitramines

2.1 Thermophysical Properties of Selected Nitramines

2.2 Polymorphic Forms of Nitramines

2.3 Thermal Decomposition of RDX

2.4 Gas-Phase Reactions of RDX

2.5 Modeling of RDX Monopropellant Combustion with Surface Reactions

Chapter Problems

Chapter 3: Burning Behavior of Homogeneous Solid Propellants

3.1 Common Ingredients in Homogeneous Propellants

3.2 Combustion Wave Structure of a Double-Base Propellant

3.3 Burning Rate Behavior of a Double-Base Propellant

3.4 Burning Rate Behavior of Catalyzed Nitrate-Ester Propellants

3.5 Thermal Wave Structure and Pyrolysis Law of Homogeneous Propellants

3.6 Modeling and Prediction of Homogeneous Propellant Combustion Behavior

3.7 Transient Burning Characterization of Homogeneous Solid Propellant

Chapter Problems

Chapter 4: Chemically Reacting Boundary-Layer Flows

4.1 Introduction

4.2 Governing Equations for Two-Dimensional Reacting Boundary-Layer Flows

4.3 Boundary Conditions

4.4 Chemical Kinetics

4.5 Laminar Boundary-Layer Flows with Surface Reactions

4.6 Laminar Boundary-Layer Flows With Gas-Phase Reactions

4.7 Turbulent Boundary-Layer Flows with Chemical Reactions

Chapter Problems

Chapter 5: Ignition and Combustion of Single Energetic Solid Particles

5.1 Why Energetic Particles Are Attractive for Combustion Enhancement in Propulsion

5.2 Metal Combustion Classification

5.3 Metal Particle Combustion Regimes

5.4 Ignition of Boron Particles

5.5 Experimental Studies

5.6 Theoretical Studies of Boron Ignition and Combustion

5.7 Theoretical Model Development of Boron Particle Combustion

5.8 Ignition and Combustion of Boron Particles in Fluorine-Containing Environments

5.9 Combustion of a Single Aluminum Particle

5.10 Ignition of Aluminum Particle in a Controlled Postflame Zone

5.11 Physical Concepts of Aluminum Agglomerate Formation

5.12 Combustion Behavior for Fine and Ultrafine Aluminum Particles

5.13 Potential Use of Energetic Nanosize Powders for Combustion and Rocket Propulsion

Chapter Problems

Chapter 6: Combustion of Solid Particles in Multiphase Flows

6.1 Void Fraction and Specific Particle Surface Area

6.2 Mathematical Formulation

6.3 Method of Characteristics Formulation

6.4 Ignition Cartridge Results

6.5 Governing Equations for the Mortar Tube

6.6 Predictions of Mortar Performance and Model Validation

6.7 Approximate Riemann Solver: Roe-Pike Method

6.8 Roe's Method

6.9 Roe-Pike Method

6.10 Entropy Condition and Entropy Fix

6.11 Flux Limiter

6.12 Higher Order Correction

6.13 Three-Dimensional Wave Propagation

Chapter Problems

Appendix A: Useful Vector and Tensor Operations

Appendix B: Constants and Conversion Factors Often Used in Combustion

Appendix C: Naming of Hydrocarbons

Appendix D: Particle Size–U.S. Sieve Size and Tyler Screen Mesh Equivalents



Title Page




Ken Kuo would like to dedicate this book to his wife, Olivia (Jeon-lin), and their daughters, Phyllis and Angela, for their love, understanding, patience, and support, and to his mother, Mrs. Wen-Chen Kuo, for her love and encouragement.


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


There is an ever-increasing need to understand turbulent and multiphase combustion due to their broad application in energy, environment, propulsion, transportation, industrial safety, and nanotechnology. More engineers and scientists with skills in these areas are needed to solve many multifaceted problems. Turbulence itself is one of the most complex problems the scientific community faces. Its complexity increases with chemical reactions and even more in the presence of multiphase flows.

