Applications of Turbulent and Multi-Phase Combustion

Preface xvii 1 Solid Propellants and Their Combustion Characteristics 1 1.1 Background of Solid Propellant Combustion, 4 1.1.1 Definition of Solid Propellants, 4 1.1.2 Desirable Characteristics of Solid Propellants, 4 1.1.3 Calculation of Oxygen Balance, 5 1.1.4 Homogeneous Propellants, 6 1.1.5 Heterogeneous Propellants (or Composite Propellants), 7 1.1.6 Major Types of Ingredients in Solid Propellants, 8 1.1.7 Applications of Solid Propellants, 16 1.1.8 Material Characterization of Propellants, 16 1.1.9 Thermal Profile in a Burning Solid Propellant, 18 1.2 Solid-Propellant Rocket and Gun Performance Parameters, 43 1.2.1 Performance Parameters of a Solid Rocket Motor, 44 1.2.2 Performance Parameters of Solid-Propellant Gun Systems, 61 2 Thermal Decomposition and Combustion of Nitramines 72 2.1 Thermophysical Properties of Selected Nitramines, 76 2.2 Polymorphic Forms of Nitramines, 78 2.2.1 Polymorphic Forms of HMX, 80 2.2.2 Polymorphic Forms of RDX, 82 2.3 Thermal Decomposition of RDX, 88 2.3.1 Explanation of Opposite Trends on alpha- and ß-RDX Decomposition with Increasing Pressure, 90 2.3.2 Thermal Decomposition Mechanisms of RDX, 92 2.3.3 Formation of Foam Layer Near RDX Burning Surface, 106 2.4 Gas-Phase Reactions of RDX, 109 2.4.1 Development of Gas-Phase Reaction Mechanism for RDX Combustion, 111 2.5 Modeling of RDX Monopropellant Combustion with Surface Reactions, 125 2.5.1 Processes in Foam-Layer Region, 126 2.5.2 Reactions Considered in the Foam Layer, 128 2.5.3 Evaporation and Condensation Consideration for RDX, 128 2.5.4 Boundary Conditions, 130 2.5.5 Numerical Methods Used for RDX Combustion Model with Foam Layer, 131 2.5.6 Predicted Flame Structure, 132 3 Burning Behavior of Homogeneous Solid Propellants 143 3.1 Common Ingredients in Homogeneous Propellants, 147 3.2 Combustion Wave Structure of a Double-Base Propellant, 148 3.3 Burning Rate Behavior of a Double-Base Propellant, 149 3.4 Burning Rate Behavior of Catalyzed Nitrate-Ester Propellants, 155 3.5 Thermal Wave Structure and Pyrolysis Law of Homogeneous Propellants, 158 3.5.1 Dark Zone Residence Time Correlation, 166 3.6 Modeling and Prediction of Homogeneous Propellant Combustion Behavior, 167 3.6.1 Multi-Ingredient Model of Miller and Anderson, 171 3.7 Transient Burning Characterization of Homogeneous Solid Propellant, 187 3.7.1 What is Dynamic Burning?, 188 3.7.2 Theoretical Models for Dynamic Burning, 190 Chapter Problems, 208 4 Chemically Reacting Boundary-Layer Flows 209 4.1 Introduction, 210 4.1.1 Applications of Reacting Boundary-Layer Flows, 211 4.1.2 High-Temperature Experimental Facilities Used in Investigation, 211 4.1.3 Theoretical Approaches and Boundary-Layer Flow Classifications, 212 4.1.4 Historical Survey, 212 4.2 Governing Equations for Two-Dimensional Reacting Boundary-Layer Flows, 216 4.3 Boundary Conditions, 221 4.4 Chemical Kinetics, 224 4.4.1 Homogeneous Chemical Reactions, 224 4.4.2 Heterogeneous Chemical Reactions, 226 4.5 Laminar Boundary-Layer Flows with Surface Reactions, 229 4.5.1 Governing Equations and Boundary Conditions, 229 4.5.2 Transformation to (xi, eta) Coordinates, 229 4.5.3 Conditions for Decoupling of Governing Equations and Self-Similar Solutions, 232 4.5.4 Damk¨ohler Number for Surface Reactions, 233 4.5.5 Surface Combustion of Graphite Near the Stagnation Region, 234 4.6 Laminar Boundary-Layer Flows With Gas-Phase Reactions, 239 4.6.1 Governing Equations and Coordinate Transformation, 239 4.6.2 Damk¨ohler Number for Gas-Phase Reactions, 240 4.6.3 Extension to Axisymmetric Cases, 242 4.7 Turbulent Boundary-Layer Flows with Chemical Reactions, 243 4.7.1 Introduction, 243 4.7.2 Boundary-Layer Integral Matrix Procedure of