LOW-SPEED AERODYNAMICS From Wing Theory to Panel Methods McGraw-Hill Series in Aeronautical and Aerospace Engineering Consulting Editor John U. Anderson, Jr., 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 Schlichling: Boundary Layer Theory White: Viscous Fluid Flow Wiesel: Spaceflight Dynamics LOW-SPEED AERODYNAMICS From Wing Theory to Panel Methods Joseph Katz Allen Plotkin Professors of Aerospace Engineering and Engineering Mechanics San Diego State University McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas Hamburg Lisbon London Madrid Mexico Milan Montreal New Delhi Paris San Juan São Paulo Singapore Sydney Tokyo Toronto LOW-SPEED AERODYNAMICS From Wing Theory to Panel Methods INTERNATIONAL EDITION 1991 Exclusive rights by McGraw-Hill Book Co. -Singapore for manufacture and export. This book cannot be re-exported from the country to which it is consigned by McGraw-Hill. 3 4 5 6 7 8 9 0 CMO PMP 9 5 4 Copyright c 1991 by McGraw-Hill, Inc. All rights reserved. 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. This bookwasset in Times Roman. The editors were John J. Corrigan and John M. Morriss; the production supervisor was Denise L. Puryear. The cover was designed by Rafael Hernandez. Project supervision was done by Universities Press. Library of Congress Cataloging-in-Publication Data Katz, Joseph, (date). Low-speed aerodynamics: from wing theory to panel methods / Joseph Katz and Allen Plotkin. p. cm.—(McGraw-Hill series in aeronautical and aerospace engineering) ISBN 0-07-050446-6 1. Aerodynamics. I. Plokin, Allen. II. Title. III. Series. TL570.K34 1991 629.132'3—dc2O 90-38041 When ordering this title use ISBN 0-07-100876-4 PrintedinSingapore ABOUT THE AUTHORS Joseph Katz is Professor of Aerospace Engineering and Engineering Mechan- ics at San Diego State University where he has been a faculty member since 1986. He received the degrees of BSc, MSc and DSc, the latter in 1977, in Aeronautical Engineering from the Technion-Israel Institute of Technology. He was a faculty member in the Mechanical Engineering Department of the Technion from 1980—1984 and headed the Automotive Program from 1982— 1984. He spent 1978—1980 and 1984—1986 at the Large Scale Aerodynamics Branch of NASA-Ames Research Center as a Research Associate and Senior Research Associate, respectively, and has maintained his ties to NASA through grant support. He has worked in the 40' by 80' full scale wind tunnel and has developed a panel method capable of calculating three-dimensional unsteady flowfields and applied it to complete aircraft and race car configura- tions. He is the author of more than 40 journal articles in computational and experimental aerodynamics. Allen Plotkin is Professor of Aerospace Engineering and Engineering Mechan- ics at San Diego State University where he has been a faculty member since 1985. He graduated from the Bronx High School of Science, received BS and MS degrees from Columbia University and a PhD from Stanford University in 1968. He was a faculty member in the Department of Aerospace Engineering of the University of Maryland from 1968—1985. In 1976 he received the Young Engineer-Scientist Award from the National Capital Section of the AIAA and in 1981 received the Engineering Sciences Award from the Washington Academy of Sciences. 1-le is an Associate Fellow of the AIAA and served two terms as an associate editor of the AIAA Journal from 1986—1991. He is the current contributor to the World Book Encyclopedia articles on Aerodynamics, Propeller, Streamlining, and Wind Tunnel. He is the author of approximately 40 journal articles in aerodynamics and fluid mechanics. V CONTENTS Preface xiii 1 Introduction and Background 1 1.1 Description of Fluid Motion 1 1.2 Choice of Coordinate System 3 1.3 Pathlines, Streaklines, and Streamlines 4 1.4 Forces in a Fluid 5 1.5 Integral Form of the Fluid Dynamic Equations 8 1.6 Differential Form of the Fluid Dynamic Equations 10 1.7 Dimensional Analysis of the Fluid Dynamic Equations 16 1.8 Flow with High Reynolds Number 20 1.9 Similarity of Flows 23 2 Fundamentals of Inviscid, Incompressible Flow 25 2.1 Angular Velocity, Vorticity and Circulation 25 2.2 Rate of Change of Vorticity 29 2.3 Rate of Change of Circulation—Kelvin's Theorem 30 2.4 Irrotational Flow and the Velocity Potential 32 2.5 Boundary and Infinity Conditions 33 2.6 Bernoulli's Equation for the Pressure 34 2.7 Simply and Multiply Connected Regions 35 2.8 Uniqueness of the Solution 36 2.9 Vortex Quantities 39 2.10 Two-Dimensional Vortex 41 2.11 The Biot—Savart Law 44 2.12 The Velocity Induced by a Straight Vortex Segment 46 2.13 The Stream Function 48 3 General Solution of the Incompressible, Potential Flow Equations 52 3.1 Statement of the Potential Flow Problem 52 vu