Internal Combustion Processes of Liquid Rocket Engines

Preface x 1 Introduction 1 1.1 Basic Configuration of Liquid Rocket Engines 2 1.1.1 Propellant Feed System 2 1.1.2 Thrust Chamber 6 1.2 Internal Combustion Processes of Liquid Rocket Engines 13 1.2.1 Start and Shutdown 13 1.2.2 Combustion Process 15 1.2.3 Performance Parameters in Working Process 18 1.3 Characteristics and Development History of Numerical Simulation of the Combustion Process in Liquid Rocket Engines 19 1.3.1 Benefits of Numerical Simulation of the Combustion Process in Liquid Rocket Engines 19 1.3.2 Main Contents of Numerical Simulations of Liquid Rocket Engine Operating Process 19 1.3.3 Development of Numerical Simulations of Combustion Process in Liquid Rocket Engines 21 1.4 Governing Equations of Chemical Fluid Dynamics 22 1.5 Outline of this Book 24 References 25 2 Physical Mechanism and Numerical Modeling of Liquid Propellant Atomization 26 2.1 Types and Functions of Injectors in a Liquid Rocket Engine 27 2.2 Atomization Mechanism of Liquid Propellant 28 2.2.1 Formation of Static Liquid Droplet 28 2.2.2 Breakup of Cylindrical Liquid Jet 29 2.2.3 Liquid Sheet Breakup 36 2.2.4 Droplet Secondary Breakup 43 2.3 Characteristics of Atomization in Liquid Rocket Engines 48 2.3.1 Distribution Function of the Droplet Size 51 2.3.2 Mean Diameter and Characteristic Diameter 53 2.3.3 Measurement of Spray Size Distribution 55 2.4 Atomization Modeling for Liquid Rocket Engine Atomizers 59 2.4.1 Straight-flow Injector 60 2.4.2 Centrifugal Injector 60 2.4.3 Impinging-stream Injectors 64 2.4.4 Coaxial Shear Injector 70 2.4.5 Coaxial Centrifugal Injectors 70 2.5 Numerical Simulation of Liquid Propellant Atomization 75 2.5.1 Theoretical Models of Liquid Propellant Atomization 75 2.5.2 Quasi-fluid Models 80 2.5.3 Particle Trajectory Models 81 2.5.4 Simulation of Liquid Jet Atomization Using Interface Tracking Method 85 2.5.5 Liquid Jet Structure Varying Flow Conditions 91 References 94 3 Modeling of Droplet Evaporation and Combustion 97 3.1 Theory for Quasi-Steady Evaporation and Combustion of a Single Droplet at Atmospheric Pressure 97 3.1.1 Quasi-Steady Evaporation Theory for Single Droplet in the Static Gas without Combustion 98 3.1.2 Quasi-Steady Evaporation Theory for Droplet in a Static Gas with Combustion 103 3.1.3 Non-Combustion Evaporation Theory for a Droplet in a Convective Flow 107 3.1.4 Evaporation Theory for a Droplet in a Convective Medium with Combustion 108 3.2 Evaporation Model for a Single Droplet under High Pressure 109 3.2.1 ZKS Droplet High Pressure Evaporation Theory 110 3.2.2 Application of the Liquid Activity Coefficient to Calculate the Gas Liquid Equilibrium at a High Pressure 115 3.3 Subcritical Evaporation Response Characteristics of Propellant Droplet in Oscillatory Environments 117 3.3.1 Physical Model 118 3.3.2 Examples and the Analysis of Results 120 3.4 Multicomponent Fuel Droplet Evaporation Model 123 3.4.1 Simple Multicomponent Droplet Evaporation Model 124 3.4.2 Continuous Thermodynamics Model of Complex Multicomponent Mixture Droplet Evaporation 135 3.5 Droplet Group Evaporation 145 3.5.1 Definition of Group Combustion Number 146 3.5.2 Droplet Group Combustion Model 146 References 149 4 Modeling of Turbulence 151 4.1 Turbulence Modeling in RANS 152 4.1.1 Algebraic Model 153 4.1.2 One-Equation Model 154 4.1.3 Two-Equation Models 156 4.1.4 Turbulence Model Modification 161 4.1.5 Nonlinear Eddy Viscosity Model 165 4.1.6 Reynolds-Stress Model 170 4.1.7 Comments on the Models 173 4.2 Theories and Equations of Large Eddy Simulation 174 4.2.1 Philosophy behind LES 174 4.2.2 LES Governing Equations 175 4.2.3 Subgrid-Scale Model 176 4.2.4 Hybrid RANS/LES Methods 182 4.3 Two-Phase Turbulence Model 187 4.3.1 Hinze Tchen Algebraic Model for Particle Turbulence 187 4.3.2 Two-Phase Turbulence Model k- -kp and k- -Ap 188 References 189 5 Turbulent Combustion Model 192 5.1 Average of Chemical Reaction Term 192 5.2 Presumed PDF Fast Chemistry Model for Diffusion Flame 194 5.2.1 Concepts and Assumptions 195 5.2.2 