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Contents Preface to the First Edition xv Preface to the Fourth Edition xix PART 1 Fundamental Principles 1 Chapter 1 Aerodynamics: Some Introductory Thoughts 3 1.1 Importance of Aerodynamics: Historical Examples 3 1.2 Aerodynamics: Classification and Practical Objectives 10 1.3 Road Map for This Chapter 12 1.4 Some Fundamental Aerodynamic Variables 12 1.5 Aerodynamic Forces and Moments 15 1.6 Center of Pressure 28 1.7 Dimensional Analysis: The Buckingham Pi Theorem 30 1.8 Flow Similarity 36 1.9 Fluid Statics: Buoyancy Force 48 1.10 Types of Flow 54 1.10.1 Continuum Versus Free Molecule Flow 54 1.10.2 Inviscid Versus Viscous Flow 54 1.10.3 Incompressible Versus Compressible Flows 56 1.10.4 Mach Number Regimes 57 1.11 Applied Aerodynamics: The Aerodynamic Coefficients Their Magnitudes and Variations 60 1.12 Historical Note: The Illusive Center of Pressure 72 1.13 Historical Note: Aerodynamic Coefficients 76 1.14 Summary 79 Problems 80 Chapter 2 Aerodynamics: Some Fundamental Principles and Equations 85 2.1 Introduction and Road Map 85 2.2 Review of Vector Relations 87 2.2.1 Some Vector Algebra 87 2.2.2 Typical Orthogonal Coordinate Systems 88 2.2.3 Scalar and Vector Fields 91 2.2.4 Scalar and Vector Products 92 2.2.5 Gradient of a Scalar Field 92 2.2.6 Divergence of a Vector Field 94 2.2.7 Curl of a Vector Field 95 2.2.8 Line Integrals 96 2.2.9 Surface Integrals 97 2.2.10 Volume Integrals 97 2.2.11 Relations Between Line, Surface, and Volume Integrals 98 2.2.12 Summary 99 2.3 Models of the Fluid: Control Volumes and Fluid Elements 99 2.3.1 Finite Control Volume Approach 100 2.3.2 Infinitesimal Fluid Element Approach 100 2.3.3 Molecular Approach 101 2.3.4 Physical Meaning of the Divergence of Velocity 101 2.3.5 Specification of the Flow Field 103 2.4 Continuity Equation 107 2.5 Momentum Equation 112 2.6 An Application of the Momentum Equation: Drag of a Two-Dimensional Body 116 2.6.1 Comment 125 2.7 Energy Equation 125 2.8 Interim Summary 131 2.9 Substantial Derivative 131 2.10 Fundamental Equations in Terms of the Substantial Derivative 134 2.11 Pathlines, Streamlines, and Streaklines of a Flow 136 2.12 Angular Velocity, Vorticity, and Strain 141 2.13 Circulation 151 2.14 Stream Function 153 2.15 Velocity Potential 158 2.16 Relationship Between the Stream Function and Velocity Potential 159 2.17 How Do We Solve the Equations? 160 2.17.1 Theoretical (Analytical) Solutions 161 2.17.2 Numerical Solutions Computational Fluid Dynamics (CFD) 162 2.17.3 The Bigger Picture 169 2.18 Summary 170 Problems 173 PART 2 Inviscid, Incompressible Flow 175 Chapter 3 Fundamentals of Inviscid, Incompressible Flow 177 3.1 Introduction and Road Map 177 3.2 Bernoulli's Equation 180 3.3 Incompressible Flow in a Duct: The Venturi and Low-Speed Wind Tunnel 184 3.4 Pitot Tube: Measurement of Airspeed 194 3.5 Pressure Coefficient 203 3.6 Condition on Velocity for Incompressible Flow 205 3.7 Governing Equation for Irrotational, Incompressible Flow: Laplace's Equation 206 3.7.1 Infinity Boundary Conditions 