Understanding Aerodynamics: Arguing from the Real PhysicsISBN: 9781119967514
576 pages
December 2012

Based on the author’s decades of industrial experience with Boeing, this book helps students and practicing engineers to gain a greater physical understanding of aerodynamics. Relying on clear physical arguments and examples, Mclean provides a muchneeded, fresh approach to this sometimes contentious subject without shying away from addressing "real" aerodynamic situations as opposed to the oversimplified ones frequently used for mathematical convenience. Motivated by the belief that engineering practice is enhanced in the long run by a robust understanding of the basics as well as real causeandeffect relationships that lie behind the theory, he provides intuitive physical interpretations and explanations, debunking commonlyheld misconceptions and misinterpretations, and building upon the contrasts provided by wrong explanations to strengthen understanding of the right ones.
 Provides a refreshing view of aerodynamics that is based on the author’s decades of industrial experience yet is always tied to basic fundamentals.
 Provides intuitive physical interpretations and explanations, debunking commonlyheld misconceptions and misinterpretations
 Offers new insights to some familiar topics, for example, what the BiotSavart law really means and why it causes so much confusion, what “Reynolds number” and “incompressible flow” really mean, and a real physical explanation for how an airfoil produces lift.
 Addresses "real" aerodynamic situations as opposed to the oversimplified ones frequently used for mathematical convenience, and omits mathematical details whenever the physical understanding can be conveyed without them.
Foreword xi
Series Preface xiii
Preface xv
List of Symbols xix
1 Introduction to the Conceptual Landscape 1
2 From Elementary Particles to Aerodynamic Flows 5
3 Continuum Fluid Mechanics and the NavierStokes Equations 13
3.1 The Continuum Formulation and Its Range of Validity 13
3.2 Mathematical Formalism 16
3.3 Kinematics: Streamlines, Streaklines, Timelines, and Vorticity 18
3.3.1 Streamlines and Streaklines 18
3.3.2 Streamtubes, Stream Surfaces, and the Stream Function 19
3.3.3 Timelines 22
3.3.4 The Divergence of the Velocity and Green’s Theorem 23
3.3.5 Vorticity and Circulation 24
3.3.6 The Velocity Potential in Irrotational Flow 26
3.3.7 Concepts that Arise in Describing the Vorticity Field 26
3.3.8 Velocity Fields Associated with Concentrations of Vorticity 29
3.3.9 The BiotSavart Law and the “Induction” Fallacy 31
3.4 The Equations of Motion and their Physical Meaning 33
3.4.1 Continuity of the Flow and Conservation of Mass 34
3.4.2 Forces on Fluid Parcels and Conservation of Momentum 35
3.4.3 Conservation of Energy 36
3.4.4 Constitutive Relations and Boundary Conditions 37
3.4.5 Mathematical Nature of the Equations 37
3.4.6 The Physics as Viewed in the Eulerian Frame 38
3.4.7 The PseudoLagrangian Viewpoint 40
3.5 Cause and Effect, and the Problem of Prediction 40
3.6 The Effects of Viscosity 43
3.7 Turbulence, Reynolds Averaging, and Turbulence Modeling 48
3.8 Important Dynamical Relationships 55
3.8.1 Galilean Invariance, or Independence of Reference Frame 55
3.8.2 Circulation Preservation and the Persistence of Irrotationality 56
3.8.3 Behavior of Vortex Tubes in Inviscid and Viscous Flows 57
3.8.4 Bernoulli Equations and Stagnation Conditions 58
3.8.5 Crocco’s Theorem 60
3.9 Dynamic Similarity 60
3.9.1 Compressibility Effects and the Mach Number 63
3.9.2 Viscous Effects and the Reynolds Number 63
3.9.3 Scaling of Pressure Forces: the Dynamic Pressure 64
3.9.4 Consequences of Failing to Match All of the Requirements for Similarity 65
3.10 “Incompressible” Flow and Potential Flow 66
3.11 Compressible Flow and Shocks 70
3.11.1 Steady 1D Isentropic Flow Theory 71
3.11.2 Relations for Normal and Oblique Shock Waves 74
4 Boundary Layers 79
4.1 Physical Aspects of BoundaryLayer Flows 80
4.1.1 The Basic Sequence: Attachment, Transition, Separation 80
4.1.2 General Development of the BoundaryLayer Flowfield 82
4.1.3 BoundaryLayer Displacement Effect 90
4.1.4 Separation from a Smooth Wall 93
4.2 BoundaryLayer Theory 99
4.2.1 The BoundaryLayer Equations 100
4.2.2 Integrated Momentum Balance in a Boundary Layer 108
4.2.3 The Displacement Effect and Matching with the Outer Flow 110
