A revised edition to applied gas dynamics with exclusive coverage on jets and additional sets of problems and examples
The revised and updated second edition of Applied Gas Dynamics offers an authoritative guide to the science of gas dynamics. Written by a noted expert on the topic, the text contains a comprehensive review of the topic; from a definition of the subject, to the three essential processes of this science: the isentropic process, shock and expansion process, and Fanno and Rayleigh flows.
In this revised edition, there are additional worked examples that highlight many concepts, including moving shocks, and a section on critical Mach number is included that helps to illuminate the concept. The second edition also contains new exercise problems with the answers added. In addition, the information on ram jets is expanded with helpful worked examples. It explores the entire spectrum of the ram jet theory and includes a set of exercise problems to aid in the understanding of the theory presented. This important text:
- Includes a wealth of new solved examples that describe the features involved in the design of gas dynamic devices
- Contains a chapter on jets; this is the first textbook material available on high-speed jets
- Offers comprehensive and simultaneous coverage of both the theory and application
- Includes additional information designed to help with an understanding of the material covered
Written for graduate students and advanced undergraduates in aerospace engineering and mechanical engineering, Applied Gas Dynamics, Second Edition expands on the original edition to include not only the basic information on the science of gas dynamics but also contains information on high-speed jets.
Table of Contents
Preface xv
Author Biography xvii
About the Companion Website xix
1 Basic Facts 1
1.1 Definition of Gas Dynamics 1
1.2 Introduction 1
1.3 Compressibility 2
1.3.1 Limiting Conditions for Compressibility 3
1.4 Supersonic Flow – What is it? 4
1.5 Speed of Sound 5
1.6 Temperature Rise 7
1.7 Mach Angle 8
1.7.1 Small Disturbance 10
1.7.2 Finite Disturbance 10
1.8 Thermodynamics of Fluid Flow 11
1.9 First Law of Thermodynamics (Energy Equation) 11
1.9.1 Energy Equation for an Open System 12
1.9.2 Adiabatic Flow Process 14
1.10 The Second Law of Thermodynamics (Entropy Equation) 15
1.11 Thermal and Calorical Properties 16
1.11.1 Thermally Perfect Gas 16
1.12 The Perfect Gas 17
1.12.1 Entropy Calculation 18
1.12.2 Isentropic Relations 20
1.12.3 Limitations on Air as a Perfect Gas 25
1.13 Wave Propagation 26
1.14 Velocity of Sound 26
1.15 Subsonic and Supersonic Flows 27
1.16 Similarity Parameters 28
1.17 Continuum Hypothesis 28
1.18 Compressible Flow Regimes 30
1.19 Summary 31
Exercise Problems 34
2 Steady One-Dimensional Flow 43
2.1 Introduction 43
2.2 Fundamental Equations 43
2.3 Discharge from a Reservoir 45
2.3.1 Mass Flow Rate per Unit Area 47
2.3.2 Critical Values 51
2.4 Streamtube Area–Velocity Relation 54
2.5 de Laval Nozzle 57
2.5.1 Mass Flow Relation in Terms of Mach Number 65
2.5.2 Maximum Mass Flow Rate per Unit Area 65
2.6 Supersonic Flow Generation 66
2.6.1 Nozzles 68
2.6.2 Physics of the Nozzle Flow Process 69
2.7 Performance of Actual Nozzles 71
2.7.1 Nozzle Efficiency 71
2.7.2 Nozzle Discharge Coefficient 73
2.8 Diffusers 75
2.8.1 Special Features of Supersonic Diffusers 77
2.8.2 Supersonic Wind Tunnel Diffusers 78
2.8.3 Supersonic Inlets 81
2.8.4 Fixed-Geometry Inlet 82
2.8.5 Variable-Geometry Inlet 83
2.8.6 Diffuser Efficiency 84
2.9 Dynamic Head Measurement in Compressible Flow 88
2.9.1 Compressibility Correction to Dynamic Pressure 91
2.10 Pressure Coefficient 95
2.11 Summary 97
Exercise Problems 99
3 Normal Shock Waves 113
3.1 Introduction 113
3.2 Equations of Motion for a Normal Shock Wave 113
3.3 The Normal Shock Relations for a Perfect Gas 115
3.4 Change of Stagnation or Total Pressure Across a Shock 118
3.5 Hugoniot Equation 121
3.5.1 Moving Shocks 123
3.6 The Propagating Shock Wave 123
3.6.1 Weak Shock 128
3.6.2 Strong Shock 130
3.7 Reflected Shock Wave 133
3.8 Centered Expansion Wave 138
3.9 Shock Tube 139