208 3.7.2 Wall Boundary Conditions 209 3.8 Interim Summary 210 3.9 Uniform Flow: Our First Elementary Flow 210 3.10 Source Flow: Our Second Elementary Flow 213 3.11 Combination of a Uniform Flow with a Source and Sink 217 3.12 Doublet Flow: Our Third Elementary Flow 221 3.13 Nonlifting Flow Over a Circular Cylinder 223 3.14 Vortex Flow: Our Fourth Elementary Flow 229 3.15 Lifting Flow Over a Cylinder 232 3.16 The Kutta-Joukowski Theorem and the Generation of Lift 244 3.17 Nonlifting Flows Over Arbitrary Bodies: The Numerical Source Panel Method 247 3.18 Applied Aerodynamics: The Flow Over a Circular Cylinder The Real Case 256 3.19 Historical Note: Bernoulli and Euler The Origins of Theoretical Fluid Dynamics 265 3.20 Historical Note: d'Alembert and His Paradox 269 3.21 Summary 270 Problems 273 Chapter 4 Incompressible Flows over Airfoils 277 4.1 Introduction 277 4.2 Airfoil Nomenclature 278 4.3 Airfoil Characteristics 281 4.4 Philosophy of Theoretical Solutions for Low-Speed Flow over Airfoils: The Vortex Sheet 285 4.5 The Kutta Condition 290 4.5.1 Without Friction Could We Have Lift? 294 4.6 Kelvin's Circulation Theorem and the Starting Vortex 295 4.7 Classical Thin Airfoil Theory: The Symmetric Airfoil 298 4.8 The Cambered Airfoil 306 4.9 The Aerodynamic Center: Additional Considerations 315 4.10 Lifting Flows over Arbitrary Bodies: The Vortex Panel Numerical Method 319 4.11 Modern Low-Speed Airfoils 325 4.12 Applied Aerodynamics: The Flow over an Airfoil The Real Case 329 4.13 Historical Note: Early Airplane Design and the Role of Airfoil Thickness 340 4.14 Historical Note: Kutta, Joukowski, and the Circulation Theory of Lift 345 4.15 Summary 347 Problems 349 Chapter 5 Incompressible Flow over Finite Wings 351 5.1 Introduction: Downwash and Induced Drag 351 5.2 The Vortex Filament, the Biot-Savart Law, and Helmholtz's Theorems 357 5.3 PrandtlOs Classical Lifting-Line Theory 360 5.3.1 Elliptical Lift Distribution 367 5.3.2 General Lift Distribution 371 5.3.3 Effect of Aspect Ratio 375 5.3.4 Physical Significance 381 5.4 A Numerical Nonlinear Lifting-Line Method 387 5.5 The Lifting-Surface Theory and the Vortex Lattice Numerical Method 391 5.6 Applied Aerodynamics: The Delta Wing 398 5.7 Historical Note: Lanchester and Prandtl The Early Development of Finite-Wing Theory 408 5.8 Historical Note: Prandtl The Man 412 5.9 Summary 415 Problems 416 Chapter 6 Three-Dimensional Incompressible Flow 419 6.1 Introduction 419 6.2 Three-Dimensional Source 420 6.3 Three-Dimensional Doublet 422 6.4 Flow Over a Sphere 424 6.5 General Three-Dimensional Flows: Panel Techniques 426 6.6 Applied Aerodynamics: The Flow Over a Sphere The Real Case 429 6.7 Summary 432 Problems 432 PART 3 Inviscid, Compressible Flow 435 Chapter 7 Compressible Flow: Some Preliminary Aspects 437 7.1 Introduction 437 7.2 A Brief Review of Thermodynamics 439 7.2.1 Perfect Gas 440 7.2.2 Internal Energy and Enthalpy 440 7.2.3 First Law of Thermodynamics 442 7.2.4 Entropy and the Second Law of Thermodynamics 443 7.2.5 Isentropic Relations 445 7.3 Definition of Compressibility 448 7.4 Governing Equations for Inviscid, Compressible Flow 449 7.5 Definition of Total (Stagnation) Conditions 451 7.6 Some Aspects of Supersonic Flow: Shock Waves 456 7.7 Summary 460 Problems 462 Chapter 8 Normal Shock Waves and Related Topics 465 8.1 Introduction 465 8.2 The Basic Normal Shock Equations 467 8.3 Speed of Sound 471 8.4 Special Forms of the Energy Equation 475 8.5 When Is a Flow Compressible? 