Evans, 243 4.7.3 Marching-Integration Procedure of Patankar and Spalding, 257 4.7.4 Metal Erosion by Hot Reactive Gases, 272 4.7.5 Thermochemical Erosion of Graphite Nozzles of Solid Rocket Motors, 281 4.7.6 Turbulent Wall Fires, 316 5 Ignition and Combustion of Single Energetic Solid Particles 330 5.1 Why Energetic Particles Are Attractive for Combustion Enhancement in Propulsion, 335 5.2 Metal Combustion Classification, 336 5.3 Metal Particle Combustion Regimes, 341 5.4 Ignition of Boron Particles, 344 5.5 Experimental Studies, 351 5.5.1 Gasification of Boron Oxides, 352 5.5.2 Chemical Kinetics Measurement, 353 5.5.3 Boron Ignition Combustion in a Controlled Hot Gas Environment, 354 5.6 Theoretical Studies of Boron Ignition and Combustion, 362 5.6.1 First-Stage Combustion Models, 362 5.6.2 Second-Stage Combustion Models, 365 5.6.3 Chemical Kinetic Mechanisms, 365 5.6.4 Methods for Enhancement of Boron Ignition, 367 5.6.5 Verification of Diffusion Mechanism of Boron Particle Combustion, 369 5.6.6 Chemical Identification of the Boron Oxide Layer, 371 5.7 Theoretical Model Development of Boron Particle Combustion, 372 5.7.1 First-Stage Combustion Model, 372 5.7.2 Second-Stage Combustion Model, 377 5.7.3 Comparison of Predicted and Measured Combustion Times, 381 5.8 Ignition and Combustion of Boron Particles in Fluorine-Containing Environments, 384 5.8.1 Multidiffusion Flat-Flame Burner, 385 5.8.2 Test Conditions, 387 5.8.3 Experimental Results and Discussions, 388 5.8.4 Surface Reaction of (BO)n with HF(g), 393 5.8.5 Surface Reaction of (BO)n with F(g), 394 5.8.6 Governing Equations During the First-Stage Combustion of Boron Particles, 395 5.8.7 Model for the "Clean" Boron Consumption Process (Second-Stage Combustion), 396 5.8.8 Numerical Solution, 403 5.9 Combustion of a Single Aluminum Particle, 410 5.9.1 Background, 413 5.9.2 Physical Model, 414 5.9.3 Aluminum-Combustion Mechanism, 417 5.9.4 Condensation Aspect of Model of Beckstead et al. (2005), 419 5.9.5 General Mathematical Model, 422 5.9.6 Boundary Conditions, 424 5.9.7 Dn Law in Aluminum Combustion, 429 5.10 Ignition of Aluminum Particle in a Controlled Postflame Zone, 437 5.11 Physical Concepts of Aluminum Agglomerate Formation, 439 5.11.1 Evolution Process of Condensed-Phase Combustion Products, 440 5.12 Combustion Behavior for Fine and Ultrafine Aluminum Particles, 443 5.12.1 10 mum Aluminum Particle--Early Transitional Structure, 444 5.12.2 100 nm Aluminum Particle--Late Transitional Structure, 446 5.13 Potential Use of Energetic Nanosize Powders for Combustion and Rocket Propulsion, 447 Chapter Problems, 452 Project No. 1, 452 Project No. 2, 454 6 Combustion of Solid Particles in Multiphase Flows 456 6.1 Void Fraction and Specific Particle Surface Area, 462 6.2 Mathematical Formulation, 463 6.2.1 Formulation of the Heat Equation for a Single Particle, 469 6.3 Method of Characteristics Formulation, 472 6.3.1 Linearization of the Characteristic Equations, 476 6.4 Ignition Cartridge Results, 477 6.5 Governing Equations for the Mortar Tube, 484 6.5.1 Initial Conditions, 488 6.5.2 Boundary Conditions, 488 6.5.3 Numerical Methods for Mortar Region Model, 490 6.6 Predictions of Mortar Performance and Model Validation, 491 6.7 Approximate Riemann Solver: Roe-Pike Method, 496 6.8 Roe's Method, 499 6.9 Roe-Pike Method, 501 6.10 Entropy Condition and Entropy Fix, 502 6.11 Flux Limiter, 503 6.12 Higher Order Correction, 504 6.13 Three-Dimensional Wave Propagation, 504 Appendix A: Useful Vector and Tensor Operations 507 Appendix B: Constants and Conversion Factors Often Used in Combustion 534 Appendix C: Naming of Hydrocarbons 538 Appendix D: Particle Size-U.S. Sieve Size and Tyler Screen Mesh Equivalents 541 Bibliography 544 Index 571