Fundamentals of Aerodynamics

Transcription

1 Fundamentals of Aerodynamics Fourth Edition John D. Anderson, Jr. Curator of Aerodynamics National Air and Space Museum Smithsonian Institution and Professor Emeritus University of Maryland Me Graw Hill Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto

2 CONTENTS Preface to the First Edition Preface to the Fourth Edition xix xxiii PART J. Fundamental Principles 1 Chapter 1 Aerodynamics: Some Introductory Thoughts Importance of Aerodynamics: Historical Examples Aerodynamics: Classification and Practical Objectives Road Map for This Chapter Some Fundamental Aerodynamic Variables Units Aerodynamic Forces and Moments Center of Pressure Dimensional Analysis: The Buckingham Pi Theorem Flow Similarity Fluid Statics: Buoyancy Force Types of Flow Continuum Versus Free Molecule Flow Inviscid Versus Viscous Flow Incompressible Versus Compressible Flows Mach Number Regimes Viscous Flow: Introduction to Boundary Layers Applied Aerodynamics: The Aerodynamic Coefficients Their Magnitudes and Variations Historical Note: The Illusive Center of Pressure Historical Note: Aerodynamic Coefficients Summary Problems 92 Chapter 2 Aerodynamics: Some Fundamental Principles and Equations Introduction and Road Map Review of Vector Relations Some Vector Algebra Typical Orthogonal Coordinate Systems Scalar and Vector Fields Scalar and Vector Products Gradient of a Scalar Field Divergence of a Vector Field Curl of a Vector Field Line Integrals Surface Integrals Volume Integrals Relations Between Line, Surface, and Volume Integrals Summary Models of the Fluid: Control Volumes and Fluid Elements Finite Control Volume Approach Infinitesimal Fluid Element Approach Molecular Approach 111

3 xii Contents Physical Meaning of the Divergence of Velocity Specification of the Flow Field 113 Continuity Equation 117 Momentum Equation 122 An Application of the Momentum Equation: Drag of a Two-Dimensional Body Comment 136 Energy Equation 136 Interim Summary 141 Substantial Derivative Fundamental Equations in Terms of the Substantial Derivative Pathlines, Streamlines, and Streaklines of a Flow Angular Velocity, Vorticity, and Strain Circulation Stream Function Velocity Potential Relationship Between the Stream Function and Velocity Potential How Do We Solve the Equations? Theoretical (Analytical) Solutions Numerical Solutions Computational Fluid Dynamics (CFD) The Bigger Picture Summary Problems 185 PART Tnvjscirt, Incompressible Flow 187 Chapter 3 Fundamentals of Inviscid, Incompressible Flow Introduction and Road Map 3.2 Bernoulli's Equation Incompressible Flow in a Duct: The Venturi and Low-Speed Wind Tunnel Pitot Tube: Measurement of Airspeed Pressure Coefficient Condition on Velocity for Incompressible Flow Governing Equation for Irrotational, Incompressible Flow: Laplace's Equation Infinity Boundary Conditions Wall Boundary Conditions Interim Summary Uniform Flow: Our First Elementary Flow Source Flow: Our Second Elementary Flow Combination of a Uniform Flow with a Source and Sink Doublet Flow: Our Third Elementary Flow Nonlifting Flow over a Circular Cylinder Vortex Flow: Our Fourth Elementary Flow Lifting Flow over a Cylinder The Kutta-Joukowski Theorem and the Generation of Lift Nonlifting Flows over Arbitrary Bodies: The Numerical Source Panel Method Applied Aerodynamics: The Flow over a Circular Cylinder The Real Case Historical Note: Bernoulli and Euler The Origins of Theoretical Fluid Dynamics Historical Note: d'alembert and His Paradox Summary Problems 291