3.9.1 Shock Tube Applications 142
3.10 Summary 145
Exercise Problems 148
4 Oblique Shock and Expansion Waves 155
4.1 Introduction 155
4.2 Oblique Shock Relations 156
4.3 Relation Between 𝛽 and 𝜃 158
4.4 Shock Polar 160
4.5 Supersonic Flow Over a Wedge 162
4.6 Weak Oblique Shocks 165
4.7 Supersonic Compression 167
4.8 Supersonic Expansion by Turning 169
4.9 The Prandtl–Meyer Expansion 170
4.9.1 Velocity Components Vr and V𝜙 172
4.9.2 The Prandtl–Meyer Function 175
4.9.3 Compression 177
4.10 Simple and Nonsimple Regions 178
4.11 Reflection and Intersection of Shocks and Expansion Waves 178
4.11.1 Intersection of Shocks of the Same Family 181
4.11.2 Wave Reflection from a Free Boundary 183
4.12 Detached Shocks 189
4.13 Mach Reflection 191
4.14 Shock-Expansion Theory 197
4.15 Thin Airfoil Theory 202
4.15.1 Application of Thin Aerofoil Theory 203
4.16 Summary 210
Exercise Problems 212
5 Compressible Flow Equations 221
5.1 Introduction 221
5.2 Crocco’s Theorem 221
5.2.1 Basic Solutions of Laplace’s Equation 224
5.3 General Potential Equation for Three-Dimensional Flow 225
5.4 Linearization of the Potential Equation 226
5.4.1 Small Perturbation Theory 227
5.5 Potential Equation for Bodies of Revolution 229
5.5.1 Conclusions 230
5.5.2 Solution of Nonlinear Potential Equation 231
5.6 Boundary Conditions 231
5.6.1 Bodies of Revolution 232
5.7 Pressure Coefficient 233
5.7.1 Bodies of Revolution 234
5.8 Summary 234
Exercise Problems 237
6 Similarity Rule 239
6.1 Introduction 239
6.2 Two-Dimensional Flow: The Prandtl–Glauert Rule for Subsonic Flow 239
6.2.1 Prandtl–Glauert Transformations 239
6.2.2 The Direct Problem (Version I) 241
6.2.3 The Indirect Problem (Case of Equal Potentials): P–G Transformation (Version II) 243
6.2.4 Streamline Analogy (Version III): Gothert’s Rule 244
6.3 Prandtl–Glauert Rule for Supersonic Flow: Versions I and II 245
6.3.1 Subsonic Flow 246
6.3.2 Supersonic Flow 246
6.4 The von Karman Rule for Transonic Flow 248
6.4.1 Use of the von Karman Rule 249
6.5 Hypersonic Similarity 250
6.6 Three-Dimensional Flow: Gothert’s Rule 252
6.6.1 General Similarity Rule 252
6.6.2 Gothert’s Rule 254
6.6.3 Application toWings of Finite Span 255
6.6.4 Application to Bodies of Revolution and Fuselages 255
6.6.5 The Prandtl–Glauert Rule 257
6.6.6 The von Karman Rule for Transonic Flow 261
6.7 Critical Mach Number 261
6.7.1 Calculation of M∗∞ 264
6.8 Summary 266
Exercise Problems 269
7 Two-Dimensional Compressible Flows 271
7.1 Introduction 271
7.2 General Linear Solution for Supersonic Flow 271
7.2.1 Existence of Characteristics in a Physical Problem 273
7.2.2 Equation for the Streamlines from Kinematic Flow Condition 274
7.3 Flow over a Wave-Shaped Wall 276
7.3.1 Incompressible Flow 276
7.3.2 Compressible Subsonic Flow 277
7.3.3 Supersonic Flow 278
7.3.4 Pressure Coefficient 278
7.4 Summary 280
Exercise Problems 280
8 Flow with Friction and Heat Transfer 283
8.1 Introduction 283
8.2 Flow in Constant Area Duct with Friction 283
8.2.1 The Fanno Line 284
8.3 Adiabatic, Constant-Area Flow of a Perfect Gas 285
8.3.1 Definition of Friction Coefficient 286
8.3.2 Effects of Wall Friction on Fluid Properties 287
8.3.3 Second Law of Thermodynamics 288
8.3.4 Working Relations 289
8.4 Flow with Heating or Cooling in Ducts 294
8.4.1 Governing Equations 294
8.4.2 Simple-Heating Relations for a Perfect Gas 295
8.5 Summary 300
Exercise Problems 303
9 Method of Characteristics 309
9.1 Introduction 309
9.2 The Concepts of Characteristics 309
9.3 The Compatibility Relation 310
9.4 The Numerical Computational Method 312
9.4.1 Solid and Free Boundary Points 313
9.4.2 Sources of Error 316
9.4.3 Axisymmetric Flow 316
9.4.4 Nonisentropic Flow 317
9.5 Theorems for Two-Dimensional Flow 318
9.6 Numerical Computation with Weak Finite Waves 320
9.6.1 Reflection of Waves 320
9.7 Design of Supersonic Nozzle 323
9.7.1 Contour Design Details 324
9.8 Summary 328
10 Measurements in Compressible Flow 329
10.1 Introduction 329
10.2 Pressure Measurements 329
10.2.1 Liquid Manometers 329
10.2.2 Measuring Principle of Manometers 330
10.2.3 Dial-Type Pressure Gauges 332
10.2.4 Pressure Transducers 333
