Aerodynamics for Engineers Book

PREFACE TO THE SIXTH EDITION xv

CHAPTER 1 WHY STUDY AERODYNAMICS? 1

1.1 Aerodynamics and the Energy-Maneuverability Technique 2

1.1.1 Specific Excess Power 6

1.1.2 Using Specific Excess Power to Change the Energy Height 7

1.1.3 John R. Boyd Meet Harry Hillaker 8

1.1.4 The Importance of Aerodynamics to Aircraft Performance 8

1.2 Solving for the Aerothermodynamic Parameters 8

1.2.1 Concept of a Fluid 8

1.2.2 Fluid as a Continuum 8

1.2.3 Fluid Properties 10

1.2.4 Pressure Variation in a Static Fluid Medium 17

1.2.5 The Standard Atmosphere 22

1.3 Description of an Airplane 26

1.4 Summary 27

Problems 28

References 32

CHAPTER 2 FUNDAMENTALS OF FLUID MECHANICS 33

2.1 Introduction to Fluid Dynamics 34

2.2 Conservation of Mass 36

2.3 Conservation of Linear Momentum 40

2.4 Applications to Constant-Property Flows 46

2.4.1 Poiseuille Flow 46

2.4.2 Couette Flow 50

2.4.3 Integral Equation Application 52

2.5 Reynolds Number and Mach Number as Similarity Parameters 55

2.6 Concept of the Boundary Layer 63

2.7 Conservation of Energy 65

2.8 First Law of Thermodynamics 66

2.9 Derivation of the Energy Equation 68

2.9.1 Integral Form of the Energy Equation 71

2.9.2 Energy of the System 71

2.9.3 Flow Work 72

2.9.4 Viscous Work 73

2.9.5 Shaft Work 73

2.9.6 Application of the Integral Form of the Energy Equation 74

2.10 Summary 76

Problems 76

References 87

CHAPTER 3 DYNAMICS OF AN INCOMPRESSIBLE, INVISCID FLOW FIELD 88

3.1 Inviscid Flows 89

3.2 Bernoulli’s Equation 90

3.3 Use of Bernoulli’s Equation to Determine Airspeed 93

3.4 The Pressure Coefficient 96

3.5 Circulation 99

3.6 Irrotational Flow 102

3.7 Kelvin’s Theorem 103

3.7.1 Implication of Kelvin’s Theorem 104

3.8 Incompressible, Irrotational Flow and the Velocity Potential 104

3.8.1 Irrotational Condition 105

3.8.2 Boundary Conditions 105

3.9 Stream Function in a Two-Dimensional, Incompressible Flow 107

3.10 Relation between Streamlines and Equipotential Lines 109

3.11 Superposition of Flows 112

3.12 Elementary Flows 113

3.12.1 Uniform Flow 113

3.12.2 Source or Sink 114

3.12.3 Doublet 116

3.12.4 Potential Vortex 117

3.12.5 The Vortex Theorems of Helmholtz 120

3.12.6 Summary of Stream Functions and of Potential Functions 123

3.13 Adding Elementary Flows to Describe Flow Around a Cylinder 126

3.13.1 Velocity Field 126

3.13.2 Pressure Distribution on the Cylinder 128

3.13.3 Lift and Drag 130

3.14 Lift and Drag Coefficients as Dimensionless Flow-Field Parameters 134

3.15 Flow Around a Cylinder with Circulation 139

3.15.1 Velocity Field 139

3.15.2 Lift and Drag 140

3.15.3 Applications of Potential Flow to Aerodynamics 142

3.16 Source Density Distribution on the Body Surface 144

3.17 Incompressible, Axisymmetric Flow 149

3.17.1 Flow Around a Sphere 150

3.18 Summary 152

Problems 152

References 165

CHAPTER 4 VISCOUS BOUNDARY LAYERS 166

4.1 Equations Governing the Boundary Layer for a Steady, Two-Dimensional, Incompressible Flow 167

4.2 Boundary Conditions 170

4.3 Incompressible, Laminar Boundary Layer 171