4.2.4 The Vorticity “Budget” in a 2D Incompressible Boundary Layer 113
4.2.5 Situations That Violate the Assumptions of BoundaryLayer Theory 114
4.2.6 Summary of Lessons from BoundaryLayer Theory 117
4.3 FlatPlate Boundary Layers and Other Simplified Cases 117
4.3.1 FlatPlate Flow 117
4.3.2 2D BoundaryLayer Flows with Similarity 121
4.3.3 Axisymmetric Flow 123
4.3.4 PlaneofSymmetry and AttachmentLine Boundary Layers 125
4.3.5 Simplifying the Effects of Sweep and Taper in 3D 128
4.4 Transition and Turbulence 130
4.4.1 BoundaryLayer Transition 131
4.4.2 Turbulent Boundary Layers 138
4.5 Control and Prevention of Flow Separation 150
4.5.1 Body Shaping and Pressure Distribution 150
4.5.2 Vortex Generators 150
4.5.3 Steady Tangential Blowing through a Slot 155
4.5.4 Active Unsteady Blowing 157
4.5.5 Suction 157
4.6 Heat Transfer and Compressibility 158
4.6.1 Heat Transfer, Compressibility, and the BoundaryLayer Temperature Field 158
4.6.2 The Thermal Energy Equation and the Prandtl Number 159
4.6.3 The Wall Temperature and Other Relations for an Adiabatic Wall 159
4.7 Effects of Surface Roughness 162
5 General Features of Flows around Bodies 163
5.1 The Obstacle Effect 164
5.2 Basic Topology of Flow Attachment and Separation 168
5.2.1 Attachment and Separation in 2D 169
5.2.2 Attachment and Separation in 3D 171
5.2.3 Streamline Topology on Surfaces and in Cross Sections 176
5.3 Wakes 186
5.4 Integrated Forces: Lift and Drag 189
6 Drag and Propulsion 191
6.1 Basic Physics and Flowfield Manifestations of Drag and Thrust 192
6.1.1 Basic Physical Effects of Viscosity 193
6.1.2 The Role of Turbulence 193
6.1.3 Direct and Indirect Contributions to the Drag Force on the Body 194
6.1.4 Determining Drag from the Flowfield: Application of Conservation Laws 196
6.1.5 Examples of Flowfield Manifestations of Drag in Simple 2D Flows 204
6.1.6 Pressure Drag of Streamlined and Bluff Bodies 207
6.1.7 Questionable Drag Categories: Parasite Drag, Base Drag, and Slot Drag 210
6.1.8 Effects of Distributed Surface Roughness on Turbulent Skin Friction 212
6.1.9 Interference Drag 222
6.1.10 Some Basic Physics of Propulsion 225
6.2 Drag Estimation 241
6.2.1 Empirical Correlations 242
6.2.2 Effects of Surface Roughness on Turbulent Skin Friction 243
6.2.3 CFD Prediction of Drag 250
6.3 Drag Reduction 250
6.3.1 Reducing Drag by Maintaining a Run of Laminar Flow 251
6.3.2 Reduction of Turbulent Skin Friction 251
7 Lift and Airfoils in 2D at Subsonic Speeds 259
7.1 Mathematical Prediction of Lift in 2D 260
7.2 Lift in Terms of Circulation and Bound Vorticity 265
7.2.1 The Classical Argument for the Origin of the Bound Vorticity 267
7.3 Physical Explanations of Lift in 2D 269
7.3.1 Past Explanations and their Strengths and Weaknesses 269
7.3.2 Desired Attributes of a More Satisfactory Explanation 284
7.3.3 A Basic Explanation of Lift on an Airfoil, Accessible to a Nontechnical Audience 286
7.3.4 More Physical Details on Lift in 2D, for the Technically Inclined 302
7.4 Airfoils 307
7.4.1 Pressure Distributions and Integrated Forces at Low Mach Numbers 307
7.4.2 Profile Drag and the Drag Polar 316
7.4.3 Maximum Lift and BoundaryLayer Separation on SingleElement Airfoils 319
7.4.4 Multielement Airfoils and the Slot Effect 329
7.4.5 Cascades 335
7.4.6 LowDrag Airfoils with Laminar Flow 338
7.4.7 LowReynoldsNumber Airfoils 341
7.4.8 Airfoils in Transonic Flow 342
7.4.9 Airfoils in Ground Effect 350
7.4.10 Airfoil Design 352
7.4.11 Issues that Arise in Defining Airfoil Shapes 354
8 Lift and Wings in 3D at Subsonic Speeds 359
8.1 The Flowfield around a 3D Wing 359
8.1.1 General Characteristics of the Velocity Field 359
8.1.2 The Vortex Wake 362
8.1.3 The Pressure Field around a 3D Wing 371
8.1.4 Explanations for the Flowfield 371
8.1.5 Vortex Shedding from Edges Other Than the Trailing Edge 375
8.2 Distribution of Lift on a 3D Wing 376
8.2.1 Basic and Additional Spanloads 376
8.2.2 Linearized LiftingSurface Theory 379
8.2.3 LiftingLine Theory 380
8.2.4 3D Lift in Ground Effect 382
8.2.5 Maximum Lift, as Limited by 3D Effects 384
8.3 Induced Drag 385
8.3.1 Basic Scaling of Induced Drag 385
8.3.2 Induced Drag from a Farfield Momentum Balance 386
8.3.3 Induced Drag in Terms of Kinetic Energy and an Idealized RolledUp Vortex Wake 389
8.3.4 Induced Drag from the Loading on the Wing Itself: TrefftzPlane Theory 391