Z g Equations 197 5.2.3 Probability Density Distribution Function 197 5.2.4 Presumed PDF 198 5.2.5 Truncated Gaussian PDF 200 5.3 Finite Rate EBU Arrhenius Model for Premixed Flames 201 5.4 Moment-Equation Model 202 5.4.1 Time-Averaged Chemical Reaction Rate 203 5.4.2 Closure for the Moments 203 5.5 Flamelet Model for Turbulent Combustion 204 5.5.1 Diffusion Flamelet Model 205 5.5.2 Premixed Flamelet Model 206 5.6 Transported PDF Method for Turbulent Combustion 208 5.6.1 Transport Equations of the Probability Density Function 208 5.6.2 The Closure Problem of Turbulence PDF Equation 211 5.6.3 Transport Equation for the Single-Point Joint PDF with Density-Weighted Average 212 5.6.4 Solution Algorithm for the Transport Equation of Probability Density Function 212 5.7 Large Eddy Simulation of Turbulent Combustion 214 5.7.1 Governing Equations of Large Eddy Simulation for Turbulent Combustion 214 5.7.2 Sub-Grid Scale Combustion Models 218 References 226 6 Heat Transfer Modeling and Simulation 228 6.1 Convective Heat Transfer Model of Combustor Wall 228 6.1.1 Model of Gas Convection Heat 229 6.1.2 Convection Cooling Model 232 6.2 Heat Conduction Model of Combustor Wall 235 6.2.1 Fourier Heat Conduction Law 235 6.2.2 1D Steady Heat Conduction 235 6.2.3 2D Steady Heat Conduction 237 6.2.4 Unsteady Heat Conduction 237 6.3 Radiation Heat Transfer Model 238 6.3.1 Basic Law of Radiation 238 6.3.2 Empirical Model of Radiation Heat Flux Density Calculation 245 6.3.3 Numerical Simulation of Combustion Heat Radiation 246 References 254 7 The Model of Combustion Instability 255 7.1 Overview 255 7.1.1 Behavior of Combustion Instability 256 7.1.2 Classification of Combustion Instability 257 7.1.3 Characteristics of Combustion Instability 259 7.2 Acoustic Basis of Combustion Instability 260 7.2.1 Rayleigh Criterion for Acoustic Oscillations Arising from Heat or Mass Supply 260 7.2.2 Acoustic and Acoustic Oscillations 261 7.2.3 Acoustic Modes in the Combustion Chamber 263 7.2.4 Self-Excited Oscillations in Rocket Engines 267 7.3 Response Characteristics of Combustion Process in Liquid Rocket Engines 269 7.3.1 Response Characteristics of the Propellant Supply System 269 7.3.2 Response Characteristics of Spray Atomization Process 271 7.3.3 Response Characteristics of Droplet Evaporation Process 272 7.4 Sensitive Time Delay Model n 272 7.4.1 Combustion Time Delay 272 7.4.2 Sensitive Time Delay Model 273 7.5 Nonlinear Theory for Combustion Stability in Liquid Rocket Engines 283 7.5.1 Nonlinear Field Oscillator Model 286 7.5.2 Continuous Stirred Tank Reactor Acoustic Model 287 7.5.3 Spatio-Temporal Interaction Dynamic Model 291 7.5.4 General Thermodynamic Analysis of Combustion Instability 293 7.6 Control of Unstable Combustion 295 7.6.1 Passive Control 295 7.6.2 Active Control 297 7.6.3 A Third Control Method 298 References 300 8 Numerical Method and Simulations of Liquid Rocket Engine Combustion Process 302 8.1 Governing Equations of Two-Phase Multicomponent Reaction Flows 302 8.1.1 Gas Phase Governing Equation 303 8.1.2 Liquid Particle Trajectory Model 305 8.1.3 Turbulence Model 308 8.1.4 Droplets Atomizing Model 309 8.1.5 Droplet Evaporation Model 311 8.1.6 Chemical Reaction Kinetics Model 313 8.2 Numerical Methodology 314 8.2.1 Overview 314 8.2.2 The Commonly-Used Discretization Scheme 315 8.2.3 Discrete Equations 320 8.2.4 Discretization of the Momentum Equation Based on the Staggered Grid 323 8.2.5 The SIMPLE Algorithm of Flow Field Computing 326 8.2.6 PISO Algorithm 329 8.3 Grid Generation Techniques 334 8.3.1 Structured Grid Generation Technology 334 8.3.2 Unstructured Mesh Generation Techniques 338 8.4 Simulations of Combustion in Liquid Rocket Engines and Results Analysis 340 8.4.1 Numerical Analysis of Dual-States Hydrogen Engine Combustion and Heat Transfer Processes 340 8.4.2 Numerical Heat Transfer Simulation of a Three-Component Thrust Chamber 349 8.4.3 Numerical Simulation of Liquid Rocket Engine Combustion Stability 356 References 376 Index 377

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