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Unsteady Aerodynamics
A comprehensive overview of unsteady aerodynamics and its applications
The study of unsteady aerodynamics goes back a century and has only become more significant as aircraft become increasingly sophisticated, fly faster, and their structures are lighter and more flexible. Progress in the understanding of flow physics, computing power and techniques, and modelling technologies has led to corresponding progress in unsteady aerodynamics, with a wide range of methods currently used to predict the performance of engineering structures under unsteady conditions.
Unsteady Aerodynamics offers a comprehensive and systematic overview of the application of potential and vortex methods to the subject. Beginning with an introduction to the fundamentals of unsteady flow, it then discusses the modelling of attached and separated, incompressible and compressible flows around two-dimensional and three-dimensional bodies. The result is an essential resource for design and simulation in aerospace engineering.
Unsteady Aerodynamics readers will also find:
* MATLAB examples and exercises throughout, with codes and solutions on an accompanying website
* Detailed discussion of most classes of unsteady phenomena, including flapping flight, transonic flow, dynamic stall, flow around bluff bodies and more
* Validation of theoretical and numerical predictions using comparisons to experimental data from the literature
Unsteady Aerodynamics is ideal for researchers, engineers, and advanced students in aerospace engineering.
List of contents
Preface xi
About the Companion Website xiii
1 Introduction 1
1.1 Why Potential and Vortex Methods? 2
1.2 Outline of This Book 3
2 Unsteady Flow Fundamentals 5
2.1 Introduction 5
2.2 From Navier-Stokes to Unsteady Incompressible Potential Flow 5
2.2.1 Irrotational Flow 6
2.2.2 Laplace's and Bernoulli's Equations 7
2.2.3 Motion in an Incompressible, Inviscid, Irrotational Fluid 9
2.3 Incompressible Potential Flow Solutions 14
2.3.1 Green's Third Identity 21
2.3.2 Solutions in Two Dimensions 40
2.4 From Navier-Stokes to Unsteady Compressible Potential Flow 42
2.4.1 The Compressible Bernoulli Equation 42
2.4.2 The Full Potential Equation 44
2.4.3 The Transonic Small Disturbance Equation 46
2.4.4 The Linearised Small Disturbance Equation 47
2.4.5 The Compressible Unsteady Pressure Coefficient 49
2.4.6 Motion in a Compressible, Inviscid, Irrotational Fluid 52
2.5 Subsonic Linearised Potential Flow Solutions 53
2.6 Supersonic Linearised Potential Flow Solutions 61
2.7 Vorticity and Circulation 66
2.7.1 Solutions of the Vorticity Transport Equations 71
2.7.2 Vorticity-Moment and Kutta-Joukowski Theorems 76
2.7.3 TheWake and the Kutta Condition 77
2.8 Concluding Remarks 79
3 Analytical Incompressible 2D Models 83
3.1 Introduction 83
3.2 Steady Thin Airfoil Theory 83
3.3 Fundamentals ofWagner and Theodorsen Theory 93
3.3.1 Flow Induced by the Source Distribution 97
3.3.2 Flow Induced by the Vortex Distribution 101
3.3.3 Imposing the Impermeability Boundary Condition 104
3.3.4 Calculating the Loads Due to the Source Distribution 108
3.3.5 Imposing the Kutta Condition 111
3.4 Wagner Theory 113
3.4.1 TheWagner Function 120
3.4.2 Drag and Thrust 123
3.4.3 General Motion 129
3.4.4 Total Loads 131
3.4.5 Quasi-Steady Aerodynamics 138
3.5 Theodorsen Theory 139
3.5.1 Theodorsen's Function 143
3.5.2 Total Loads for Sinusoidal Motion 146
3.5.3 General Motion 153
3.6 Finite State Theory 157
3.6.1 Glauert Expansions 161
3.6.2 Solution of the Impermeability Equation 170
3.6.3 Completing the Equations 172
3.6.4 Kutta Condition and Aerodynamic Loads 175
3.7 Concluding Remarks 183
3.8 Exercises 184
4 Numerical Incompressible 2D Models 187
4.1 Introduction 187
4.2 Lumped Vortex Method 187
4.2.1 Unsteady Flows 197
4.2.2 FreeWakes 206
4.3 Gust Encounters 212
4.3.1 Pitching and Plunging Wings 216
4.4 Frequency Domain Formulation of the Lumped Vortex Method 227
4.5 Source and Vortex Panel Method 233
4.5.1 Impulsively Started Flow 245
4.5.2 Thrust and Propulsive Efficiency 254
4.6 Theodorsen's Function andWake Shape 259
4.7 Steady and Unsteady Kutta Conditions 261
4.7.1 The Unsteady Kutta Condition 267
4.8 Concluding Remarks 275
4.9 Exercises 275
5 Finite Wings 279
5.1 Introduction 279
5.1.1 Rigid Wings and Flexible Wings 280
5.2 Finite Wings in Steady Flow 281
5.3 The Impulsively Started Elliptical Wing 290
5.3.1 The Solution by Jones 290
5.3.2 Unsteady Lifting Line Solution 302
5.4 The Unsteady Vortex Lattice Method 306
5.4.1 Impulsive Start of an Elliptical Wing
About the author
Grigorios Dimitriadis, PhD, is Professor of Fluid Structure Interaction and Experimental Aerodynamics in the Aerospace and Mechanical Engineering Department, University of Liège, Belgium and Adjunct Professor in Aeroelasticity at the von Karman Institute for Fluid Dynamics, Belgium. He has published extensively on unsteady aerodynamics and related fields.