8.3.5 Ideal (Minimum) InducedDrag Theory 394
8.3.6 SpanEfficiency Factors 396
8.3.7 The InducedDrag Polar 397
8.3.8 The SinSeries Spanloads 398
8.3.9 The Reduction of Induced Drag in Ground Effect 401
8.3.10 The Effect of a Fuselage on Induced Drag 402
8.3.11 Effects of a Canard or Aft Tail on Induced Drag 404
8.3.12 Biplane Drag 409
8.4 Wingtip Devices 411
8.4.1 Myths Regarding the Vortex Wake, and Some Questionable Ideas for Wingtip Devices 411
8.4.2 The Facts of Life Regarding Induced Drag and InducedDrag Reduction 414
8.4.3 Milestones in the Development of Theory and Practice 420
8.4.4 Wingtip Device Concepts 422
8.4.5 Effectiveness of Various Device Configurations 423
8.5 Manifestations of Lift in the Atmosphere at Large 427
8.5.1 The Net Vertical Momentum Imparted to the Atmosphere 427
8.5.2 The Pressure Far above and below the Airplane 429
8.5.3 Downwash in the Trefftz Plane and Other MomentumConservation Issues 431
8.5.4 Sears’s Incorrect Analysis of the Integrated Pressure Far Downstream 435
8.5.5 The Real Flowfield Far Downstream of the Airplane 436
8.6 Effects of Wing Sweep 444
8.6.1 Simple Sweep Theory 444
8.6.2 Boundary Layers on Swept Wings 449
8.6.3 Shock/BoundaryLayer Interaction on Swept Wings 464
8.6.4 LaminartoTurbulent Transition on Swept Wings 465
8.6.5 Relating a Swept, Tapered Wing to a 2D Airfoil 468
8.6.6 Tailoring of the Inboard Part of a Swept Wing 469
9 Theoretical Idealizations Revisited 471
9.1 Approximations Grouped According to how the Equations were Modified 471
9.1.1 Reduced Temporal and/or Spatial Resolution 472
9.1.2 Simplified Theories Based on Neglecting Something Small 472
9.1.3 Reductions in Dimensions 472
9.1.4 Simplified Theories Based on Ad hoc Flow Models 472
9.1.5 Qualitative Anomalies and Other Consequences of Approximations 481
9.2 Some Tools of MFD (Mental Fluid Dynamics) 482
9.2.1 Simple Conceptual Models for Thinking about Velocity Fields 482
9.2.2 Thinking about Viscous and Shock Drag 485
9.2.3 Thinking about Induced Drag 486
9.2.4 A Catalog of Fallacies 487
10 Modeling Aerodynamic Flows in Computational Fluid Dynamics 491
10.1 Basic Definitions 493
10.2 The Major Classes of CFD Codes and Their Applications 493
10.2.1 NavierStokes Methods 493
10.2.2 Coupled Viscous/Inviscid Methods 497
10.2.3 Inviscid Methods 498
10.2.4 Standalone BoundaryLayer Codes 501
10.3 Basic Characteristics of Numerical Solution Schemes 501
10.3.1 Discretization 501
10.3.2 Spatial Field Grids 502
10.3.3 Grid Resolution and Grid Convergence 506
10.3.4 Solving the Equations, and Iterative Convergence 507
10.4 Physical Modeling in CFD 508
10.4.1 Compressibility and Shocks 508
10.4.2 Viscous Effects and Turbulence 510
10.4.3 Separated Shear Layers and Vortex Wakes 511
10.4.4 The Farfield 513
10.4.5 Predicting Drag 514
10.4.6 Propulsion Effects 515
10.5 CFD Validation? 515
10.6 Integrated Forces and the Components of Drag 516
10.7 Solution Visualization 517
10.8 Things a User Should Know about a CFD Code before Running it 524
References 527
Index 539
“As someone who has been involved with aerodynamics for more years than I care to remember, I have rarely come across a book that is so readable and that provides so many (to me a least) genuinely new insights into the subject and its applications. This book should be high on the wish list of any practising aerodynamicist, whether in industry or academia.” (Aeronautical Journal, 1 August 2013)
“This is a sophisticated book for people immersed in the study of fluid dynamics and aerodynamics; it will give them indepth knowledge of both the physical phenomena and the mathematical equations that are used to describe and predict these phenomena. Summing Up: Recommended. Graduate students in aerospace engineering, researchers/faculty, and aircraft design professionals.” (Choice, 1 July 2013)
“Based on the author’s decades of industrial experience with Boeing, this book helps students and practicing engineers to gain a greater physical understanding of aerodynamics. Relying on clear physical arguments and examples, Mcleanprovides a muchneeded, fresh approach to this sometimes contentious subject without shying away from addressing "real" aerodynamic situations as opposed to the oversimplified ones frequently used for mathematical convenience.” (Expofairs.com, 11 March 2013)