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    Fundamentals of Gas Dynamics

    Oscar Biblarz,D. Robert|2019.10.15

    Preface

    To the Student

    1 Definitions and Fundamental Principles 1

    1.1 Introduction 1

    1.2 Units and Notation

    1.3 Why we use non-dimensional quantities

    1.4 Thermodynamic Concepts for Control Mass Analysis

    Review Questions

    Review Problems

    2 Control Volume Analysis—Part I

    2.1 Introduction

    2.2 Objectives

    2.3 Flow Dimensionality and Average Velocity

    2.4 Transformation of a Material Derivative to a Control Volume Approach

    2.5 Conservation of Mass

    2.6 Conservation of Energy

    2.7 Summary 44

    Problems 46

    Check Test 48

    3 Control Volume Analysis-Part II 51

    3.1 Introduction 51

    3.2 Objectives 51

    3.3 Comments on Entropy 52

    3.4 Pressure–Energy Equation 54

    3.5 The Stagnation Concept 55

    3.6 Stagnation Pressure–Energy Equation 59

    3.7 Consequences of Constant Density 61

    3.8 Momentum Equation 66

    3.9 Summary 75

    Problems 77

    Check Test 81

    4 Introduction to Compressible Flow 83

    4.1 Introduction 83

    4.2 Objectives 83

    4.3 Sonic Speed and Mach Number 84

    4.4 Wave Propagation 89

    4.5 Equations for Perfect Gases in Terms of Mach Number 92

    4.6 h–s and T–s Diagrams 97

    4.7 Summary 99

    Problems 100

    Check Test 102

    5 Varying-Area Adiabatic Flow 105

    5.1 Introduction 105

    5.2 Objectives 105

    5.3 General Fluid—No Losses 106

    5.4 Perfect Gases with Losses 111

    5.5 The * Reference Concept 115

    5.6 Isentropic Table 118

    5.7 Nozzle Operation 124

    5.8 Nozzle Performance 131

    5.9 Diffuser Performance 133

    5.10 When Γ Is Not Equal to 1.4 135

    5.11 (Optional) Beyond the Tables 135

    5.12 Summary 138

    Problems 139

    Check Test 144

    6 Standing Normal Shocks 147

    6.1 Introduction 147

    6.2 Objectives 147

    6.3 Shock Analysis—General Fluid 148

    6.4 Working Equations for Perfect Gases 151

    6.5 Normal-Shock Table 154

    6.6 Shocks in Nozzles 159

    6.7 Supersonic Wind Tunnel Operation 164

    6.8 When Γ Is Not Equal to 1.4 166

    6.9 (Optional) Beyond the Tables 168

    6.10 Summary 169

    Problems 170

    Check Test 174

    7 Moving and Oblique Shocks 175

    7.1 Introduction 175

    7.2 Objectives 175

    7.3 Normal Velocity Superposition: Moving Normal Shocks 176

    7.4 Tangential Velocity Superposition: Oblique Shocks 179

    7.5 Oblique-Shock Analysis: Perfect Gas 185

    7.6 Oblique-Shock Table and Charts 187

    7.7 Boundary Condition of Flow Direction 189

    7.8 Boundary Condition of Pressure Equilibrium 193

    7.9 Conical Shocks 195

    7.10 The Shock Tube

    7.11 (Optional) Beyond the Tables 198

    7.12 Summary 200

    Problems 201

    Check Test 205

    8 Prandtl-Meyer Flow 207

    8.1 Introduction 207

    8.2 Objectives 207

    8.3 Argument for Isentropic Turning Flow 208

    8.4 Analysis of Prandtl–Meyer Flow 214

    8.5 Prandtl–Meyer Function 218

    8.6 Overexpanded and Underexpanded Nozzles 221

    8.7 Supersonic Airfoils 226

    8.8 Aerospike Nozzle

    8.9 When Γ Is Not Equal to 1.4 230

    8.10 (Optional) Beyond the Tables 231

    8.11 Summary 232

    Problems 233

    Check Test 238

    9 Fanno Flow 241

    9.1 Introduction 241

    9.2 Objectives 241

    9.3 Analysis for a General Fluid 242

    9.4 Working Equations for Perfect Gases 248

    9.5 Reference State and Fanno Table 253

    9.6 Applications 257

    9.7 Correlation with Shocks 261

    9.8 Friction Choking 264

    9.9 (Optional) How the Left-Hand-Side of Equation 9.40 Is Derived

    9.10 When Γ Is Not Equal to 1.4 267

    9.11 (Optional) Beyond the Tables 268

    9.12 Summary 269

    Problems 270

    Check Test 274

    10 Rayleigh Flow 277

    10.1 Introduction 277

    10.2 Objectives 278

    10.3 Analysis for a General Fluid 278

    10.4 Working Equations for Perfect Gases 288

    10.5 Reference State and the Rayleigh Table 293

    10.6 Applications 295

    10.7 Correlation with Shocks 298

    10.8 Thermal Choking due to Heating 302

    10.9 When Γ Is Not Equal to 1.4 305

    10.10 (Optional) Beyond the Tables 306

    10.11 Summary 307

    Problems 308

    Check Test 313

    11 Real Gas Effects 315

    11.1 Introduction 315

    11.2 Objectives 316

    11.3 What’s Really Going On 317

    11.4 Semiperfect Gas Behavior, Development of the Gas Table 319

    11.5 Real Gas Behavior, Equations of State and Compressibility Factors 325

    11.6 Variable γ—Variable-Area Flows 329

    11.7 Variable γ—Constant-Area Flows 336

    11.8 High-Energy Gas Lasers

    11.9 Summary 338

    Problems 340

    Check Test 341

    12 Propulsion Systems 343

    12.1 Introduction 343

    12.2 Objectives 343

    12.3 Brayton Cycle 344

    12.4 Propulsion Engines 353

    12.5 General Performance Parameters, Thrust, Power, and Efficiency 369

    12.6 Air-Breathing Propulsion Systems Performance Parameters 375

    12.7 Air-Breathing Propulsion Systems Incorporating Real Gas Effects 380

    12.8 Rocket Propulsion Systems Performance Parameters 381

    12.9 Supersonic Diffusers 384

    12.10 Summary 387

    Problems 388

    Check Test 392

    Appendixes

    A. Summary of the English Engineering (EE) System of Units 396

    B. Summary of the International System (SI) of Units 400

    C. Friction-Factor Chart 404

    D. Oblique-Shock Charts (Γ = 1.4) (Two-Dimensional) 406

    E. Conical-Shock Charts (Γ = 1.4) (Three-Dimensional) 410

    F. Generalized Compressibility Factor Chart 414

    G. Isentropic Flow Parameters (Γ = 1.4) (including Prandtl–Meyer Function) 416

    H. Normal-Shock Parameters (Γ = 1.4) 428

    I. Fanno Flow Parameters (Γ = 1.4) 438

    J. Rayleigh Flow Parameters (Γ = 1.4) 450

    K. Properties of Air at Low Pressures 462

    L. Specific Heats of Air at Low Pressures 470

    Selected References 473

    Answers to Problems 477

    Index

     

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