4 Contents xiii Chapter 4 Incompressible Flow over Airfoils Introduction Airfoil Nomenclature Airfoil Characteristics Philosophy of Theoretical Solutions for Low-Speed Flow over Airfoils: The Vortex Sheet The Kutta Condition Without Friction Could We Have Lift? Kelvin's Circulation Theorem and the Starting Vortex Classical Thin Airfoil Theory: The Symmetric Airfoil The Cambered Airfoil The Aerodynamic Center: Additional Considerations Lifting Flows over Arbitrary Bodies: The Vortex Panel Numerical Method Modern Low-Speed Airfoils Viscous Flow: Airfoil Drag Estimating Skin-Friction Drag: Laminar Flow Estimating Skin-Friction Drag: Turbulent Flow Transition Flow Separation Comment Applied Aerodynamics: The Flow over an Airfoil The Real Case Historical Note: Early Airplane Design and the Role of Airfoil Thickness Historical Note: Kutta, Joukowski, and the Circulation Theory of Lift Summary Problems 388 Chapter 5 Incompressible Flow over Finite Wings Introduction: Downwash and Induced Drag The Vortex Filament, the Biot-Savart Law, and Helmholtz's Theorems Prandtl's Classical Lifting-Line Theory Elliptical Lift Distribution General Lift Distribution Effect of Aspect Ratio Physical Significance A Numerical Nonlinear Lifting-Line Method The Lifting-Surface Theory and the Vortex Lattice Numerical Method Applied Aerodynamics: The Delta Wing Historical Note: Lanchester and Prandtl The Early Development of Finite-Wing Theory Historical Note: Prandtl The Man Summary Problems 464 Chapter 6 Three-Dimensional Incompressible Flow Introduction Three-Dimensional Source Three-Dimensional Doublet Flow over a Sphere Comment on the Three-Dimensional Relieving Effect General Three-Dimensional Flows: Panel Techniques Applied Aerodynamics: The Flow over a Sphere The Real Case Summary Problems 481

5 xiv Contents PART mj Tnviscid, Compressible Flow 483 Chapter 7 Compressible Flow: Some Preliminary Aspects Introduction A Brief Review of Thermodynamics Perfect Gas Internal Energy and Enthalpy First Law of Thermodynamics Entropy and the Second Law of Thermodynamics Isentropic Relations Definition of Compressibility Governing Equations for Inviscid, Compressible Flow Definition of Total (Stagnation) Conditions Some Aspects of Supersonic Flow: Shock Waves Summary Problems 513 Chapter 8 Normal Shock Waves and Related Topics Introduction The Basic Normal Shock Equations Speed of Sound Special Forms of the Energy Equation When Is a Flow Compressible? Calculation of Normal Shock-Wave Properties Measurement of Velocity in a Compressible Flow Subsonic Compressible Flow Supersonic Flow Summary Problems 556 Chapter 9 Oblique Shock and Expansion Waves Introduction Oblique Shock Relations Supersonic Flow over Wedges and Cones Shock Interactions and Reflections Detached Shock Wave in Front of a Blunt Body Prandtl-Meyer Expansion Waves Shock-Expansion Theory: Applications to Supersonic Airfoils A Comment on Lift and Drag Coefficients Viscous Flow: Shock-Wave/ Boundary-Layer Interaction Historical Note: Ernst Mach A Biographical Sketch Summary Problems 612 Chapter 10 Compressible Flow Through Nozzles, Diffusers, and Wind Tunnels Introduction Governing Equations for Quasi-One-Dimensional Flow Nozzle Flows More on Mass Flow Diffusers Supersonic Wind Tunnels Viscous Flow: Shock-Wave/ Boundary-Layer Interaction Inside Nozzles Summary Problems 655

