Fundamentals of Aerodynamics

Cover
Title Page
Copyright Page
About the Authors
Contents
Preface to the Seventh Edition
Acknowledgments
PART 1 Fundamental Principles
Chapter 1 Aerodynamics: Some Introductory Thoughts
1.1 Importance of Aerodynamics: Historical Examples
1.2 Aerodynamics: Classification and Practical Objectives
1.3 Road Map for This Chapter
1.4 Some Fundamental Aerodynamic Variables
1.4.1 Units
1.5 Aerodynamic Forces and Moments
1.6 Center of Pressure
1.7 Dimensional Analysis: The Buckingham Pi Theorem
1.8 Flow Similarity
1.9 Fluid Statics: Buoyancy Force
1.10 Types of Flow
1.10.1 Continuum Versus Free Molecule Flow
1.10.2 Inviscid Versus Viscous Flow
1.10.3 Incompressible Versus Compressible Flows
1.10.4 Mach Number Regimes
1.11 Viscous Flow: Introduction to Boundary Layers
1.12 Applied Aerodynamics: The Aerodynamic Coefficients—Their Magnitudes and Variations
1.13 Historical Note: The Illusive Center of Pressure
1.14 Historical Note: Aerodynamic Coefficients
1.15 Summary
1.16 Integrated Work Challenge: Forward-Facing Axial Aerodynamic Force on an Airfoil—Can It Happen and, If So, How?
1.17 Problems
Chapter 2 Aerodynamics: Some Fundamental Principles and Equations
2.1 Introduction and Road Map
2.2 Review of Vector Relations
2.2.1 Some Vector Algebra
2.2.2 Typical Orthogonal Coordinate Systems
2.2.3 Scalar and Vector Fields
2.2.4 Scalar and Vector Products
2.2.5 Gradient of a Scalar Field
2.2.6 Divergence of a Vector Field
2.2.7 Curl of a Vector Field
2.2.8 Line Integrals
2.2.9 Surface Integrals
2.2.10 Volume Integrals
2.2.11 Relations Between Line, Surface, and Volume Integrals
2.2.12 Summary
2.3 Models of the Fluid: Control Volumes and Fluid Elements
2.3.1 Finite Control Volume Approach
2.3.2 Infinitesimal Fluid Element Approach
2.3.3 Molecular Approach
2.3.4 Physical Meaning of the Divergence of Velocity
2.3.5 Specification of the Flow Field
2.4 Continuity Equation
2.5 Momentum Equation
2.6 An Application of the Momentum Equation: Drag of a Two-Dimensional Body
2.6.1 Comment
2.7 Energy Equation
2.8 Interim Summary
2.9 Substantial Derivative
2.10 Fundamental Equations in Terms of the Substantial Derivative
2.11 Pathlines, Streamlines, and Streaklines of a Flow
2.12 Angular Velocity, Vorticity, and Strain
2.13 Circulation
2.14 Stream Function
2.15 Velocity Potential
2.16 Relationship Between the Stream Function and Velocity Potential
2.17 How Do We Solve the Equations?
2.17.1 Theoretical (Analytical) Solutions
2.17.2 Numerical Solutions—Computational Fluid Dynamics (CFD)
2.17.3 The Bigger Picture
2.18 Summary
2.19 Problems
PART 2 Inviscid, Incompressible Flow
Chapter 3 Fundamentals of Inviscid, Incompressible Flow
3.1 Introduction and Road Map
3.2 Bernoulli’s Equation
3.3 Incompressible Flow in a Duct: The Venturi and Low-Speed Wind Tunnel
3.4 Pitot Tube: Measurement of Airspeed
3.5 Pressure Coefficient
3.6 Condition on Velocity for Incompressible Flow
3.7 Governing Equation for Irrotational, Incompressible Flow: Laplace’s Equation
3.7.1 Infinity Boundary Conditions
3.7.2 Wall Boundary Conditions
3.8 Interim Summary
3.9 Uniform Flow: Our First Elementary Flow
3.10 Source Flow: Our Second Elementary Flow
3.11 Combination of a Uniform Flow with a Source and Sink
3.12 Doublet Flow: Our Third Elementary Flow
3.13 Nonlifting Flow over a Circular Cylinder
3.14 Vortex Flow: Our Fourth Elementary Flow
3.15 Lifting Flow over a Cylinder