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

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

Turbulence, turbulent combustion, and multiphase reacting flows have been major research topics for many decades, and research in these areas is expected to continue at even a greater pace. Usually the research has focused on experimental studies with phenomenological approaches, resulting in the development of empirical correlations. Theoretical approaches have achieved some degree of success. However, in the past 20 years, advances in computational capability have enabled significant progress to be made toward comprehensive theoretical modeling and numerical simulation. Experimental diagnostics, especially nonintrusive laser-based measurement techniques, have been developed and used to obtain accurate data, which have been used for model validation. There is a greater synergy between the experimental and theoretical/numerical approaches. Due to these ongoing developments and advancements, theoretical modeling and numerical simulation hold great potential for future solutions of problems. In these two new books, we have attempted to integrate the fundamental theories of turbulence, combustion, and multiphase phenomena as well as experimental techniques, so that readers can acquire a firm background in both contemporary and classical approaches. The first book volume is called Fundamentals of Turbulent and Multiphase Combustion; the second is called Applications of Turbulent and Multiphase Combustion. The first volume can serve as a graduate-level textbook that covers the area of turbulent combustion and multiphase reacting flows as well as material that builds on these fundamentals. This volume also can be useful 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 eight basic topical areas in combustion and multiphase flows, including laminar premixed and nonpremixed flames; theory of turbulence; turbulent premixed and nonpremixed flames; background of multiphase flows; and spray atomization and combustion. A deep understanding of these topics is necessary for researchers in the field of combustion.

The six chapters in the second volume build on the ground covered in the first volume. Its chapters include: solid propellant combustion, thermal decomposition and combustion of nitramines burning behavior of homogeneous solid propellants, chemically reacting boundary-layer flows, ignition and combustion of combustion of single energetic solid particles, and combustion of solid particles in multiphase flows. The major reason for including solid-propellant combustion here is to provide concepts for condensed-phase combustion modeling as an example. Nitramines are explosive or propellant ingredients; their decomposition and reaction mechanisms are also good examples for combustion behavior of condensed-phase materials. Chapters in Volume 2 focus on the application aspect of fundamental concepts and can form the framework for an advanced graduate-level course in combustion of condensed-phase materials. However, the selection of materials for instruction depends extirely on the interests of instructors and students. Although several chapters address solid propellant combustion, this volume is not a textbook for solid propellant combustion; many topics in this area are not included due to space limitations.

Volume 1, Fundamentals of Turbulent and Multiphase Combustion

Chapter 1 introduces and stresses the importance of combustion and multiphase flows in research. It also provides a succinct review of major conservation equations. Appendix A provides the vector and tensor operations frequently used in the formulation and manipulation of these equations.

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

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

Chapter 4 is devoted entirely to turbulent flows. It covers the fundamental understanding of turbulence from a statistical point of view; homogeneous and/or isotropic turbulence, averaging procedures, statistical moments, and correlation functions; Kolmogorov hypotheses; turbulent scales; filtering and large-eddy simulation (LES) concepts along with various subgrid scale models; and basic definitions to prepare readers for the probability density function (pdf) approach in later chapters. This chapter also includes the governing equations for compressible 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 turbulent flame-speed correlation development; Borghi diagram and physical interpretation of various regimes; eddy breakup models; measurements in premixed turbulent flames; flame-turbulence interaction (effects of turbulence on flame as well as effect of flame on turbulence); turbulence combustion modeling approaches; Bray-Moss-Libby model (gradient and counter-gradient transport); level set approach and G-equation for flame surfaces; and the pdf approach and closure of chemical reaction source term. In Chapter 6, the discussion focuses on major problems in nonpremixed turbulent combustion; turbulent Damkgthler number and 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 edge flames.

The fundamentals of multiphase flows are covered in Chapter 7, which has sections on classification of multiphase flows; homogeneous versus multiphase mixtures; averaging methods; local instant formulation; Eulerian-Eulerian modeling; Eulerian-Lagrangian modeling; interface transport (tracking and capturing) methods (volume of fluid, surface fitted method, markers on interface); and discrete particle methods. This chapter also provides many contemporary approaches for modeling two-phase flows.

Spray combustion is an extremely important topic for combustion, and Chapter 8 provides a comprehensive account of various modeling approaches to spray combustion associated with single drop behavior, drop breakup mechanisms, jet breakup models, group combustion models, droplet-droplet collisions, and dense sprays. Experimental approaches and results are also presented in this chapter.

