Fundamentals of Aerodynamics

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Contents
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 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 AngularVelocity,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 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 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 Man
		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 Summary
		6.8 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 ShockWaves and Related Topics
		8.1 Introduction
		8.2 The Basic Normal Shock Equations
		8.3 Speed of Sound
		8.4 Special Forms of the Energy Equation
		8.5 When Is a Flow Compressible?
		8.6 Calculation of Normal Shock-Wave Properties
		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 ExpansionWaves
		9.1 Introduction
		9.2 Oblique Shock Relations
		9.3 Supersonic Flow over Wedges and Cones
		9.4 Shock Interactions and Reflections
		9.5 Detached Shock Wave in Front of a Blunt Body
		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 Viscous Flow: Shock-Wave/ Boundary-Layer Interaction
		9.10 Historical Note: Ernst Mach—A Biographical Sketch
		9.11 Summary
		9.12 Problems
	Chapter 10: Compressible FlowThrough Nozzles, Diffusers, andWind 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 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 Historical Note: High-Speed Airfoils—Early Research and Development
		11.12 Historical Note: Richard T. Whitcomb— Architect of the Area Rule and the Supercritical Wing
		11.13 Summary
		11.14 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 Summary
		13.7 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 Summary
		14.9 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: Some Special Cases; Couette and Poiseuille Flows
		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 Two-Dimensional Poiseuille Flow
		16.6 Summary
			16.6.1 Couette Flow
			16.6.2 Poiseuille Flow
	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 Aerodynamic Research Activities in India
Appendix B Isentropic Flow Properties
Appendix C Normal Shock Properties
Appendix D Prandtl-Meyer Function and Mach Angle
Appendix E Standard Atmosphere, SI Units
Appendix F Standard Atmosphere, English Engineering Units
Bibliography
Index