3.16 The Kutta-Joukowski Theorem and the Generation of Lift
3.17 Nonlifting Flows over Arbitrary Bodies: The Numerical Source Panel Method
3.18 Applied Aerodynamics: The Flow over a Circular Cylinder—The Real Case
3.19 Historical Note: Bernoulli and Euler—The Origins of Theoretical Fluid Dynamics
3.20 Historical Note: d’Alembert and His Paradox
3.21 Summary
3.22 Integrated Work Challenge: Relation Between Aerodynamic Drag and the Loss of Total Pressure in the Flow field
3.23 Integrated Work Challenge: Conceptual Design of a Subsonic Wind Tunnel
3.24 Problems
Chapter 4 Incompressible Flow over Airfoils
4.1 Introduction
4.2 Airfoil Nomenclature
4.3 Airfoil Characteristics
4.4 Philosophy of Theoretical Solutions for Low-Speed Flow over Airfoils: The Vortex Sheet
4.5 The Kutta Condition
4.5.1 Without Friction Could We Have Lift?
4.6 Kelvin’s Circulation Theorem and the Starting Vortex
4.7 Classical Thin Airfoil Theory: The Symmetric Airfoil
4.8 The Cambered Airfoil
4.9 The Aerodynamic Center: Additional Considerations
4.10 Lifting Flows over Arbitrary Bodies: The Vortex Panel Numerical Method
4.11 Modern Low-Speed Airfoils
4.12 Viscous Flow: Airfoil Drag
4.12.1 Estimating Skin-Friction Drag: Laminar Flow
4.12.2 Estimating Skin-Friction Drag: Turbulent Flow
4.12.3 Transition
4.12.4 Flow Separation
4.12.5 Comment
4.13 Applied Aerodynamics: The Flow over an Airfoil—The Real Case
4.14 Historical Note: Early Airplane Design and the Role of Airfoil Thickness
4.15 Historical Note: Kutta, Joukowski, and the Circulation Theory of Lift
4.16 Summary
4.17 Integrated Work Challenge: Wall Effects on Measurements Made in Subsonic Wind Tunnels
4.18 Problems
Chapter 5 Incompressible Flow over Finite Wings
5.1 Introduction: Downwash and Induced Drag
5.2 The Vortex Filament, the Biot-Savart Law, and Helmholtz’s Theorems
5.3 Prandtl’s Classical Lifting-Line Theory
5.3.1 Elliptical Lift Distribution
5.3.2 General Lift Distribution
5.3.3 Effect of Aspect Ratio
5.3.4 Physical Significance
5.4 A Numerical Nonlinear Lifting-Line Method
5.5 The Lifting-Surface Theory and the Vortex Lattice Numerical Method
5.6 Applied Aerodynamics: The Delta Wing
5.7 Historical Note: Lanchester and Prandtl—The Early Development of Finite-Wing Theory
5.8 Historical Note: Prandtl—The Person
5.9 Summary
5.10 Problems
Chapter 6 Three-Dimensional Incompressible Flow
6.1 Introduction
6.2 Three-Dimensional Source
6.3 Three-Dimensional Doublet
6.4 Flow over a Sphere
6.4.1 Comment on the Three-Dimensional Relieving Effect
6.5 General Three-Dimensional Flows: Panel Techniques
6.6 Applied Aerodynamics: The Flow over a Sphere—The Real Case
6.7 Applied Aerodynamics: Airplane Lift and Drag
6.7.1 Airplane Lift
6.7.2 Airplane Drag
6.7.3 Application of Computational Fluid Dynamics for the Calculation of Lift and Drag
6.8 Summary
6.9 Problems
PART 3 Inviscid, Compressible Flow
Chapter 7 Compressible Flow: Some Preliminary Aspects
7.1 Introduction
7.2 A Brief Review of Thermodynamics
7.2.1 Perfect Gas
7.2.2 Internal Energy and Enthalpy
7.2.3 First Law of Thermodynamics
7.2.4 Entropy and the Second Law of Thermodynamics
7.2.5 Isentropic Relations
7.3 Definition of Compressibility
7.4 Governing Equations for Inviscid, Compressible Flow
7.5 Definition of Total (Stagnation) Conditions
7.6 Some Aspects of Supersonic Flow: Shock Waves
7.7 Summary
7.8 Problems
Chapter 8 Normal Shock Waves and Related Topics
8.1 Introduction