Volume 2, Applications of Turbulent and Multiphase Combustion

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

Chapter 2 focuses on nitramine decomposition and combustion; phase transformation; and three different approaches for thermal decomposition of royal demolition explosive (RDX) as well as gas-phase reactions. This chapter also describes a modeling approach for RDX combustion.

Chapter 3 covers the burning behavior of homogeneous (e.g., double-base) propellants, describing both the experimental and modeling approaches to study and predict the burning rate and temperature sensitivities of common solid propellants. The transient burning characteristics of a typical homogeneous propellant is also presented in detail, including the Zel'dovich map technique and the Novozhilov stability parameters.

Chapter 4 covers reacting turbulent boundary-layer flows, a topic of research for the last six decades. The chapter discusses the modeling approaches from 1940s to the current date. Graphite nozzle erosion process by high-temperature combustion product gases through heterogeneous chemical reactions is covered in detail. Turbulent wall fires are also covered.

Chapter 5 contains the ignition and combustion studies of single energetic particles (such as micron-size boron and aluminum particles) including multistage combustion models for cases with and without the presence of oxide layers, 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 strong dependency on kinetic rates.

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

We would like to acknowledge the contributions of many of our combustion and turbulence colleagues for reviewing and providing a critical assessment of multiple chapters of these volumes includes Professor Forman A. Williams of the University of California-San Diego; Professor Stephen B. Pope, Cornell University; Dr. Richard Behrens, Jr. of Sandia National Laboratory; Dr. William R. Anderson of the U.S. Army Research Laboratory; Professor Luigi T. 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 the material covered in Volume 1 and Volume 2. We also want to thank Professor Michael Frenklach of University of California-Berkeley for providing us the detailed information on soot formation kinetics used in Appendix D of Volume 1. We also like to thank Professor William A. Sirignano of University of California-Irvine for his valuable input on evaporation and combustion of droplet arrays. Professor Norbert Peters of the Institut fdeltar Technische Mechanik of Aachen, Germany, was very geneous to provide his book draft to Kenneth Kuo while he was visiting the Pennsylvania State University. His notes were very 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 Army Research Office (ARO) hosted and supported a series of his lectures. The lecture materials, which we prepared jointly, were used in the development of several chapters of Volume 2. We greatly appreciate the encouragement and support of Dr. Forch and Dr. Anthenien.

Kenneth Kuo would like to take this opportunity to thank his many research project sponsors, since his in-depth understanding of many topics in turbulent and multiphase combustion has been acquired through multi-year research. These sponsors 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, Ralph A. Anthenien, Jr. of ARO; Dr. Martin S. Miller of ARL; Mr. Carl Gotzmer of NSWC-Indian Head; Dr. Rich Bowen of NAVSEA of the US Navy, Drs. William H. Wilson and Suhithi Peiris of the Defense Threat Reduction Agency (DTRA); and Drs. Jeff Rybak, Claudia Meyer, and Matthew Cross of NASA. The authors would like to thank Mr. Henry T. Rand of ARDEC and Mr. Jack Sacco of Savit Corporation for sponsoring our project on granular propellant combustion.

Ragini Acharya would like to thank several professors at The Pennsylvania State University for developing the framework and knowledge base to aid her in writing the book manuscript, including Professors Andrgt 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 Givi of the University of Pittsburgh for granting us full permission to use some of his numerical simulation results of RANS, LES, and DNS of a turbulent jet flame on the jacket of Volume 1. For the cover of Volume 2, we would like to thank Dr. Larry P. Goss of Innovative Scientific Solutions, Inc and Dr. J. Eric Boyer of the High Pressure Combustion Lab of PSU for the photograph of metalized propellant combustion. Also, Professor Luigi De Luca and his colleagues Dr. Filippo Maggi at the Polytechnic Institute of Milan for granting the permission to use their close-up photographs of the burning surface region of metallized solid propellants, showing the dynamic motion of the burning of aluminum/Al2O3 particles.

