Unsteady Aerodynamics: Potential and Vortex Methods (Aerospace Series)

Title Page
Copyright
Contents
Preface
About the Companion Website
Chapter 1 Introduction
	1.1 Why Potential and Vortex Methods?
	1.2 Outline of This Book
	References
Chapter 2 Unsteady Flow Fundamentals
	2.1 Introduction
	2.2 From Navier–Stokes to Unsteady Incompressible Potential Flow
		2.2.1 Irrotational Flow
		2.2.2 Laplace\'s and Bernoulli\'s Equations
		2.2.3 Motion in an Incompressible, Inviscid, Irrotational Fluid
	2.3 Incompressible Potential Flow Solutions
		2.3.1 Green\'s Third Identity
		2.3.2 Solutions in Two Dimensions
	2.4 From Navier–Stokes to Unsteady Compressible Potential Flow
		2.4.1 The Compressible Bernoulli Equation
		2.4.2 The Full Potential Equation
		2.4.3 The Transonic Small Disturbance Equation
		2.4.4 The Linearised Small Disturbance Equation
		2.4.5 The Compressible Unsteady Pressure Coefficient
		2.4.6 Motion in a Compressible, Inviscid, Irrotational Fluid
	2.5 Subsonic Linearised Potential Flow Solutions
	2.6 Supersonic Linearised Potential Flow Solutions
	2.7 Vorticity and Circulation
		2.7.1 Solutions of the Vorticity Transport Equations
		2.7.2 Vorticity‐Moment and Kutta–Joukowski Theorems
		2.7.3 The Wake and the Kutta Condition
	2.8 Concluding Remarks
	References
Chapter 3 Analytical Incompressible 2D Models
	3.1 Introduction
	3.2 Steady Thin Airfoil Theory
	3.3 Fundamentals of Wagner and Theodorsen Theory
		3.3.1 Flow Induced by the Source Distribution
		3.3.2 Flow Induced by the Vortex Distribution
		3.3.3 Imposing the Impermeability Boundary Condition
		3.3.4 Calculating the Loads Due to the Source Distribution
		3.3.5 Imposing the Kutta Condition
	3.4 Wagner Theory
		3.4.1 The Wagner Function
		3.4.2 Drag and Thrust
		3.4.3 General Motion
		3.4.4 Total Loads
		3.4.5 Quasi‐Steady Aerodynamics
	3.5 Theodorsen Theory
		3.5.1 Theodorsen\'s Function
		3.5.2 Total Loads for Sinusoidal Motion
		3.5.3 General Motion
	3.6 Finite State Theory
		3.6.1 Glauert Expansions
		3.6.2 Solution of the Impermeability Equation
		3.6.3 Completing the Equations
		3.6.4 Kutta Condition and Aerodynamic Loads
	3.7 Concluding Remarks
	3.8 Exercises
	References
Chapter 4 Numerical Incompressible 2D Models
	4.1 Introduction
	4.2 Lumped Vortex Method
		4.2.1 Unsteady Flows
		4.2.2 Free Wakes
	4.3 Gust Encounters
		4.3.1 Pitching and Plunging Wings
	4.4 Frequency Domain Formulation of the Lumped Vortex Method
	4.5 Source and Vortex Panel Method
		4.5.1 Impulsively Started Flow
		4.5.2 Thrust and Propulsive Efficiency
	4.6 Theodorsen\'s Function and Wake Shape
	4.7 Steady and Unsteady Kutta Conditions
		4.7.1 The Unsteady Kutta Condition
	4.8 Concluding Remarks
	4.9 Exercises
	References
Chapter 5 Finite Wings
	5.1 Introduction
		5.1.1 Rigid Wings and Flexible Wings
	5.2 Finite Wings in Steady Flow
	5.3 The Impulsively Started Elliptical Wing
		5.3.1 The Solution by Jones
		5.3.2 Unsteady Lifting Line Solution
	5.4 The Unsteady Vortex Lattice Method
		5.4.1 Impulsive Start of an Elliptical Wing
		5.4.2 Other Planforms
	5.5 Rigid Harmonic Motion
		5.5.1 Longitudinal Harmonic Motion
		5.5.2 Frequency Domain Load Calculations
		5.5.3 Lateral Harmonic Motion
		5.5.4 Aerodynamic Stability Derivatives
	5.6 The 3D Source and Doublet Panel Method
	5.7 Flexible Motion
		5.7.1 Source and Doublet Panel Method in the Frequency Domain
	5.8 Concluding Remarks
	5.9 Exercises
	References
Chapter 6 Unsteady Compressible Flow
	6.1 Introduction
	6.2 Steady Subsonic Potential Flow
	6.3 Unsteady Subsonic Potential Flow
		6.3.1 The Doublet Lattice Method
		6.3.2 Unsteady 3D Subsonic Source and Doublet Panel Method
		6.3.3 Steady Correction of the Doublet Lattice Method
		6.3.4 Unsteady 2D Subsonic Source and Doublet Panel Method
	6.4 Unsteady Supersonic Potential Flow
		6.4.1 The Mach Box Method
		6.4.2 The Mach Panel Method
	6.5 Transonic Flow
		6.5.1 Steady Transonic Flow
		6.5.2 Time Linearised Transonic Small Perturbation Equation
		6.5.3 Unsteady Transonic Correction Methods
	6.6 Concluding Remarks
	6.7 Exercises
	References
Chapter 7 Viscous Flow
	7.1 Introduction
		7.1.1 Steady Flow Separation Mechanisms
		7.1.2 Dynamic Stall
	7.2 Impulsively Started Flow around a 2D Flat Plate at High Angles of Attack
		7.2.1 Flow Separation Criteria
	7.3 Flow Around a 2D Circular Cylinder
		7.3.1 The Discrete Vortex Method for Bluff Bodies
		7.3.2 Modelling the Flow Past a Circular Cylinder Using the DVM
	7.4 Flow Past 2D Rectangular Cylinders
		7.4.1 Modelling the Flow Past Rectangular Cylinders Using the DVM
	7.5 Concluding Remarks
	7.6 Exercises
	References
A Fundamental Solutions of Laplace\'s Equation
	A.1 The 2D Point Source
	A.2 The 2D Point Vortex
	A.3 The Source Line Panel
	A.4 The Vortex Line Panel
	A.5 The Horseshoe Vortex
	A.6 The Vortex Line Segment
	A.7 The Vortex Ring
	A.8 The 3D Point Source
	A.9 The 3D Point Doublet
	A.10 The Source Surface Panel
	A.11 The Doublet Surface Panel
	References
B Fundamental Solutions of the Linearized Small Disturbance Equation
	B.1 The Subsonic Doublet Surface Panel
	B.2 The Acoustic Source Surface Panel
	B.3 The Acoustic Doublet Surface Panel
	B.4 The Supersonic Source Surface Panel
	References
C Wagner\'s Derivation of the Kutta Condition
	Reference
Index