8.2 The Basic Normal Shock Equations
8.3 Speed of Sound
8.3.1 Comments
8.4 Special Forms of the Energy Equation
8.5 When Is a Flow Compressible?
8.6 Calculation of Normal Shock-Wave Properties
8.6.1 Comment on the Use of Tables to Solve Compressible Flow Problems
8.7 Measurement of Velocity in a Compressible Flow
8.7.1 Subsonic Compressible Flow
8.7.2 Supersonic Flow
8.8 Summary
8.9 Problems
Chapter 9 Oblique Shock and Expansion Waves
9.1 Introduction
9.2 Oblique Shock Relations
9.3 Supersonic Flow over Wedges and Cones
9.3.1 A Comment on Supersonic Lift and Drag Coefficients
9.4 Shock Interactions and Reflections
9.5 Detached Shock Wave in Front of a Blunt Body
9.5.1 Comment on the Flow Field Behind a Curved Shock Wave: Entropy Gradients and Vorticity
9.6 Prandtl-Meyer Expansion Waves
9.7 Shock-Expansion Theory: Applications to Supersonic Airfoils
9.8 A Comment on Lift and Drag Coefficients
9.9 The X-15 and Its Wedge Tail
9.10 VISCOUS FLOW: Shock-Wave/ Boundary-Layer Interaction
9.11 Historical Note: Ernst Mach—A Biographical Sketch
9.12 Summary
9.13 Integrated Work Challenge: Relation Between Supersonic Wave Drag and Entropy Increase—Is There a Relation?
9.14 Integrated Work Challenge: The Sonic Boom
9.15 Problems
Chapter 10 Compressible Flow Through Nozzles, Diffusers, and Wind Tunnels
10.1 Introduction
10.2 Governing Equations for Quasi-One-Dimensional Flow
10.3 Nozzle Flows
10.3.1 More on Mass Flow
10.4 Diffusers
10.5 Supersonic Wind Tunnels
10.6 Viscous Flow: Shock-Wave/Boundary-Layer Interaction Inside Nozzles
10.7 Summary
10.8 Integrated Work Challenge: Conceptual Design of a Supersonic Wind Tunnel
10.9 Problems
Chapter 11 Subsonic Compressible Flow over Airfoils: Linear Theory
11.1 Introduction
11.2 The Velocity Potential Equation
11.3 The Linearized Velocity Potential Equation
11.4 Prandtl-Glauert Compressibility Correction
11.5 Improved Compressibility Corrections
11.6 Critical Mach Number
11.6.1 A Comment on the Location of Minimum Pressure (Maximum Velocity)
11.7 Drag-Divergence Mach Number: The Sound Barrier
11.8 The Area Rule
11.9 The Supercritical Airfoil
11.10 CFD Applications: Transonic Airfoils and Wings
11.11 Applied Aerodynamics: The Blended Wing Body
11.12 Historical Note: High-Speed Airfoils—Early Research and Development
11.13 Historical Note: The Origin of the Swept-Wing Concept
11.14 Historical Note: Richard T. Whitcomb—Architect of the Area Rule and the Supercritical Wing
11.15 Summary
11.16 Integrated Work Challenge: Transonic Testing by the Wing-Flow Method
11.17 Problems
Chapter 12 Linearized Supersonic Flow
12.1 Introduction
12.2 Derivation of the Linearized Supersonic Pressure Coefficient Formula
12.3 Application to Supersonic Airfoils
12.4 Viscous Flow: Supersonic Airfoil Drag
12.5 Summary
12.6 Problems
Chapter 13 Introduction to Numerical Techniques for Nonlinear Supersonic Flow
13.1 Introduction: Philosophy of Computational Fluid Dynamics
13.2 Elements of the Method of Characteristics
13.2.1 Internal Points
13.2.2 Wall Points
13.3 Supersonic Nozzle Design
13.4 Elements of Finite-Difference Methods
13.4.1 Predictor Step
13.4.2 Corrector Step
13.5 The Time-Dependent Technique: Application to Supersonic Blunt Bodies
13.5.1 Predictor Step
13.5.2 Corrector Step
13.6 Flow over Cones
13.6.1 Physical Aspects of Conical Flow
13.6.2 Quantitative Formulation
13.6.3 Numerical Procedure
13.6.4 Physical Aspects of Supersonic Flow over Cones