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

Kenneth K. Kuo and Ragini Acharya

University Park, Pennsylvania

Chapter 1

Solid Propellants and Their Combustion Characteristics

Symbols (An optimized version of this table can be viewed at

Symbol Description Dimension
Ae Exit area of a rocket nozzle L2
As Arrhenius factor in Equation 1.27 (L/t)/(T)alpha
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/L
CF Dimensionless thrust coefficient
Cp Constant-pressure specific heat Q/(MT)
C* Characteristic velocity, defined in Equation 1.62 L/t
DIsp Density impulse defined in Equation 1.60 Mt/L3
Symbol Description Dimension
Ea Activation energy in the Arrhenius law of Equation 1.24 Q/N
F Thrust force of a solid propellant rocket F
Fe Net force acting on the exterior surface of a rocket motor F
Fi Net force acting on the interior surface of a rocket motor F
If Radiative energy flux Q/(L2t)
Im Impetus of a gun propellant Q/M
Ist Specific impulse t
Symbol Description Dimension
It Total impulse of a rocket Ft
Kn 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)
images/c01_I0001.gif Dynamic vivacity, defined in Equation 1.96 L2/(Ft)
Lw Web thickness L
M Mass M
Mi The ith molecular species
Mw Molecular weight of the combustion products M/N
images/c01_I0002.gif Propellant mass burning rate per unit area M/(L2t)
N Total number of chemical species
Symbol Description Dimension
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/M
Qs Heat release per unit mass at burning propellant surface Q/M
images/c01_I0003.gif Radiative heat flux Q/(L2t)
rb Burning rate of solid propellant L/t
R 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 T
Symbol Description Dimension
Ti Initial temperature T
Ts Surface temperature of a burning propellant T
t Time t
U Internal energy Q
Ug Gas velocity L/t
images/c01_I0004.gif or V Volume L3
Ve Exhaust jet velocity from a rocket motor, or muzzle velocity L/t
Ve, vac Effective vacuum exhaust jet velocity of a rocket motor L/t
W Work Q
Xk Mole fraction of the kth species
x Distance measured away from burning propellant surface L
Symbol Description Dimension
Yi Mass fraction of ith species, defined in Equation 2.59
y Subsurface distance normal to the burning surface of a propellant L
Symbol Description Dimension
Greek Symbols
alphad Divergence angle of the nozzle exit station measured from centerline °
alphap Thermal diffusivity of solid propellant L2/t
alpha Dimensionless temperature exponent, defined in Equation 1.27
gt Dimensionless parameter defined in Equation 1.44
deltath Thermal wave thickness L
images/c01_I0005.gif Heat of explosion per unit mass, defined in Equation 1.91 Q/M
delta Strain
images/c01_I0006.gif Characteristic coefficient of a gun system
gtb Ballistic efficiency, defined in Equation 1.85
images/c01_I0007.gif Thrust coefficient efficiency, defined in Equation 1.71
gtp Piezometric efficiency, defined in Equation 1.83
Symbol Description Dimension
gtth Thermal efficiency of a gun system, defined in Equation 1.88
gt Dimensionless temperature defined in Equation 1.5
gt Ratio of propellant mass to rocket motor mass
gt Paremeter associated with the divergence angle of the nozzle exit section, defined in Equation 1.40
images/c01_I0008.gif Stoichiometric coefficient of the ith reactant — or N
images/c01_I0009.gif Stoichiometric coefficient of the ith product — or N
gtk Pressure insensitivity of the rocket motor, defined in Equation 1.66 1/T
gt Density M/L3
gtp Temperature sensitivity of a propellant 1/T
gt Stress F/L2
images/c01_I0010.gif Gas-phase reaction rate per unit volume M/(L3t)
Symbol Description Dimension
f Forward reaction
g Gas
i Initial or ith species
p Propellant
s Surface