4.3.1 Numerical Solutions for the Falkner-Skan Problem 174

4.4 Boundary-Layer Transition 189

4.5 Incompressible, Turbulent Boundary Layer 193

4.5.1 Derivation of the Momentum Equation for Turbulent Boundary Layer 195

4.5.2 Approaches to Turbulence Modeling 197

4.5.3 Turbulent Boundary Layer for a Flat Plate 199

4.6 Eddy Viscosity and Mixing Length Concepts 202

4.7 Integral Equations for a Flat-Plate Boundary Layer 204

4.7.1 Application of the Integral Equations of Motion to a Turbulent, Flat-Plate Boundary Layer 208

4.7.2 Integral Solutions for a Turbulent Boundary Layer with a Pressure Gradient 213

4.8 Thermal Boundary Layer for Constant-Property Flows 215

4.8.1 Reynolds Analogy 216

4.8.2 Thermal Boundary Layer for Pr _ 1 218

4.9 Summary 221

Problems 221

References 225

CHAPTER 5 CHARACTERISTIC PARAMETERS FOR AIRFOIL AND WING AERODYNAMICS 226

5.1 Characterization of Aerodynamic Forces and Moments 227

5.1.1 General Comments 227

5.1.2 Parameters That Govern Aerodynamic Forces 230

5.2 Airfoil Geometry Parameters 231

5.2.1 Airfoil-Section Nomenclature 232

5.2.2 Leading-Edge Radius and Chord Line 233

5.2.3 Mean Camber Line 234

5.2.4 Maximum Thickness and Thickness Distribution 234

5.2.5 Trailing-Edge Angle 235

5.3 Wing-Geometry Parameters 236

5.4 Aerodynamic Force and Moment Coefficients 244

5.4.1 Lift Coefficient 244

5.4.2 Moment Coefficient 250

5.4.3 Drag Coefficient 252

5.4.4 Boundary-Layer Transition 256

5.4.5 Effect of Surface Roughness on the Aerodynamic Forces 259

5.4.6 Method for Predicting Aircraft Parasite Drag 263

5.5 Wings of Finite Span 273

5.5.1 Lift 274

5.5.2 Drag 279

5.5.3 Lift/Drag Ratio 283

Problems 288

References 292

CHAPTER 6 INCOMPRESSIBLE FLOWS AROUND AIRFOILS OF INFINITE SPAN 294

6.1 General Comments 295

6.2 Circulation and the Generation of Lift 296

6.2.1 Starting Vortex 296

6.3 General Thin-Airfoil Theory 298

6.4 Thin, Flat-Plate Airfoil (Symmetric Airfoil) 301

6.5 Thin, Cambered Airfoil 306

6.5.1 Vorticity Distribution 306

6.5.2 Aerodynamic Coefficients for a Cambered Airfoil 308

6.6 Laminar-Flow Airfoils 317

6.7 High-Lift Airfoil Sections 321

6.8 Multielement Airfoil Sections for Generating High Lift 327

6.9 High-Lift Military Airfoils 334

Problems 337

References 339

CHAPTER 7 INCOMPRESSIBLE FLOW ABOUT WINGS OF FINITE SPAN 341

7.1 General Comments 342

7.2 Vortex System 345

7.3 Lifting-Line Theory for Unswept Wings 346

7.3.1 Trailing Vortices and Downwash 348

7.3.2 Case of Elliptic Spanwise Circulation Distribution 351

7.3.3 Technique for General Spanwise Circulation Distribution 357

7.3.4 Lift on the Wing 362

7.3.5 Vortex-Induced Drag 362

7.3.6 Some Final Comments on Lifting-Line Theory 373

7.4 Panel Methods 375

7.4.1 Boundary Conditions 376

7.4.2 Solution Methods 377

7.5 Vortex Lattice Method 379

7.5.1 Velocity Induced by a General Horseshoe Vortex 382

7.5.2 Application of the Boundary Conditions 386

7.5.3 Relations for a Planar Wing 387

7.6 Factors Affecting Drag Due-to-Lift at Subsonic Speeds 401

7.7 Delta Wings 404

