COMPRESSIBLE FLUID DYNAMICS with Personal Computer ...
9
COMPRESSIBLE FLUID DYNAMICS with Personal Computer Applications В. К. HODGE Thermal and Fluid Dynamics Laboratory Department of Mechanical Engineering Mississippi State University KEITH KOENIG Department of Aerospace Engineering Mississippi State University Prentice Hall Englewood Cliffs, New Jersey, 07632
Transcript of COMPRESSIBLE FLUID DYNAMICS with Personal Computer ...
COMPRESSIBLE FLUID DYNAMICS
with Personal Computer Applications
В. К. HODGE
Thermal and Fluid Dynamics Laboratory Department of Mechanical Engineering Mississippi State University
KEITH KOENIG
Department of Aerospace Engineering Mississippi State University
Prentice Hall Englewood Cliffs, New Jersey, 07632
Contents
PREFACE xi
Parti FUNDAMENTAL PRINCIPLES
Fundamental Concepts of Compressible Fluid Dynamics 3
1.1 INTRODUCTION 3
1.2 THERMODYNAMIC CONSIDERATIONS 3 The Continuum Approach versus the Molecular Approach 3 An Examination of the Microscopic Approach 5 Thermodynamic Properties of a Gas 7
1.3 THE LAWS OF THERMODYNAMICS 8
1.4 EQUATIONS OF STATE FOR A PERFECT GAS 10
1.5 CHANGES IN ENTROPY AND ISENTROPIC RELATIONS 14
1.6 THE INTEGRAL CONSERVATION EQUATIONS 15 Conservation Concepts 15 Conservation of Mass 17 Conservation of Momentum 19 Conservation of Energy 24
iv Contents
1.7 THE SPEED OF SOUND 26
1.8 THE STEADY-STATE ENERGY EQUATION 33
1.9 THE ISENTROPIC FLOW EQUATIONS 38
1.10 CONCLUSION 40
REVIEW QUESTIONS 40
CHAPTER QUESTIONS 41
Part II WAVES IN COMPRESSIBLE FLOW
2 Normal Shock Waves 51 2.1 INTRODUCTION 51
2.2 WAVE MOTION IN A COMPRESSIBLE MEDIUM 52
2.3 NORMAL SHOCK WAVE ANALYSIS 54
2.4 THE RANKINE-HUGONIOT RELATIONS 62
2.5 NORMAL SHOCK WAVE APPLICATIONS 64
2.6 MOVING NORMAL SHOCK WAVES 66
REVIEW QUESTIONS 76
CHAPTER QUESTIONS 76
О Oblique and Conical Shock Waves 80 3.1 INTRODUCTION 80
3.2 OBLIQUE SHOCK WAVE ANALYSIS 81
3.3 OBLIQUE SHOCK WAVE APPLICATIONS 90
3.4 SUPERSONIC FLOW OVER A CONE 102
REVIEW QUESTIONS 115
CHAPTER QUESTIONS 116
Contents v
Prandtl-Meyer Flows and the Shock-Expansion Procedure 121
4.1 INTRODUCTION 121
4.2 EXPANSION WAVE ANALYSIS 123
4.3 PRANDTL-MEYER APPLICATIONS 126
4.4 THE SHOCK-EXPANSION PROCEDURE 130
4.5 CONCLUSION 142
REVIEW QUESTIONS 143
CHAPTER QUESTIONS 144
Part III GENERALIZED AND SIMPLE ONE-DIMENSIONAL COMPRESSIBLE FLOWS
Simple One-Dimensional Flow Formulations 151
5.1 INTRODUCTION 151
5.2 DEVELOPMENT OF THE EQUATIONS FOR GENERALIZED ONE-DIMENSIONAL COMPRESSIBLE FLOW 152
5.3 SIMPLE FLOWS 160
5.4 OTHER GENERALIZED FORMULATIONS 164
5.5 CONCLUSION 165
REVIEW QUESTIONS 166
CHAPTER QUESTIONS 166
Simple Area Change (Isentropic) 167
6.1 INTRODUCTION 167
6.2 THE BEHAVIOR OF SIMPLE AREA CHANGE FLOW 167
6.3 SIMPLE AREA CHANGE (ISENTROPIC) BASIC APPLICATIONS 178
6.4 SUPERSONIC WIND TUNNELS 197
6.5 SUBSONIC AND SUPERSONIC INLETS 213
vi Contents
6.6 CONCLUSION 233
REVIEW QUESTIONS 233
CHAPTER QUESTIONS 235
Other Simple Flows 249
7.1 INTRODUCTION 249
7.2 SIMPLE FRICTIONAL FLOW (FANNO FLOW) 249
7.3 FANNO FLOW APPLICATIONS 259
7.4 FANNO FLOW APPLICATIONS INVOLVING NOZZLES 265
7.5 SIMPLE HEAT ADDITION OR REJECTION (RAYLEIGH FLOW) 290
7.6 RAYLEIGH FLOW APPLICATIONS 302
7.7 RAYLEIGH FLOW APPLICATIONS INVOLVING NOZZLES 306
7.8 NORMAL SHOCKS AND RAYLEIGH AND FANNO LINES 311
7.9 SIMPLE MASS ADDITION OR REMOVAL 314
7.10 CONCLUSION 327
REVIEW QUESTIONS 329
CHAPTER QUESTIONS 331
Nonsimple and Generalized Flows 342