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

The chapter includes performance parameter considerations for solid propellant rocket motors and gun propulsion systems. Definitions and significance of many important parameters for rocket motors are covered at the beginning of the chapter, including specific impulse, characteristic velocity, thrust coefficient, density Isp, pressure sensitivity parameter, thrust-coefficient efficiency, and others. Various performance parameters for solid-propellant gun systems are also covered, including muzzle velocity, pressure-travel curve, maximum pressure, velocity-travel curves, piezometeric efficiency, ballistic efficiency, gun-propellant impetus, thermal efficiency, characteristic coefficient, relative quickness, relative force, and dynamic vivacity. Many of these parameters have been considered in the formulation and development of modern solid propellants for both rocket and gun propulsion systems for space propulsion and military applications. The chapter also addresses the relationship between propellant burning rate behavior and 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 and fuel and is able to burn in the absence of ambient air. Solid propellants usually generate a large number of gaseous molecules at high temperatures (Tf = 2,300–3,800 K) during combustion. Condensed phase species are produced, especially from metallized solid propellants. High-temperature combustion products are used mainly for propulsion and gas generation purposes. There are two types of solid propellants, which are differentiated by the condition in which their ingredients are connected:

1. In homogeneous propellants, the oxidizer and fuel are chemically linked and form a single chemical structure. These propellants are physically homogeneous.
2. In heterogeneous propellants, the oxidizer and fuel are physically mixed but do not have chemical bonds between them. These propellants are physically heterogeneous.

1.1.2 Desirable Characteristics of Solid Propellants

1.1.3 Calculation of Oxygen Balance

The oxygen balance of a propellant is the amount of oxygen in weight percentage that is liberated as a result of complete conversion of the energetic material into CO2, H2O, SO2, Al2O3, and others. If the equilibrium products of a propellant contain an excess amount of oxygen, the oxygen balance of this propellant is positive. If oxygen is needed for the complete combustion of the energetic material (EM), the oxygen balance is negative. Usually the oxygen balance of a solid propellant is negative. Oxygen balance is defined as:

1.1 1

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


Example 1.1
RDX (C3H6O6N6); Calculate the oxygen balance of which is a propellant ingredient that also can be considered a monopropellant for its oxygen balance calculation.
3C gt 3 CO2 6 O-atoms are needed
6H gt 3 H2O 3 O-atoms are needed
6N gt 3 N2 0 O-atoms are needed
Total O-atoms needed = 6 + 3 + 0 = 9
For a complete combustion, 9 oxygen atoms are needed. The RDX molecule supplies 6 atoms, which means that 3 atoms are still required. The molecular weight of 3 g-atoms of oxygen is equal to 3 gt 15.9994 = 47.998 g. The molecular weight of the RDX compound is 222.117 g, which corresponds to 100%; 47.998 g gt 222.117 g = 0.2161. Therefore, the oxygen balance of RDX is −21.61%.

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

1.1.4 Homogeneous Propellants

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

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


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


Figure 1.3 Molecular structure and thermochemical properties of trimethylolethane trinitrate (TMETN) and diethylene glycol dinitrate (DEGDN).

1.3 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 the other fragment of NO2 acting as an oxidizer. Since nitrocellulose is a fibrous material, it is difficult to form a specified propellant grain using it as a single ingredient (called monopropellant). Liquid materials called plasticizers usually are mixed with the nitrocellulose to gelatinize it and to form a specific shape for the propellant grain. Typical examples of plasticizers include nitroglycerin (NG) and trimethylolethane trinitrate (TMETN). Both NG and TMETN are also nitrated materials which can function individually as propellants in the liquid form.

1.1.5 Heterogeneous Propellants (or Composite Propellants)

Heterogeneous (composite) propellants have a non-uniform physical structure (see Figures 1.4 and 1.5). The fuel usually has a polymeric hydrocarbon structure, such as hydroxyl-terminated polybutadiene (HTPB). The fuel has a dual function:

1. To produce energy when burned with oxidizer-rich species
2. To bind the oxidizer particles together to form a specified propellant grain shape

The organic fuel material is initially in a liquid or semiliquid form that can be cured to form a solid.

Figure 1.4 (a) Cross-sectional view of a composite propellant and (b) a photograph of the top view of an AP-based solid propellant with ~65 wt% AP loading (modified from Summerfield et al., 1960).


Figure 1.5 Flame structure of ammonium perchlorate (AP)–based composite propellant.


Composite propellants usually are made of a polymeric matrix, loaded with a solid powder oxidizer and possibly a metal powder (e.g., aluminum) that plays the role of a secondary (but highly energetic) fuel component. In composite propellants, the oxidizer and fuel containing molecules come from separate components. Therefore, the flame structure is three dimensional and nonpremixed (see Figure 1.5).