7.8 Leading-Edge Extensions 414

7.9 Asymmetric Loads on the Fuselage at High Angles of Attack 418

7.9.1 Asymmetric Vortex Shedding 419

7.9.2 Wakelike Flows 422

7.10 Flow Fields for Aircraft at High Angles of Attack 422

7.11 Unmanned Air Vehicle Wings 424

7.12 Summary 426

Problems 426

References 428

CHAPTER 8 DYNAMICS OF A COMPRESSIBLE FLOW FIELD 431

8.1 Thermodynamic Concepts 432

8.1.1 Specific Heats 432

8.1.2 Additional Important Relations 435

8.1.3 Second Law of Thermodynamics and Reversibility 435

8.1.4 Speed of Sound 438

8.2 Adiabatic Flow in a Variable-Area Streamtube 441

8.3 Isentropic Flow in a Variable-Area Streamtube 445

8.4 Converging-diverging Nozzles 451

8.5 Characteristic Equations and Prandtl-Meyer Flows 454

8.6 Shock Waves 462

8.7 Viscous Boundary Layer 473

8.7.1 Effects of Compressibility 476

8.8 Shock-Wave/Boundary-Layer Interactions 480

8.9 Shock/Shock Interactions 482

8.10 The Role of Experiments for Generating Information Defining the Flow Field 486

8.10.1 Ground-Based Tests 486

8.10.2 Flight Tests 490

8.11 Comments About The Scaling/Correction Process(es) for Relatively Clean Cruise Configurations 494

8.12 Summary 495

Problems 495

References 502

CHAPTER 9 COMPRESSIBLE, SUBSONIC FLOWS AND TRANSONIC FLOWS 505

9.1 Compressible, Subsonic Flow 506

9.1.1 Linearized Theory for Compressible Subsonic Flow About a Thin Wing at Relatively Small Angles of Attack 507

9.1.2 The Göthert Transformation 509

9.1.3 Additional Compressibility Corrections 512

9.1.4 The Motivation for Determining the Critical Mach Number 513

9.1.5 Critical Mach Number 513

9.1.6 Drag Divergence Mach Number 516

9.2 Transonic Flow Past Unswept Airfoils 517

9.3 Wave Drag Reduction by Design 526

9.3.1 Airfoil Contour Wave Drag Approaches 526

9.3.2 Supercritical Airfoil Sections 526

9.4 Swept Wings at Transonic Speeds 527

9.4.1 Wing—Body Interactions and the “Area Rule” 529

9.4.2 Second-Order Area-Rule Considerations 538

9.4.3 Forward Swept Wing 540

9.5 Transonic Aircraft 543

9.6 Summary 548

Problems 548

References 548

CHAPTER 10 TWO-DIMENSIONAL, SUPERSONIC FLOWS AROUND THIN AIRFOILS 551

10.1 Linear Theory 553

10.1.1 Lift 555

10.1.2 Drag 556

10.1.3 Pitch Moment 558

10.2 Second-Order Theory (Busemann’s Theory) 561

10.3 Shock-Expansion Technique 566

10.4 Summary 572

Problems 572

References 575

CHAPTER 11 SUPERSONIC FLOWS OVER WINGS AND AIRPLANE CONFIGURATIONS 577

11.1 General Remarks About Lift and Drag 579

11.2 General Remarks About Supersonic Wings 581

11.3 Governing Equation and Boundary Conditions 583

11.4 Consequences of Linearity 584

11.5 Solution Methods 585

11.6 Conical-Flow Method 585

11.6.1 Rectangular Wings 586

11.6.2 Swept Wings 591

11.6.3 Delta and Arrow Wings 595

11.7 Singularity-Distribution Method 598

11.7.1 Find the Pressure Distribution Given the Configuration 600

11.7.2 Numerical Method for Calculating the Pressure Distribution Given the Configuration 608

11.7.3 Numerical Method for the Determination of Camber Distribution 622