13.7 Summary
13.8 Problem
Chapter 14 Elements of Hypersonic Flow
14.1 Introduction
14.2 Qualitative Aspects of Hypersonic Flow
14.3 Newtonian Theory
14.4 The Lift and Drag of Wings at Hypersonic Speeds: Newtonian Results for a Flat Plate at Angle of Attack
14.4.1 Accuracy Considerations
14.5 Hypersonic Shock-Wave Relations and Another Look at Newtonian Theory
14.6 Mach Number Independence
14.7 Hypersonics and Computational Fluid Dynamics
14.8 Hypersonic Viscous Flow: Aerodynamic Heating
14.8.1 Aerodynamic Heating and Hypersonic Flow—The Connection
14.8.2 Blunt Versus Slender Bodies in Hypersonic Flow
14.8.3 Aerodynamic Heating to a Blunt Body
14.9 Applied Hypersonic Aerodynamics: Hypersonic Waveriders
14.9.1 Viscous-Optimized Waveriders
14.10 Summary
14.11 Problems
PART 4 Viscous Flow
Chapter 15 Introduction to the Fundamental Principles and Equations of Viscous Flow
15.1 Introduction
15.2 Qualitative Aspects of Viscous Flow
15.3 Viscosity and Thermal Conduction
15.4 The Navier-Stokes Equations
15.5 The Viscous Flow Energy Equation
15.6 Similarity Parameters
15.7 Solutions of Viscous Flows: A Preliminary Discussion
15.8 Summary
15.9 Problems
Chapter 16 A Special Case: Couette Flow
16.1 Introduction
16.2 Couette Flow: General Discussion
16.3 Incompressible (Constant Property) Couette Flow
16.3.1 Negligible Viscous Dissipation
16.3.2 Equal Wall Temperatures
16.3.3 Adiabatic Wall Conditions (Adiabatic Wall Temperature)
16.3.4 Recovery Factor
16.3.5 Reynolds Analogy
16.3.6 Interim Summary
16.4 Compressible Couette Flow
16.4.1 Shooting Method
16.4.2 Time-Dependent Finite-Difference Method
16.4.3 Results for Compressible Couette Flow
16.4.4 Some Analytical Considerations
16.5 Summary
Chapter 17 Introduction to Boundary Layers
17.1 Introduction
17.2 Boundary-Layer Properties
17.3 The Boundary-Layer Equations
17.4 How Do We Solve the Boundary-Layer Equations?
17.5 Summary
Chapter 18 Laminar Boundary Layers
18.1 Introduction
18.2 Incompressible Flow over a Flat Plate: The Blasius Solution
18.3 Compressible Flow over a Flat Plate
18.3.1 A Comment on Drag Variation with Velocity
18.4 The Reference Temperature Method
18.4.1 Recent Advances: The Meador-Smart Reference Temperature Method
18.5 Stagnation Point Aerodynamic Heating
18.6 Boundary Layers over Arbitrary Bodies: Finite-Difference Solution
18.6.1 Finite-Difference Method
18.7 Summary
18.8 Problems
Chapter 19 Turbulent Boundary Layers
19.1 Introduction
19.2 Results for Turbulent Boundary Layers on a Flat Plate
19.2.1 Reference Temperature Method for Turbulent Flow
19.2.2 The Meador-Smart Reference Temperature Method for Turbulent Flow
19.2.3 Prediction of Airfoil Drag
19.3 Turbulence Modeling
19.3.1 The Baldwin-Lomax Model
19.4 Final Comments
19.5 Summary
19.6 Problems
Chapter 20 Navier-Stokes Solutions: Some Examples
20.1 Introduction
20.2 The Approach
20.3 Examples of Some Solutions
20.3.1 Flow over a Rearward-Facing Step
20.3.2 Flow over an Airfoil
20.3.3 Flow over a Complete Airplane
20.3.4 Shock-Wave/Boundary-Layer Interaction
20.3.5 Flow over an Airfoil with a Protuberance
20.4 The Issue of Accuracy for the Prediction of Skin Friction Drag
20.5 Summary
Appendix A Isentropic Flow Properties
Appendix B Normal Shock Properties
Appendix C Prandtl-Meyer Function and Mach Angle
Appendix D Standard Atmosphere, SI Units
Appendix E Standard Atmosphere, English Engineering Units
References
Index