8.1 INTRODUCTION 342
8.2 ISOTHERMAL FLOW 342
8.3 ONE-DIMENSIONAL GENERALIZED FLOW CONCEPTS 351
8.4 GENERALIZED FLOW ANALYSIS WITH NO SONIC POINT PRESENT 356
8.5 GENERALIZED FLOW ANALYSIS WITH A SONIC POINT LOCATION 375
8.6 CONCLUSION 393
REVIEW QUESTIONS 393
CHAPTER QUESTIONS 394
PROJECTS 396
Contents vii
Part IV MULTIDIMENSIONAL COMPRESSIBLE FLOW
yj The Equations of Inviscid Multidimensional Compressible Flow 403
9.1 INTRODUCTION 403
9.2 DIFFERENTIAL FORMS OF THE CONSERVATION EQUATIONS 404 Conservation of Mass 404 Conservation of Momentum 406 Conservation of Energy 408 Divergence Theorem Approach 410
9.3 ALTERNATE FORMS OF THE DIFFERENTIAL EQUATIONS 412
9.4 THE POTENTIAL EQUATION 418
9.5 THE SMALL DISTURBANCE EQUATION 420 Subsonic Wavy Wall 425 Supersonic Wavy Wall 429
9.6 CONCLUSION 432
REVIEW QUESTIONS 432
CHAPTER QUESTIONS 433
10 _ The Method of Characteristics 435
10.1 INTRODUCTION 435
10.2 EQUATION DEVELOPMENT 436
10.3 THE METHOD OF CHARACTERISTICS FOR PLANAR FLOW 444 Planar Flow Equations 444 Field Point Unit Process 446 Wall Point Unit Process 448 Free Surface Point Unit Process 450 Shock Point Unit Process 453 Initial Value Line 455 Zones of Influence and Dependence 457 Properties of Characteristic Regions 459 Centered Expansions 462 Compression Turns 463
10.4 SUPERSONIC NOZZLES 466 Introduction 466 Terminology 467
viii Contents
Minimum-Length Nozzle Expansion Conditions 470 Design of a Planar Minimum-Length Nozzle with Uniform Exit Flow 471 The Programs CHARQ and CHARP 475
10.5 GENERALIZATIONS OF THE METHOD OF CHARACTERISTICS 478 Introduction 478 Axisymmetric Flow 478 Rotational Flow 479 Three-Dimensional Flow 480 Improved Throat Flow Prediction 480 Unsteady Flow 484 Chemically Reacting Flows 485
10.6 CONCLUSION 486
REVIEW QUESTIONS 487
CHAPTER QUESTIONS 487
Party HIGH-TEMPERATURE GAS DYNAMICS
High-Temperature Gas Dynamics 491
11.1 INTRODUCTION 491
11.2 BEHAVIORAL CLASSDJICATION OF GASES 492 The Thermal Equation of State 492 Calorically Perfect Gas 493 Thermally Perfect Gas 494 Chemically Reacting Mixtures of Perfect Gases 494 Real Gas 495
11.3 THE THERMODYNAMICS OF HIGH-TEMPERATURE GASES 505
11.5 APPLICATIONS INVOLVING CALORICALLY IMPERFECT GASES 521
11.6 GAS DYNAMICS WITH CHEMICAL ACTIVITY 527
11.7 EXAMPLES INVOLVING CHEMICALLY REACTING GASES IN EQUILIBRIUM 550
11.8 ADDITIONAL CONSIDERATIONS 564
REVIEW QUESTIONS 565
CHAPTER QUESTIONS 565
Contents
APPENDICES 569
/л . Isentropic Flow 571
TABLE A-l ISENTROPIC FLOW TABLES, 7 = 1.4 571
В Normal Shock Waves 577
TABLE B-l NORMAL SHOCK WAVE TABLES 577
С Oblique and Conical Shock Waves 581
FIG. C-l OBLIQUE SHOCK WAVES: 6 vs 8 582 FIG. C-2 OBLIQUE SHOCK WAVES: M2 vs 8 584 FIG. C-3 OBLIQUE SHOCK WAVES: Cp vs 8 586 FIG. C-4 CONICAL SHOCK WAVES: в vs 8C 588 FIG. C-5 CONICAL SHOCK WAVES: M2 vs 8, 590 FIG. C-6 CONICAL SHOCK WAVES: C„ vs 8C 592
D Prandtl-Meyer Flow 594
TABLE D-1 PRANDTL-MEYER FUNCTIONS, 7 = 1.4 594
С Fanno FLow 596
TABLE E-l FANNO FLOW TABLES, 7 = 1.4 596
F Rayleigh Flow 601
TABLE F-l RAYLEIGH FLOW TABLES, 7 = 1.4 601
(j Simple Mass Addition 606
TABLE G-1 SIMPLE MASS ADDITION TABLES, 7 = 1.4
/ 7 Isothermal Flow 611
TABLE H I ISOTHERMAL FLOW TABLES, 7 = 1.4 611
X Contents
/ The Friction Factor 614
FIG. I-l THE MOODY DIAGRAM 615
TABLE I-l ABSOLUTE ROUGHNESS OF VARIOUS MATERIALS 616
J Standard Atmosphere 619
TABLE J-1 THE STANDARD ATMOSPHERE 620
REFERENCES 621
INDEX 627