Figure 1.6 Molecular structures of selected explosive or propellant ingredients.


The major propellant properties, such as burning rate, rheology, and mechanical behavior, are directly dependent on the size and distribution of fuel and oxidizer particles in the composite propellant matrix. Oxidizer and metallic fuel ingredients are usually in the form of solid powders, which must be mixed with a binder to provide cohesion and even distribution.

1.1.6 Major Types of Ingredients in Solid Propellants

A solid propellant consists of several different types of ingredients. Each of these ingredients serves a specific function. The most common ingredients are shown in Table 1.1 for homogeneous propellants and in Table 1.2 for heterogeneous propellants. Molecular structures of certain ingredients that are used in propellants and explosives are shown in Figure 1.6. The functions of propellant ingredients is described next.

Figure 1.7 Molecular structure of GAP.


Table 1.1 Ingredients Used in Homogeneous Propellants

Ingredient Examples
Plasticizer (fuel and oxidizer) NG: nitroglycerin
 TMETN: trimethylolethane trinitrate
 TEGDN: triethylene glycol dinitrate
 DEGDN: diethylene glycol dinitrate
Plasticizer (fuel) DEP: diethylphtalate
 TA: triacetine
 PU: polyurethane
Binder (fuel and oxidizer) NC: nitrocellulose
Stabilizer EC: ethyl centralite
 2NDPA: 2-nitrodiphenilamine
Burning rate catalyst PbSa: lead salicylate
 Pb2EH: lead 2-ethylhexoate
 PbST: lead stearate
 CuSa: copper salicylate
 CuSt: copper stearate
 LiF: lithium fluoride
High-energy additive RDX: cyclotrimethylene trinitramine
 HMX: cyclotetramethylene tetranitramine
 NGD: nitroguanidine
Coolant OXM: oxamide
Opacifier C: carbon black
Flame suppressant KNO3: potassium nitrate
 K2SO4: potassium sulfate
Metal fuel Al: aluminum
Combustion instability suppressant Al: aluminum
 Zr: zirconium
 ZrC: zirconium carbide

Table 1.2 Ingredients Used in Heterogeneous Propellants

Type of Ingredient Examples
Oxidizer AP: ammonium perchlorate
 AN: ammonium nitrate
 NP: nitronium perchlorate
 KP: potassium perchlorate
 RDX: cyclotrimethylene trinitramine
 HMX: cyclotetramethylene tetranitramine
Binder PBAN: polybutadiene acrylonitrile
 CTPB: carboxyl terminated polybutadiene
 HTPB: hydroxyl terminated polybutadiene
Curing and/or cross-linking agents PQD: paraquinone dioxime
 TDI: toluene-2,4-diisocyanate
 MAPO: tris {1-(2-methyl) aziridinyl} phosphine oxide
 ERLA-05I0: N,N,O-tri (1,2-epoxy propyl)-4-aminophenol
 IPDI: isophorone diisocyanate
Bonding agent MAPO: tris{1-(2-methyl) aziridinyl} phosphine oxide
 TEA: triethanolamine
 MT-4: adduct of 2.0 moles MAPO, 0.7 mole azipic acid, and 0.3 mole tararic acid
Plasticizer DOA: dioctyl adipate
 IDP: isodecyl pelargonete
 DOP: dioctyl phthalate
Burning rate catalyst Fe2O3: ferric oxide
 FeO(OH): hydrated-ferric oxide
 nBF: n-butyl ferrocene
 DnBF: di-n-butyl ferrocene
Metal fuel Al: aluminum
Combustion instability suppressant Al: aluminum
 Zr: zirconium
 ZrC: zirconium carbide

Table 1.3 Properties of Several Solid Oxidizers

c01tnt003.jpg Description of Oxidizer Ingredients

Oxidizer ingredients usually have positive oxygen balance, as shown in Table 1.3 for many commonly used oxidizers. Among them, ammonium perchlorate (AP, with a chemical formula of NH4ClO4) is the most widely used oxidizer. It is a white crystalline material that is usually orthorhombic but transforms into cubic form at 513 K. It starts to decompose at approximately 470 K according to the next global chemical reaction:

1.R1 1.R1

Beyond 620 K, it decomposes according to this global chemical reaction:

1.R2 1.R2

When AP is burned with polymeric hydrocarbon fuels, it produces mainly CO2, H2O, N2, and HCl. Even though AP has some undesirable features—including the production of HCl for acid rain; groundwater pollution; causing thyroid problems, especially for women; and generation of partially toxic combustion products—it is still widely used for propellants and explosives due to its high oxygen balance and relative stability to mechanical shocks. Because of the drawbacks of AP, one of the current aims of the propellant field is to find a suitable replacement for future applications in space propulsion, military, and commercial areas.