10.3 Temperature Measurements 335
10.4 Velocity and Direction 338
10.5 Density Problems 339
10.6 Compressible Flow Visualization 339
10.6.1 Supersonic Flows 340
10.7 Interferometer 341
10.7.1 Formation of Interference Patterns 341
10.7.2 Quantitative Evaluation 342
10.7.3 Fringe-Displacement Method 344
10.8 Schlieren System 344
10.8.1 Range and Sensitivity of the Schlieren System 347
10.8.2 Optical Components Quality Requirements 347
10.8.3 Sensitivity of the Schlieren Method for Shock and Expansion Studies 350
10.9 Shadowgraph 352
10.9.1 Comparison of the Schlieren and Shadowgraph Methods 353
10.10 Wind Tunnels 354
10.10.1 High-SpeedWind Tunnels 354
10.10.2 Blowdown TypeWind Tunnels 354
10.10.3 Induction Type Tunnels 355
10.10.4 Continuous Supersonic Wind Tunnels 356
10.10.5 Losses in Supersonic Tunnels 357
10.10.6 Supersonic Wind Tunnel Diffusers 358
10.10.7 Effects of Second Throat 360
10.10.8 Compressor Tunnel Matching 362
10.10.9 The Mass Flow Rate 365
10.10.10 Blowdown Tunnel Operation 369
10.10.11 Optimum Conditions 372
10.10.12 Running Time of Blowdown Wind Tunnels 373
10.11 Hypersonic Tunnels 375
10.11.1 Hypersonic Nozzle 377
10.12 Instrumentation and Calibration ofWind Tunnels 380
10.12.1 Calibration of SupersonicWind Tunnels 380
10.12.2 Calibration 381
10.12.3 Mach Number Determination 381
10.12.4 Pitot Pressure Measurement 382
10.12.5 Static Pressure Measurement 382
10.12.6 Determination of Flow Angularity 383
10.12.7 Determination of Turbulence Level 383
10.12.8 Determination of Test-Section Noise 384
10.12.9 Use of Calibration Results 384
10.12.10 Starting of Supersonic Tunnels 384
10.12.11 Starting Loads 385
10.12.12 Reynolds Number Effects 385
10.12.13 Model Mounting-Sting Effects 385
10.13 Calibration and Use of Hypersonic Tunnels 386
10.13.1 Calibration of Hypersonic Tunnels 386
10.13.2 Mach Number Determination 386
10.13.3 Determination of Flow Angularity 388
10.13.4 Determination of Turbulence Level 388
10.13.5 Reynolds Number Effects 389
10.13.6 Force Measurements 389
10.14 Flow Visualization 390
10.15 Summary 390
Exercise Problems 393
11 Ramjet 395
11.1 Introduction 395
11.2 The Ideal Ramjet 396
11.3 Aerodynamic Losses 401
11.4 Aerothermodynamics of Engine Components 404
11.4.1 Engine Inlets 404
11.5 Flow Through Inlets 405
11.5.1 Inlet Flow Process 406
11.5.2 Boundary Layer Separation 406
11.5.3 Flow Over the Inlet 406
11.6 Performance of Actual Intakes 410
11.6.1 Isentropic Efficiency 410
11.6.2 Stagnation Pressure Ratio 411
11.6.3 Supersonic Inlets 411
11.6.4 Supersonic Diffusers 412
11.6.5 Starting Problem 413
11.7 Shock–Boundary Layer Interaction 418
11.8 Oblique Shock Wave Incident on Flat Plate 419
11.9 Normal Shocks in Ducts 420
11.10 External Supersonic Compression 422
11.11 Two-Shock Intakes 423
11.12 Multi-Shock Intakes 427
11.13 Isentropic Compression 429
11.14 Limits of External Compression 431
11.15 External Shock Attachment 433
11.16 Internal Shock Attachment 433
11.17 Pressure Loss 434
11.18 Supersonic Combustion 442
11.19 Summary 444
Exercise Problems 447
12 Jets 451
12.1 Introduction 451
12.1.1 Subsonic Jets 453
12.2 Mathematical Treatment of Jet Profiles 454
12.3 Theory of Turbulent Jets 455
12.3.1 Mean Velocity and Mean Temperature 456
12.3.2 Turbulence Characteristics of Free Jets 457
12.3.3 Mixing Length 458
12.4 Experimental Methods for Studying Jets and the Techniques Used for Analysis 461
12.4.1 Pressure Measurement 462
12.5 Expansion Levels of Jets 464
12.5.1 Overexpanded Jets 464
12.5.2 Correctly Expanded Jets 467
12.5.3 Underexpanded Jets 469
12.6 Control of Jets 471
12.6.1 Classification of Control Methods 473
12.6.2 Role of Shear Layer in Flow Control 474
12.6.3 Supersonic Shear Layers 475
12.6.4 Use of Tabs for Jet Control 477
12.6.5 Evaluation of the Effectiveness of Some Specific Passive Controls 481
12.6.6 Grooves and Cutouts 519
12.7 Noncircular Jets and Shifted Tabs 519
12.7.1 Jet Control with Tabs 523
12.7.2 Shifted Tabs 527
12.7.3 Ventilated Triangular Tabs 532
12.7.4 Tab Edge Effect 535
12.8 Summary 541
Appendix A 547
References 619
Index 625
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