482 8.6 Calculation of Normal Shock-Wave Properties 485 8.7 Measurement of Velocity in a Compressible Flow 494 8.7.1 Subsonic Compressible Flow 495 8.7.2 Supersonic Flow 495 8.8 Summary 498 Problems 501 Chapter 9 Oblique Shock and Expansion Waves 503 9.1 Introduction 503 9.2 Oblique Shock Relations 508 9.3 Supersonic Flow Over Wedges and Cones 521 9.4 Shock Interactions and Reflections 525 9.5 Detached Shock Wave in Front of a Blunt Body 530 9.6 Prandtl-Meyer Expansion Waves 532 9.7 Shock-Expansion Theory: Applications to Supersonic Airfoils 544 9.8 A Comment on Lift and Drag Coefficients 548 9.9 Historical Note: Ernst Mach A Biographical Sketch 548 9.10 Summary 550 Problems 551 Chapter 10 Compressible Flow through Nozzles, Diffusers, and Wind Tunnels 555 10.1 Introduction 555 10.2 Governing Equations for Quasi-One-Dimensional Flow 558 10.3 Nozzle Flows 566 10.4 Diffusers 577 10.5 Supersonic Wind Tunnels 579 10.6 Summary 584 Problems 585 Chapter 11 Subsonic Compressible Flow over Airfoils: Linear Theory 587 11.1 Introduction 587 11.2 The Velocity Potential Equation 589 11.3 The Linearized Velocity Potential Equation 592 11.4 Prandtl-Glauert Compressibility Correction 597 11.5 Improved Compressibility Corrections 602 11.6 Critical Mach Number 604 11.6.1 A Comment on the Location of Minimum Pressure (Maximum Velocity) 612 11.7 Drag-Divergence Mach Number: The Sound Barrier 612 11.8 The Area Rule 619 11.9 The Supercritical Airfoil 622 11.10 CFD Applications: Transonic Airfoils and Wings 624 11.11 Historical Note: High-Speed Airfoils Early Research and Development 629 11.12 Historical Note: Richard T. Whitcomb Architect of the Area Rule and the Supercritical Wing 633 11.13 Summary 635 Problems 636 Chapter 12 Linearized Supersonic Flow 639 12.1 Introduction 639 12.2 Derivation of the Linearized Supersonic Pressure Coefficient Formula 640 12.3 Application to Supersonic Airfoils 643 12.4 Summary 649 Problems 650 Chapter 13 Introduction to Numerical Techniques for Nonlinear Supersonic Flow 651 13.1 Introduction: Philosophy of Computational Fluid Dynamics 651 13.2 Elements of the Method of Characteristics 654 13.2.1 Internal Points 659 13.2.2 Wall Points 661 13.3 Supersonic Nozzle Design 662 13.4 Elements of Finite-Difference Methods 664 13.4.1 Predictor Step 670 13.4.2 Corrector Step 670 13.5 The Time-Dependent Technique: Application to Supersonic Blunt Bodies 671 13.5.1 Predictor Step 675 13.5.2 Corrector Step 675 13.6 Summary 679 Problems 680 Chapter 14 Elements of Hypersonic Flow 681 14.1 Introduction 681 14.2 Qualitative Aspects of Hypersonic Flow 682 14.3 Newtonian Theory 686 14.4 The Lift and Drag of Wings at Hypersonic