FUNDAMENTALS OF AERODYNAMICS ~,. ~,,~ \~/!)AI~,~~ McGraw-Hill Series in Aeronautical and Aerospace Engineering Consulting Editor John D., University of Maryland Anderson: Fundamentals of Aerodynamics Anderson: Hypersonic and High Temperature Gas Dynamics Anderson: Introduction to Flight Anderson: Modern Compressible Flow With Historical Perspective D' Azzo and Houpis: Linear Control System Analysis and Design Kane, Likins and Levinson: Spacecraft Dynamics Katz and Plotkin: Low-Speed Aerodynamics: From Wing Theory to Panel Methods Nelson: Flight Stability and Automatic Control Peery and Azar: Aircraft Structures Rivello: Theory and Analysis of Flight Structures Schlichting: Boundary Layer Theory White: Viscous Fluid Flow Wiesel: Spaceflight Dynamics FUNDAMENTALS OF AERODYNAMICS Second Edition John D. Professor of Aerospace Engineering University of Maryland McGraw-Hill, Inc. New York St.
Louis San Francisco Auckland Bogota Caracas Hamburg Lisbon London Madrid Mexico Milan Montreal New Delhi Paris San Juan Sao Paulo Singapore Sydney Tokyo Toronto This book was set in Tunes Roman. The editors were Lyn Bearnesderfer and Eleanor Castellano; the production supervisor was Janelle S. The cover designer was Joan O·Connor. New drawings were done by Oxford illustrators Limited.
Arcata GraphicsIHalliday was printer and binder. FUNDAMENTALS OF AERODYNAMICS Copyright © 1991, 1984 by McGraw-Hill, Inc. All rights reserved. Printed in the United States of America.
Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. 234567890HALHAL954321 ISBN 0-07-001679-8 Library of Congress Cataloging-in-Publication Data Anderson, John David. Fundamentals of aerodynamics/ John D.-(McGraw-Hill series in aeronautical and aerospace engineering) Includes bibliographical references and index. 132'3-dc20 90-42291 ABOUT THE AUTHOR John D., was born in Lancaster, Pennsylvania, on October 1, 1937.
He attended the University of Florida, graduating in 1959 with high honors and a bachelor of aeronautical engineering degree. From 1959 to 1962, he was a lieutenant and task scientist at the Aerospace Research Laboratory at Wright- Patterson Air Force Base. From 1962 to 1966, he attended the Ohio State University under the National Science Foundation and NASA Fellowships, graduating with a Ph. in aeronautical and astronautical engineering.
In 1966, he joined the U. Naval Ordnance Laboratory as Chief of the Hypersonic Group. In 1973, he became Chairman of the Department of Aerospace Engineering at the University of Maryland, and since 1980 has been professor of Aerospace Engineering at Maryland. In 1982, he was designated a Distinguished Scholar/Teacher by the University.
During 1986-1987, while on sabbatical from the University, Dr. Anderson occupied the Charles Lindbergh chair at the National Air and Space Museum of the Smithsonian Institution. Anderson has published five books: Gasdynamic Lasers: An Introduction, Academic Press (1976), and under McGraw-Hill: Introduction to Flight (1978, 1985, and 1989), Modern Compressible Flow (1982 and 1990), Fundamentals of Aerodynamics (1984 and 1990), and Hypersonic and High Temperature Gas Dynamics (1989). He is the author of over 90 papers on radiative gas dynamics, reentry aerothermodynamics, gas dynamic and chemical lasers, computational fluid dynamics, applied aerodynamics, and hypersonic flow.
