Theoretical Aerodynamics (eBook)

Ethirajan Rathakrishnan (Autor)

eBook Download: PDF

2013
John Wiley & Sons (Verlag)
978-1-118-47936-0 (ISBN)

Infos

Theoretical Aerodynamics is a user-friendly text for a full course on theoretical aerodynamics. The author systematically introduces aerofoil theory, its design features and performance aspects, beginning with the basics required, and then gradually proceeding to higher level. The mathematics involved is presented so that it can be followed comfortably, even by those who are not strong in mathematics. The examples are designed to fix the theory studied in an effective manner. Throughout the book, the physics behind the processes are clearly explained. Each chapter begins with an introduction and ends with a summary and exercises. This book is intended for graduate and advanced undergraduate students of Aerospace Engineering, as well as researchers and Designers working in the area of aerofoil and blade design.

Provides a complete overview of the technical terms, vortex theory, lifting line theory, and numerical methods Presented in  an easy-to-read style making full use of figures and illustrations to enhance understanding, and moves well simpler to more advanced topics Includes a complete section on fluid mechanics and thermodynamics, essential background topics to the theory of aerodynamics Blends the mathematical and physical concepts of design and performance aspects of lifting surfaces, and introduces the reader to the thin aerofoil theory, panel method, and finite aerofoil theory Includes a Solutions Manual for end-of-chapter exercises, and Lecture slides on the book’s Companion Website