Speeds: Newtonian Results for a Flat Plate at Angle of Attack 690 14.4.1 Accuracy Considerations 697 14.5 Hypersonic Shock-Wave Relations and Another Look at Newtonian Theory 699 14.6 Mach Number Independence 704 14.7 Hypersonics and Computational Fluid Dynamics 706 14.8 Summary 709 Problems 709 PART 4 Viscous Flow 711 Chapter 15 Introduction to the Fundamental Principles and Equations of Viscous Flow 713 15.1 Introduction 713 15.2 Qualitative Aspects of Viscous Flow 715 15.3 Viscosity and Thermal Conduction 722 15.4 The Navier-Stokes Equations 727 15.5 The Viscous Flow Energy Equation 730 15.6 Similarity Parameters 734 15.7 Solutions of Viscous Flows: A Preliminary Discussion 738 15.8 Summary 742 Problems 743 Chapter 16 Some Special Cases; Couette and Poiseuille Flows 745 16.1 Introduction 745 16.2 Couette Flow: General Discussion 746 16.3 Incompressible (Constant Property) Couette Flow 749 16.3.1 Negligible Viscous Dissipation 756 16.3.2 Equal Wall Temperatures 757 16.3.3 Adiabatic Wall Conditions (Adiabatic Wall Temperature) 759 16.3.4 Recovery Factor 761 16.3.5 Reynolds Analogy 763 16.3.6 Interim Summary 764 16.4 Compressible Couette Flow 766 16.4.1 Shooting Method 767 16.4.2 Time-Dependent Finite-Difference Method 769 16.4.3 Results for Compressible Couette Flow 773 16.4.4 Some Analytical Considerations 775 16.5 Two-Dimensional Poiseuille Flow 781 16.6 Summary 785 16.6.1 Couette Flow 785 16.6.2 Poiseuille Flow 785 Chapter 17 Introduction to Boundary Layers 787 17.1 Introduction 787 17.2 Boundary-Layer Properties 789 17.3 The Boundary-Layer Equations 795 17.4 How Do We Solve the Boundary-Layer Equations? 799 17.5 Summary 800 Chapter 18 Laminar Boundary Layers 803 18.1 Introduction 803 18.2 Incompressible Flow over a Flat Plate: The Blasius Solution 804 18.3 Compressible Flow over a Flat Plate 811 18.3.1 A Comment on Drag Variation with Velocity 822 18.4 The Reference Temperature Method 823 18.5 Stagnation Point Aerodynamic Heating 825 18.6 Boundary Layers over Arbitrary Bodies: Finite-Difference Solution 831 18.6.1 Finite-Difference Method 833 18.7 Summary 837 Chapter 19 Turbulent Boundary Layers 839 19.1 Introduction 839 19.2 Results for Turbulent Boundary Layers on a Flat Plate 840 19.2.1 Reference Temperature Method for Turbulent Flow 841 19.3 Turbulence Modeling 843 19.3.1 The Baldwin-Lomax Model 843 19.4 Final Comments 846 19.5 Summary 847 Problems 847 Chapter 20 Navier-Stokes Solutions: Some Examples 849 20.1 Introduction 849 20.2 The Approach 849 20.3 Examples of Some Solutions 851 20.3.1 Flow over a Rearward-Facing Step 851 20.3.2 Flow over an Airfoil 852 20.3.3 Flow over a Complete Airplane 852 20.3.4 Shock-Wave/Boundary-Layer Interaction 853 20.3.5 Flow over an Airfoil with a Protuberance 856 20.4 The Issue of Accuracy for the Prediction of Skin Friction Drag 858 20.5 Summary 864 Appendix A Isentropic Flow Properties 865 Appendix B Normal Shock Properties 871 Appendix C Prandtl-Meyer Function and Mach Angle 875 Bibliography 877 Index 882
Library of Congress Subject Headings for this publication:
Aerodynamics.