Anderson is in lVho's lVho in America, and is a Fellow of the American Institute of Aeronautics and Astronautics. He is also a fellow of the Washington Academy of Sciences, and a member of Tau Beta Pi, Sigma Tau, Phi Kappa Phi, Phi Eta Sigma, the American Society for Engineering Education, and the American Physical Society. In 1989, he was awarded the John Leland Atwood Medal for excellence in Aerospace Engineering Education, given jointly by the American Institute of Aeronautics and Astronautics and the American Society for Engineering Edu- cation. DEDICATED TO MY FAMILY Sarah-Allen, Katherine, and Elizabeth CONTENTS Preface to the Second Edition xv Preface to the First Edition xvii Part 1 Fundamental Principles Chapter 1 Aerodynamics: Some Introductory Thoughts 3 1.1 Importance of Aerodynamics: Historical Examples 3 1.2 Aerodynamics: Classification and Practical Objectives 10 1.3 Road Map for This Chapter 12 1.4 Some Fundamental Aerodynamic Variables 12 1.5 Aerodynamic Forces and Moments 15 1.6 Center of Pressure 28 1.7 Dimensional Analysis: The Buckingham Pi Theorem 30 1.9 Fluid Statics: Buoyancy Force 41 1.10 Types of Flow 48 1.11 Applied Aerodynamics: The Aerodynamic Coefficients- Their Magnitudes and Variations 54 1.12 Historical Note: The Illusive Center of Pressure 66 1.13 Summary 70 Problems 71 Chapter 2 Aerodynamics: Some Fundamental Principles and Equations 75 2.1 Introduction and Road Map 75 2.2 Review of Vector Relations 76 2.3 Models of the Fluid: Control Volumes and Fluid Elements 88 2.5 Momentum Equation 97 ix X CONTENTS 2.6 An Application of the Momentum Equation: Drag of a Two-Dimensional Body 102 2.10 Fundamental Equations in Terms of the Substantial Derivative 120 2.11 Pathlines and Streamlines of a Flow 122 2.12 Angular Velocity, Vorticity, and Strain 126 2.16 Relationship between the Stream Function and Velocity Potential 143 2.17 Summary 144 Problems 148 Part II Inviscid, Incompressible Flow Chapter 3 Fundamentals of Inviscid, Incompressible Flow 153 3.1 Introduction and Road Map 153 3.3 Incompressible Flow in a Duct: The Venturi and Low-Speed Wind Tunnel 160 3.4 Pitot Tube: Measurement of Airspeed 170 3.6 Condition on Velocity for Incompressible Flow 177 3.7 Governing Equation for Irrotational, Incompressible Flow: Laplace's Equation 178 3.9 Uniform Flow: Our First Elementary Flow 182 3.10 Source Flow: Our Second Elementary Flow 185 3.11 Combination of a Uniform Flow with a Source and Sink 189 3.12 Doublet Flow: Our Third Elementary Flow 192 3.13 Nonlifting Flow over a Circular Cylinder 195 3.14 Vortex Flow: Our Fourth Elementary Flow 200 3.15 Lifting Flow over a Cylinder 204 3.16 The Kutta-loukowski Theorem and the Generation of Lift 216 3.17 Nonlifting Flows over Arbitrary Bodies: The Numerical Source Panel Method 218 3.18 Applied Aerodynamics: The Flow over a Circular Cylinder-The Real Case 228 3.19 Historical Note: Bernouli and Euler-The Origins of Theoretical Fluid Dynamics 236 3.20 Historical Note: d' Alembert and His Paradox 241 3.21 Summary 242 Problems 245 CONTENTS xi Chapter 4 Incompressible Flow over Airfoils 247 4.4 Philosophy of Theoretical Solutions for Low-Speed Flow over Airfoils: The Vortex Sheet 255 4.5 The Kutta Condition 260 4.6 Kelvin's Circulation Theorem and the Starting Vortex 263 4.7 Classical Thin Airfoil Theory: The Symmetric Airfoil 266 4.8 The Cambered Airfoil 275 4.9 Lifting Flows over Arbitrary Bodies: The Vortex Panel Numerical Method 282 4.10 Modern Low-Speed Airfoils 289 4.11 Applied Aerodynamics: The Flow over an Airfoil-The Real Case 291 4.12 Historical Note: Early Airplane Design and the Role of Airfoil Thickness 305 4.l3 Historical Note: Kutta, loukowski, and the Circulation Theory of Lift 310 4.14 Summary 312 Problems 314 Chapter 5 Incompressible Flow over Finite Wings 315 5.1 Introduction: Downwash and Induced Drag 315 5.2 The Vortex Filament, the Biot-Savart Law, and Helmholtz's Theorems 320 5.3 Prandtl's Classical Lifting-Line Theory 324 5.4 A Numerical Nonlinear Lifting-Line Method 347 5.5 Lifting-Surface Theory; Vortex Lattice Numerical Method 351 5.6 Applied Aerodynamics: The Delta Wing 357 5.7 Historical Note: Lanchester and Prandtl-The Early Development of Finite-Wing Theory 366 5.8 Historical Note: Prandtl-The Man 370 5.9 Summary 373 Problems 374 Chapter 6 Three- Dimensional Incompressible Flow 377 6.2 Three-Dimensional Source 378 6.4 Flow over a Sphere 382 6.5 General Three-Dimensional Flows: Panel Techniques 385 6.6 Applied Aerodynamics: The Flow over a Sphere-The Real Case 387 6.7 Summary 390 Problems 390 xii CONTENTS Part III Inviscid, Compressible Flow Chapter 7 Compressible Flow: Some Preliminary Aspects 393 7.2 A Brief Review of Thermodynamics 395 7.3 Definition of Compressibility 404 7.4 Governing Equations for Inviscid, Compressible Flow 406 7.5 Definition of Total (Stagnation) Conditions 408 7.6 Some Aspects of Supersonic Flow: Shock Waves 411 7.7 Summary 415 Problems 418 Chapter 8 Normal Shock Waves and Related Topics 421 8.2 The Basic Normal Shock Equations 423 8.3 Speed of Sound 426 8.4 Special Forms of the Energy Equation 431 8.5 When Is a Flow Compressible? 