Autor

ETHIRAJAN RATHAKRISHNAN, Indian Institute of Technology Kanpur, India

Inhalt

Theoretical Aerodynamics 1
Contents 9
About the Author 17
Preface 19
1 Basics 21
1.1 Introduction 21
1.2 Lift and Drag 21
1.3 Monoplane Aircraft 24
1.3.1 Types of Monoplane 25
1.4 Biplane 25
1.4.1 Advantages and Disadvantages 26
1.5 Triplane 26
1.5.1 Chord of a Profile 27
1.5.2 Chord of an Aerofoil 28
1.6 Aspect Ratio 29
1.7 Camber 30
1.8 Incidence 31
1.9 Aerodynamic Force 32
1.10 Scale Effect 35
1.11 Force and Moment Coefficients 37
1.12 The Boundary Layer 38
1.13 Summary 40
Exercise Problems 41
Reference 42
2 Essence of Fluid Mechanics 43
2.1 Introduction 43
2.2 Properties of Fluids 43
2.2.1 Pressure 43
2.2.2 Temperature 44
2.2.3 Density 44
2.2.4 Viscosity 45
2.2.5 Absolute Coefficient of Viscosity 45
2.2.6 Kinematic Viscosity Coefficient 47
2.2.7 Thermal Conductivity of Air 47
2.2.8 Compressibility 48
2.3 Thermodynamic Properties 48
2.3.1 Specific Heat 48
2.3.2 The Ratio of Specific Heats 49
2.4 Surface Tension 50
2.5 Analysis of Fluid Flow 51
2.5.1 Local and Material Rates of Change 52
2.5.2 Graphical Description of Fluid Motion 53
2.6 Basic and Subsidiary Laws 54
2.6.1 System and Control Volume 54
2.6.2 Integral and Differential Analysis 55
2.6.3 State Equation 55
2.7 Kinematics of Fluid Flow 55
2.7.1 Boundary Layer Thickness 57
2.7.2 Displacement Thickness 58
2.7.3 Transition Point 59
2.7.4 Separation Point 59
2.7.5 Rotational and Irrotational Motion 60
2.8 Streamlines 61
2.8.1 Relationship between Stream Function and Velocity Potential 61
2.9 Potential Flow 62
2.9.1 Two-dimensional Source and Sink 63
2.9.2 Simple Vortex 65
2.9.3 Source-Sink Pair 66
2.9.4 Doublet 66
2.10 Combination of Simple Flows 69
2.10.1 Flow Past a Half-Body 69
2.11 Flow Past a Circular Cylinder without Circulation 77
2.11.1 Flow Past a Circular Cylinder with Circulation 79
2.12 Viscous Flows 83
2.12.1 Drag of Bodies 85
2.12.2 Turbulence 90
2.12.3 Flow through Pipes 95
2.13 Compressible Flows 98
2.13.1 Perfect Gas 99
2.13.2 Velocity of Sound 100
2.13.3 Mach Number 100
2.13.4 Flow with Area Change 100
2.13.5 Normal Shock Relations 102
2.13.6 Oblique Shock Relations 103
2.13.7 Flow with Friction 104
2.13.8 Flow with Simple T0-Change 106
2.14 Summary 107
Exercise Problems 117
References 122
3 Conformal Transformation 123
3.1 Introduction 123
3.2 Basic Principles 123
3.2.1 Length Ratios between the Corresponding Elements in the Physical and Transformed Planes 126
3.2.2 Velocity Ratios between the Corresponding Elements in the Physical and Transformed Planes 126
3.2.3 Singularities 127
3.3 Complex Numbers 127
3.3.1 Differentiation of a Complex Function 130
3.4 Summary 132
Exercise Problems 133
4 Transformation of Flow Pattern 135
4.1 Introduction 135
4.2 Methods for Performing Transformation 135
4.2.1 By Analytical Means 136
4.3 Examples of Simple Transformation 139
4.4 Kutta-Joukowski Transformation 142
4.5 Transformation of Circle to Straight Line 143
4.6 Transformation of Circle to Ellipse 144
4.7 Transformation of Circle to Symmetrical Aerofoil 145
4.7.1 Thickness to Chord Ratio of Symmetrical Aerofoil 147
4.7.2 Shape of the Trailing Edge 149
4.8 Transformation of a Circle to a Cambered Aerofoil 149
4.8.1 Thickness-to-Chord Ratio of the Cambered Aerofoil 152
4.8.2 Camber 154
4.9 Transformation of Circle to Circular Arc 154
4.9.1 Camber of Circular Arc 157
4.10 Joukowski Hypothesis 157
4.10.1 The Kutta Condition Applied to Aerofoils 159
4.10.2 The Kutta Condition in Aerodynamics 160
4.11 Lift of Joukowski Aerofoil Section 161
4.12 The Velocity and Pressure Distributions on the Joukowski Aerofoil 164
4.13 The Exact Joukowski Transformation Process and Its Numerical Solution 166
4.14 The Velocity and Pressure Distribution 167
4.15 Aerofoil Characteristics 175
4.15.1 Parameters Governing the Aerodynamic Forces 177
4.16 Aerofoil Geometry 177
4.16.1 Aerofoil Nomenclature 177
4.16.2 NASA Aerofoils 181
4.16.3 Leading-Edge Radius and Chord Line 181
4.16.4 Mean Camber Line 181
4.16.5 Thickness Distribution 182
4.16.6 Trailing-Edge Angle 182
4.17 Wing Geometrical Parameters 182
4.18 Aerodynamic Force and Moment Coefficients 186
4.18.1 Moment Coefficient 189
4.19 Summary 191
Exercise Problems 200
Reference 201
5 Vortex Theory 203
5.1 Introduction 203
5.2 Vorticity Equation in Rectangular Coordinates 204
5.2.1 Vorticity Equation in Polar Coordinates 206
5.3 Circulation 208
5.4 Line (point) Vortex 212
5.5 Laws of Vortex Motion 214
5.6 Helmholtz’s Theorems 215
5.7 Vortex Theorems 216
5.7.1 Stoke’s Theorem 220
5.8 Calculation of uR, the Velocity due to Rotational Flow 224
5.9 Biot-Savart Law 227
5.9.1 A Linear Vortex of Finite Length 230
5.9.2 Semi-Infinite Vortex 231
5.9.3 Infinite Vortex 231
5.9.4 Helmholtz’s Second Vortex Theorem 236
5.9.5 Helmholtz’s Third Vortex Theorem 240
5.9.6 Helmholtz’s Fourth Vortex Theorem 240
5.10 Vortex Motion 240
5.11 Forced Vortex 243
5.12 Free Vortex 244
5.12.1 Free Spiral Vortex 246
5.13 Compound Vortex 249
5.14 Physical Meaning of Circulation 250
5.15 Rectilinear Vortices 255
5.15.1 Circular Vortex 256
5.16 Velocity Distribution 257
5.17 Size of a Circular Vortex 259
5.18 Point Rectilinear Vortex 259
5.19 Vortex Pair 260
5.20 Image of a Vortex in a Plane 261
5.21 Vortex between Parallel Plates 262
5.22 Force on a Vortex 264
5.23 Mutual action of Two Vortices 264
5.24 Energy due to a Pair of Vortices 264
5.25 Line Vortex 267
5.26 Summary 268
Exercise Problems 274
References 276
6 Thin Aerofoil Theory 277
6.1 Introduction 277
6.2 General Thin Aerofoil Theory 278
6.3 Solution of the General Equation 281
6.3.1 Thin Symmetrical Flat Plate Aerofoil 282
6.3.2 The Aerodynamic Coefficients for a Flat Plate 285
6.4 The Circular Arc Aerofoil 289