Even though RDX and HMX were initially developed as explosive ingredients, they have been utilized as oxidizers for some solid propellants due to their higher thermal stability, lower toxicity, and lack of HCl production upon combustion. Description of Fuel Binders

The fuel binder provides the structural glue or matrix in which solid granular ingredients (such as oxidizer particles and/or metal fuels) are held together in heterogeneous (composite) propellants. The binder raw materials are liquid prepolymers or monomers. After they are mixed with the solid ingredients, cast, and cured, they form a hard rubberlike material that constitutes the propellant grain. In short, a prepolymer is a molecule formed by the repetition (in several orders of magnitudes) of a monomer form (butadiene, polypropylene oxide, etc.), generally ending with reactive functions (telechelic prepolymers). Binders inherit their essential properties from the prepolymers. These properties can be derived from the nature of the polymeric chain or the properties of the functional group at its ends. The molecular structure of polyether prepolymer is:


A curing agent or cross linker causes the prepolymers to form longer chains of larger molecular mass and interlocks between chains. (It causes the binder to solidify and become hard.) Polymerization occurs when the binder monomer and its cross-linking agent react (beginning in the mixing process) to form long chains and complex three-dimensional polymers. The binder ingredient has important effects on rocket motor reliability, mechanical properties, propellant processing complexity, storability, aging, and costs. Characteristics of Glycidyl Azide Polymer Binder

Glycidyl azide polymer (GAP) is an example of an energetic, thermally stable, hydroxyl-terminated prepolymer that can be polymerized (Sutton and Biblarz, 2001). According to (Bathelt, Volk, and Weindel (2001); and as shown in Figure 1.7, the GAP formulation is:

Molecular weight: 99.092 g/mol
Oxygen balance: −121.09%
Density: 1.29 g/cm3
Melting point: gt200°C
Enthalpy of formation: 141.0 kJ/mol (340.09 kcal/kg). Characteristics of Hydroxyl-Terminated Polybutadiene Binder

Hydroxyl-terminated polybutadiene (HTPB) is the most commonly used prepolymer binder material. It allows a high solid fraction (88% to 90% of AP and Al by mass) and relatively good physical properties at the temperature range from −50° to 65°C (Sutton and Biblarz, 2001). Several different chemical formulae exist for HTPB. A typical one (Bathelt, Volk, and Weindel, 2001) is shown in Figure 1.8:

Molecular weight: 136.752 g/mol
Oxygen balance: −323.26%
Density: 0.916 g/cm3
Melting point: 241°C
Enthalpy of formation: −51.88 kJ/mol (−90.68 kcal/kg)

Figure 1.8 Molecular structures of HTPB.

1.8 Desired Properties of a Binder

The binder must be in liquid form during the preliminary phase of the preparation of the intimate mixture of oxidizer and fuel ingredients, although its elements must have sufficiently low volatility characteristics to withstand the high vacuum used during the mixing of the slurry and the casting of the propellant into a particular grain shape. It must be chemically compatible with the oxidizer, which means that it will not cause even a slight temperature increase that may result in an exothermic reaction leading to any unwanted autoignition of the propellant. It must be capable of accepting very high solid loading ratios (up to 80% in volume). The mixing operation must remain feasible, and the resulting slurry must be easily cast into the rocket motor case with molding devices of shapes that are often complex and include some very narrow regions. The mechanical properties of the propellant depend strongly on the selected binder. Curing and Cross-Linking Agents

A curing agent or cross-linker causes the prepolymers to form longer chains of larger molecular mass and interlocks between chains. Even though these materials are present in small amounts (0.2 to 3%), a minor change in the percentage can have a major effect on the propellant physical properties, manufacturability, and aging. A curing agent and/or cross-linker are used only with composite propellants. These ingredients cause the binder to solidify and become hard (Sutton and Biblarz, 2001).