6 Contents Chapter 11 Subsonic Compressible Flow over Airfoils: Linear Theory 657 Chapter 13 Introduction to Numerical Techniques for Nonlinear Supersonic Flow Introduction The Velocity Potential Equation The Linearized Velocity Potential Equation Prandtl-Glauert Compressibility Correction Improved Compressibility Corrections Critical Mach Number A Comment on the Location of Minimum Pressure (Maximum Velocity) Drag-Divergence Mach Number: The Sound Barrier The Area Rule The Supercritical Airfoil CFD Applications: Transonic Airfoils and Wings Historical Note: High-Speed Airfoils Early Research and Development Historical Note: Richard T. Whitcomb Architect of the Area Rule and the Supercritical Wing Summary Problems 707 Chapter 12 Linearized Supersonic Flow Introduction Derivation of the Linearized Supersonic Pressure Coefficient Formula Application to Supersonic Airfoils Viscous Flow: Supersonic Airfoil Drag Summary Problems Introduction: Philosophy of Computational Fluid Dynamics Elements of the Method of Characteristics Internal Points Wall Points Supersonic Nozzle Design Elements of Finite-Difference Methods Predictor Step Corrector Step The Time-Dependent Technique: Application to Supersonic Blunt Bodies Predictor Step Corrector Step Summary Problem 754 Chapter 14 Elements of Hypersonic Flow Introduction Qualitative Aspects of Hypersonic Flow Newtonian Theory The Lift and Drag of Wings at Hypersonic Speeds: Newtonian Results for a Flat Plate at Angle of Attack Accuracy Considerations Hypersonic Shock-Wave Relations and Another Look at Newtonian Theory Mach Number Independence Hypersonics and Computational Fluid Dynamics Summary Problems 787

7 xvi Contents PART *T Viscous Flow 789 Chapter 15 Introduction to the Fundamental Principles and Equations of Viscous Flow Introduction Qualitative Aspects of Viscous Flow Viscosity and Thermal Conduction The Navier-Stokes Equations The Viscous Flow Energy Equation Similarity Parameters Solutions of Viscous Flows: A Preliminary Discussion Summary Problems 823 Chapter 16 Some Special Cases; Couette and Poiseuille Flows Introduction Couette Flow: General Discussion Incompressible (Constant Property) Couette Flow Negligible Viscous Dissipation Equal Wall Temperatures Adiabatic Wall Conditions (Adiabatic Wall Temperature) Recovery Factor Reynolds Analogy Interim Summary Compressible Couette Flow Shooting Method Time-Dependent Finite-Difference Method Results for Compressible Couette Flow Some Analytical Considerations Two-Dimensional Poiseuille Flow Summary Couette Flow Poiseuille Flow 865 Chapter 17 Introduction to Boundary Layers Introduction Boundary-Layer Properties The Boundary-Layer Equations How Do We Solve the Boundary-Layer Equations? Summary 881 Chapter 18 Laminar Boundary Layers Introduction Incompressible Flow over a Flat Plate: The Blasius Solution Compressible Flow over a Flat Plate A Comment on Drag Variation with Velocity The Reference Temperature Method Recent Advances: The Meador-Smart Reference Temperature Method Stagnation Point Aerodynamic Heating Boundary Layers over Arbitrary Bodies: Finite-Difference Solution Finite-Difference Method Summary Problems 920 Chapter 19 Turbulent Boundary Layers Introduction Results for Turbulent Boundary Layers on a Flat Plate 922

8 Contents xvii Reference Temperature Method for Turbulent Flow The Meador-Smart Reference Temperature Method for Turbulent Flow Prediction of Airfoil Drag Turbulence Modeling The Baldwin-Lomax Model Final Comments Summary Problems 932 Chapter 20 Navier-Stokes Solutions: Some Examples Introduction The Approach Examples of Some Solutions Flow over a Rearward-Facing Step Flow over an Airfoil Flow over a Complete Airplane Shock-Wave/Boundary-Layer Interaction Flow over an Airfoil with a Protuberance The Issue of Accuracy for the Prediction of Skin Friction Drag Summary 947 Appendix A Isentropic Flow Properties 949 Appendix B Normal Shock Properties 955 Appendix C Prandtl-Meyer Function and Mach Angle 959 Appendix D Standard Atmosphere, SI Units 963 Appendix E Standard Atmosphere, English Engineering Units 973 Bibliography 981 Index 987