6.4.1 Lift, Pitching Moment, and the Center of Pressure Location for Circular Arc Aerofoil 291
6.5 The General Thin Aerofoil Section 295
6.6 Lift, Pitching Moment and Center of Pressure Coefficients for a Thin Aerofoil 298
6.7 Flapped Aerofoil 303
6.7.1 Hinge Moment Coefficient 306
6.7.2 Jet Flap 308
6.7.3 Effect of Operating a Flap 308
6.8 Summary 309
Exercise Problems 314
References 315
7 Panel Method 317
7.1 Introduction 317
7.2 Source Panel Method 317
7.2.1 Coefficient of Pressure 320
7.3 The Vortex Panel Method 322
7.3.1 Application of Vortex Panel Method 322
7.4 Pressure Distribution around a Circular Cylinder by Source Panel Method 325
7.5 Using Panel Methods 329
7.5.1 Limitations of Panel Method 329
7.5.2 Advanced Panel Methods 329
7.6 Summary 349
Exercise Problems 350
Reference 350
8 Finite Aerofoil Theory 351
8.1 Introduction 351
8.2 Relationship between Spanwise Loading and Trailing Vorticity 351
8.3 Downwash 352
8.4 Characteristics of a Simple Symmetrical Loading – Elliptic Distribution 355
8.4.1 Lift for an Elliptic Distribution 356
8.4.2 Downwash for an Elliptic Distribution 356
8.4.3 Drag Dv due to Downwash for Elliptical Distribution 358
8.5 Aerofoil Characteristic with a More General Distribution 359
8.5.1 The Downwash for Modified Elliptic Loading 361
8.6 The Vortex Drag for Modified Loading 363
8.6.1 Condition for Vortex Drag Minimum 365
8.7 Lancaster – Prandtl Lifting Line Theory 367
8.7.1 The Lift 369
8.7.2 Induced Drag 370
8.8 Effect of Downwash on Incidence 373
8.9 The Integral Equation for the Circulation 375
8.10 Elliptic Loading 376
8.10.1 Lift and Drag for Elliptical Loading 377
8.10.2 Lift Curve Slope for Elliptical Loading 379
8.10.3 Change of Aspect Ratio with Incidence 379
8.10.4 Problem II 380
8.10.5 The Lift for Elliptic Loading 383
8.10.6 The Downwash Velocity for Elliptic Loading 386
8.10.7 The Induced Drag for Elliptic Loading 386
8.10.8 Induced Drag Minimum 389
8.10.9 Lift and Drag Calculation by Impulse Method 390
8.10.10 The Rectangular Aerofoil 391
8.10.11 Cylindrical Rectangular Aerofoil 392
8.11 Aerodynamic Characteristics of Asymmetric Loading 392
8.11.1 Lift on the Aerofoil 392
8.11.2 Downwash 392
8.11.3 Vortex Drag 393
8.11.4 Rolling Moment 394
8.11.5 Yawing Moment 396
8.12 Lifting Surface Theory 398
8.12.1 Velocity Induced by a Lifting Line Element 398
8.12.2 Munk’s Theorem of Stagger 401
8.12.3 The Induced Lift 402
8.12.4 Blenk’s Method 403
8.12.5 Rectangular Aerofoil 404
8.12.6 Calculation of the Downwash Velocity 405
8.13 Aerofoils of Small Aspect Ratio 407
8.13.1 The Integral Equation 408
8.13.2 Zero Aspect Ratio 410
8.13.3 The Acceleration Potential 410
8.14 Lifting Surface 411
8.15 Summary 414
Exercise Problems 421
9 Compressible Flows 425
9.1 Introduction 425
9.2 Thermodynamics of Compressible Flows 425
9.3 Isentropic Flow 429
9.4 Discharge from a Reservoir 431
9.5 Compressible Flow Equations 433
9.6 Crocco’s Theorem 434
9.6.1 Basic Solutions of Laplace’s Equation 438
9.7 The General Potential Equation for Three-Dimensional Flow 438
9.8 Linearization of the Potential Equation 440
9.8.1 Small Perturbation Theory 440
9.9 Potential Equation for Bodies of Revolution 443
9.9.1 Solution of Nonlinear Potential Equation 445
9.10 Boundary Conditions 445
9.10.1 Bodies of Revolution 447
9.11 Pressure Coefficient 448
9.11.1 Bodies of Revolution 449
9.12 Similarity Rule 449
9.13 Two-Dimensional Flow: Prandtl-Glauert Rule for Subsonic Flow 449
9.13.1 The Prandtl-Glauert Transformations 449
9.13.2 The Direct Problem-Version I 451
9.13.3 The Indirect Problem (Case of Equal Potentials): P-G Transformation – Version II 454
9.13.4 The Streamline Analogy (Version III): Gothert’s Rule 455
9.14 Prandtl-Glauert Rule for Supersonic Flow: Versions I and II 456
9.14.1 Subsonic Flow 456
9.14.2 Supersonic Flow 456
9.15 The von Karman Rule for Transonic Flow 459
9.15.1 Use of Karman Rule 460
9.16 Hypersonic Similarity 462
9.17 Three-Dimensional Flow: The Gothert Rule 464
9.17.1 The General Similarity Rule 464
9.17.2 Gothert Rule 466
9.17.3 Application to Wings of Finite Span 467
9.17.4 Application to Bodies of Revolution and Fuselage 468
9.17.5 The Prandtl-Glauert Rule 470
9.17.6 The von Karman Rule for Transonic Flow 474
9.18 Moving Disturbance 475
9.18.1 Small Disturbance 476
9.18.2 Finite Disturbance 477
9.19 Normal Shock Waves 477
9.19.1 Equations of Motion for a Normal Shock Wave 477
9.19.2 The Normal Shock Relations for a Perfect Gas 478
9.20 Change of Total Pressure across a Shock 482
9.21 Oblique Shock and Expansion Waves 483
9.21.1 Oblique Shock Relations 484
9.21.2 Relation between ? and ? 486
9.21.3 Supersonic Flow over a Wedge 489
9.21.4 Weak Oblique Shocks 491
9.21.5 Supersonic Compression 493
9.21.6 Supersonic Expansion by Turning 495
9.21.7 The Prandtl-Meyer Function 497
9.21.8 Shock-Expansion Theory 497
9.22 Thin Aerofoil Theory 499
9.22.1 Application of Thin Aerofoil Theory 500
9.23 Two-Dimensional Compressible Flows 505
9.24 General Linear Solution for Supersonic Flow 506
9.24.1 Existence of Characteristics in a Physical Problem 508
9.24.2 Equation for the Streamlines from Kinematic Flow Condition 509
9.25 Flow over a Wave-Shaped Wall 511
9.25.1 Incompressible Flow 511
9.25.2 Compressible Subsonic Flow 512
9.25.3 Supersonic Flow 513
9.25.4 Pressure Coefficient 514
9.26 Summary 515
Exercise Problems 529
References 532
10 Simple Flights 533
10.1 Introduction 533
10.2 Linear Flight 533
10.3 Stalling 534
10.4 Gliding 536
10.5 Straight Horizontal Flight 538
10.6 Sudden Increase of Incidence 540
10.7 Straight Side-Slip 541
10.8 Banked Turn 542
10.9 Phugoid Motion 543
10.10 The Phugoid Oscillation 545
10.11 Summary 549
Exercise Problems 551
Further Readings 553
Index 555