436 8.6 Calculation of Normal Shock-Wave Properties 439 8.7 Measurement of Velocity in a Compressible Flow 447 8.8 Summary 450 Problems 452 Chapter 9 Oblique Shock and Expansion Waves 455 9.2 Oblique Shock Relations 460 9.3 Supersonic Flow over Wedges and Cones 474 9.4 Shock Interactions and Reflections 477 9.5 Detached Shock Wave in Front of a Blunt Body 482 9.6 Prandtl-Meyer Expansion Waves 484 9.7 Shock-Expansion Theory: Applications to Supersonic Airfoils 489 9.8 Historical Note: Ernst Mach-A Biographical Sketch 493 9.9 Summary 496 Problems 497 Chapter 10 Compressible Flow through Nozzles, Diffusers, and Wind Tunnels 499 10.2 Governing Equations for Quasi-One-Dimensional Flow 501 10.5 Supersonic Wind Tunnels 522 10.6 Summary 528 Problems 529 CONH.NTS xiii Chapter 11 Subsonic Compressible Flow over Airfoils: Linear Theory 531 ILl Introduction 531 11.2 The Velocity Potential Equation 533 11.3 The Linearized Velocity Potential Equation 536 11.4 Prandtl-Glauert Compressibility Correction 542 1l.5 Improved Compressibility Corrections 546 11.6 Critical Mach Number 547 11.7 Drag-Divergence Mach Number: The Sound Barrier 551 1l.8 The Area Rule 554 11.9 The Supercritical Airfoil 556 11.10 Historical Note: High-Speed Airfoils-Early Research and Development 559 11.11 Historical Note: Richard T.
Whitcomb-Architect of the Area Rule and the Supercritical Wing 563 11.12 Summary 564 Problems 566 Chapter 12 Linearized Supersonic Flow 569 12.2 Derivation of the Linearized Supersonic Pressure Coefficient Formula 570 12.3 Application to Supersonic Airfoils 573 12.4 Summary 577 Problems 577 Chapter 13 Introduction to Numerical Techniques for Nonlinear Supersonic Flow 579 13.1 Introduction: Philosophy of Computational Fluid Dynamics 579 13.2 Elements of the Method of Characteristics 581 13.3 Supersonic Nozzle Design 589 13.4 Elements of Finite-Difference Methods 592 13.5 The Time-Dependent Technique: Application to Supersonic Blunt Bodies 600 13.6 Summary 608 Problems 608 Chapter 14 Elements of Hypersonic Flow 611 14.2 Qualitative Aspects of Hypersonic Flow 612 14.4 The Lift and Drag of Wings at Hypersonic Speeds: Newtonian Results for a Flat Plate at Angle of Attack 620 14.5 Hypersonic Shock-Wave Relations and Another Look at Newtonian Theory 627 14.6 Mach Number Independence 632 14.7 Summary 634 Problems 635 xiv CONTENTS Part IV Viscous Flow Chapter 15 Introduction to the Fundamental Principles and Equations of Viscous Flow 637 15.2 Qualitative Aspects of Viscous Flow 638 15.3 Viscosity and Thermal Conduction 646 15.4 The Navier-Stokes Equations 651 15.5 The Viscous Flow Energy Equation 655 15.7 Solutions of Viscous Flows: A Preliminary Discussion 663 15.8 Summary 666 Problems 668 Chapter 16 Some Special Cases; Couette and Poiseuille Flows 669 16.2 Couette Flow: General Discussion 670 16.3 Incompressible (Constant Property) Couette Flow 673 16.4 Compressible Couette Flow 691 16.5 Two-Dimensional Poiseuille Flow 705 16.6 Summary 708 Chapter 17 Introduction to Boundary Layers 711 17.2 Boundary-Layer Properties 713 17.3 The Boundary-Layer Equations 719 17.4 Incompressible Flow over a Flat Plate: The Blasius Solution 723 17.5 Compressible Flow over a Flat Plate 729 17.6 Results for Turbulent Boundary Layers 735 17.8 Summary 737 Problems 739 Chapter 18 Navier-Stokes Solutions: Some Examples 741 18.3 Examples of Some Solutions 742 18.4 Summary 747 Appendixes 749 A Insentropic Flow Properties 749 B Normal Shock Properties 754 C Prandtl-Meyer Function and Mach Angle 758 Bibliography 761 Index 765 I - PREFACE TO THE SECOND EDITION The purpose of this second edition is the same as the first-to be read, understood, and enjoyed. Due to the extremely favorable comments from readers and users of the first edition, virtually all the first edition has been carried over intact to the second edition. Therefore, all the basic philosophy, approach, and content discussed and itemized by the author in the Preface to the First Edition is equally applicable now. Since that preface is repeated on the following pages, no further elaboration will be given here.
Question: What distinguishes the second edition from the first? Answer: Much new material has been added in order to enhance and expand that covered in the first edition. In particular, the second edition has: 1. A much larger number of worked examples. These new worked examples provide the reader with a better understanding of how the fundamental principles of aerodynamics are used for the solution of practical problems.