11.8 Design Considerations for Supersonic Aircraft 625

11.9 Some Comments about the Design of the SST and of the HSCT 627

11.9.1 The Supersonic Transport (SST), the Concorde 627

11.9.2 The High-Speed Civil Transport (HSCT) 629

11.9.3 Reducing the Sonic Boom 630

11.9.4 Classifying High-Speed Aircraft Designs 631

11.10 Slender Body Theory 634

11.11 Base Drag 636

11.12 Aerodynamic Interaction 639

11.13 Aerodynamic Analysis for Complete Configurations in a Supersonic Free Stream 642

11.14 Summary 643

Problems 644

References 646

CHAPTER 12 HYPERSONIC FLOWS 649

12.1 The Five Distinguishing Characteristics 652

12.1.1 Thin Shock Layers 652

12.1.2 Entropy Layers 653

12.1.3 Viscous-Inviscid Interactions 653

12.1.4 High Temperature Effects 654

12.1.5 Low-Density Flows 655

12.2 Newtonian Flow Model 657

12.3 Stagnation Region Flow-Field Properties 660

12.4 Modified Newtonian Flow 665

12.5 High L/D Hypersonic Configurations–Waveriders 682

12.6 Aerodynamic Heating 691

12.6.1 Similarity Solutions for Heat Transfer 694

12.7 A Hypersonic Cruiser for the Twenty-First Century? 697

12.8 Importance of Interrelating CFD, Ground-Test Data, and Flight-Test Data 700

12.9 Boundary-Layer-Transition Methodology 702

12.10 Summary 706

Problems 706

References 708

CHAPTER 13 AERODYNAMIC DESIGN CONSIDERATIONS 711

13.1 High-Lift Configurations 712

13.1.1 Increasing the Area 712

13.1.2 Increasing the Lift Coefficient 713

13.1.3 Flap Systems 716

13.1.4 Multi-element Airfoils 719

13.1.5 Power-Augmented Lift 723

13.2 Circulation Control Wing 725

13.3 Design Considerations for Tactical Military Aircraft 727

13.4 Drag Reduction 731

13.4.1 Variable-Twist, Variable-Camber Wings 731

13.4.2 Laminar-Flow Control 734

13.4.3 Wingtip Devices 737

13.4.4 Wing Planform 740

13.5 Development of an Airframe Modification to Improve the Mission Effectiveness of an Existing Airplane 742

13.5.1 The EA-6B 742

13.5.2 The Evolution of the F-16 745

13.5.3 External Carriage of Stores 752

13.5.4 Additional Comments 758

13.6 Considerations for Wing/Canard, Wing/Tail, and Tailless Configurations 758

13.7 Comments on the F-15 Design 763

13.8 The Design of the F-22 764

13.9 The Design of the F-35 767

13.10 Summary 770

Problems 770

References 772

CHAPTER 14 TOOLS FOR DEFINING THE AERODYNAMIC ENVIRONMENT 775

14.1 Computational Tools 777

14.1.1 Semiempirical Methods 777

14.1.2 Surface Panel Methods for Inviscid Flows 778

14.1.3 Euler Codes for Inviscid Flow Fields 779

14.1.4 Two-Layer Flow Models 779

14.1.5 Computational Techniques That Treat the Entire Flow Field in a Unified Fashion 780

14.1.6 Integrating the Diverse Computational Tools 781

14.2 Establishing the Credibility of CFD Simulations 783

14.3 Ground-Based Test Programs 785

14.4 Flight-Test Programs 788

14.5 Integration of Experimental and Computational Tools: The Aerodynamic Design Philosophy 789

14.6 Summary 790

References 790

APPENDIX A THE EQUATIONS OF MOTION WRITTEN IN CONSERVATION FORM 793

APPENDIX B A COLLECTION OF OFTEN USED TABLES 799

ANSWERS TO SELECTED PROBLEMS 806

INDEX