Rezensionen

"Theoretical Aerodynamics is a user-friendly text for a full course on theoretical aerodynamics.... Presented in an easy-to-read style making full use of figures and illustrations to enhance understanding, and moves well simpler to more advanced topics." (Expofairs.com, 20 June 2013)

"The main objective of the book is to cover the classical theory for inviscid flow using exact solutions of the linear equations or approximations to the equations with, for example, panel methods and thin aerofoil theory. This provides a good grounding for the student in the basic properties of the fluid flow and results can be achieved by simple calculation." (The Aeronautical Journal, 2015)

Produkt-Details

• Erscheint lt. Verlag: 8.3.2013
• Sprache: englisch
• Themenwelt: Technik ► Fahrzeugbau / Schiffbau
• Themenwelt: Technik ► Luft- / Raumfahrttechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Aerodynamik • Aeronautic & Aerospace Engineering • fluid mechanics • Luft- u. Raumfahrttechnik • Maschinenbau • mechanical engineering • Strömungsmechanik • Strömungsmechanik • Theoretical Aerodynamics, Fluid Mechanics, Conformal Transformation, Flow Pattern, Joukowski transformation, Vortex Dynamics, Wing Theory, Thin Aerofoil Theory, Finite Aerofoil Theory, Compressible Flows, Linear Flight • thermodynamics • Thermodynamik
• ISBN-10: 1-118-47936-X / 111847936X
• ISBN-13: 978-1-118-47936-0 / 9781118479360