The cross-linking agent in its most simple state could be a polyfunctional molecule (frequently trifunctional) with a low molecular weight or a mixture of bifunctional and trifunctional molecules. This approach can ensure an average functionality (i.e., number of reactive functions, divided by the total number of molecules) greater than 2 for the whole cross-linking system. The bifunctional molecules are generally called chain extenders, and their role is to increase the length of the chain of prepolymers. Chemical reaction occurs between the prepolymer and the cross-linking agent after the polymer addition and the three-dimensional links are created (Davenas, 1993). An example of a curing agent is isophorone diisocyanate (IPDI), as shown in Figure 1.9:

Molecular weight: 222.287 g/mol
Oxygen balance: −223.13%
Density: 1.061 g/cm3
Enthalpy of formation: −372.00 kJ/mol (−399.98 kcal/kg)

Figure 1.9 Molecular structure of IPDI.

1.9 Desired Properties of a Curing Agent/Cross-Linker

After the slurry (mixed oxidizer and prepolymer) is in the casting mold, cross-linking must ensure its transformation into a solid through a chemical reaction that obeys these criteria (Davenas, 1993): Aging

The term “aging” when used in regard to solid propellants in rocket motors refers to the deterioration of their physical properties with time. It is caused by the cumulative damage to the grain (such as by thermal cycling and load applications) during storage, handling, or transport. It can also be caused by chemical changes with time, such as the gradual depletion (evaporation) of certain liquid plasticizers or moisture absorption. The ability to carry stress or to allow elongation in propellants diminishes with cumulative damage. The aging limit is the estimated time when a rocket motor is no longer able to perform its operation reliably or safely. Depending on the propellant and the grain design, this aging limit or motor life can be between 8 and 25 years (Sutton and Biblarz, 2001).

With small tactical rocket motors, the aging limit usually is determined by full-scale motor firings tests at various time periods after manufacture, say two or three years. Accelerated temperature aging (more severe thermal cycles) and accelerated mechanical pulse loads and overstressing often are used to reduce the time needed for these tests (Sutton and Biblarz, 2001). The term “rocket motor aging” refers not only to the propellant but also to other components, such as the igniter's pyrotechnic charge, initiator material, O-rings and other organic material, and metals.

1.1.7 Applications of Solid Propellants

Solid propellants have been used for both military and commercial purposes. Military applications include missiles, guns, and air-breathing propulsion systems. Commercial applications include, among others, rockets for space explorations, satellite deployment, air bags in automobiles, electric cable connections, emergency airplane crew and passenger escape systems, gas generator systems for fire extinguishers. Hazard Classifications of Solid Propellants

The classification of a given propellant (mostly 1.1 or 1.3) determines the method of labeling and the cost of shipping rocket propellants, loaded military missiles, explosives, or ammunition; it also determines the required limits on the amount of that propellant stored or manufactured in any one site and the minimum separation distance of that site to the next building or site. Class 1.1

Propellants that can experience a transition from deflagration to detonation are considered more hazardous and usually are designated as class 1.1-type propellants. With a class 1.1 propellant, a powerful detonation sometimes can occur that rapidly gasifies all the remaining propellant and is much more powerful and destructive than the bursting of the rocket motor case under high pressures. Unfortunately, the term “explosion” has been used to describe both a bursting of a case with fragmentation of the motor and the higher rate of energy release of a detonation, which leads to a very rapid and more energetic fragmentation of the rocket motor. Class 1.3

Under normal conditions, most propellants “burn” and do not “detonate.” The rocket motor case may burst when the chamber pressure becomes too high. If the rocket motor case should burst violently with a class 1.3 propellant, then much of the remaining unburnted propellant would be thrown out but eventually would stop burning. (Note: “Class 1.2” corresponds to non–mass-detonating and fragment-producing device. “Class 1.4” corresponds to moderate fire, no detonation, and no fragment.)

1.1.8 Material Characterization of Propellants Propellant Density Calculation

For a propellant with multiple components (Nc