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Aerodynamics for Engineering Students Aerodynamics for Engineering Students Sixth Edition E.L Houghton P.W Carpenter Steven H Collicott Daniel T Valentine AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Butterworth-Heinemann is an imprint of Elsevier Butterworth-Heinemann is an imprint of Elsevier 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK c 2013 Elsevier, Ltd All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein) Notices Knowledge and best practice in this field are constantly changing As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein MATLAB is a trademark of The MathWorks, Inc and is used with permission The MathWorks does not warrant the accuracy of the text or exercises in this book This book’s use or discussion of MATLAB software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB software Library of Congress Cataloging-in-Publication Data Aerodynamics for engineering students / E.L Houghton [et al.] – 6th ed p cm ISBN: 978-0-08-096632-8 (pbk.) Aerodynamics Airplanes–Design and construction I Houghton, E L (Edward Lewis) TL570.H64 2012 629.132'5–dc23 2011047033 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library For information on all Butterworth-Heinemann publications visit our Web site at www.elsevierdirect.com Printed in the United States 12 13 14 15 16 17 18 10 Preface This volume is intended for engineering students in introductory aerodynamics courses and as a reference useful for reviewing foundational topics for graduate courses The sequence of subject development in this edition begins with definitions and concepts and then moves on to incompressible flow, low speed airfoil and wing theories, compressible flow, high speed wing theories, viscous flow, boundary layers, transition and turbulence, wing design, and concludes with propellers and propulsion Reinforcing or teaching first the units, dimensions, and properties of the physical quantities used in aerodynamics addresses concepts that are perhaps both the simplest and the most critical Common aeronautical definitions are covered before lessons on the aerodynamic forces involved and how the forces drive our definitions of airfoil characteristics The fundamental fluid dynamics required for the development of aerodynamic studies and the analysis of flows within and around solid boundaries for air at subsonic speeds is explored in depth in the next two chapters Classical airfoil and wing theories for the estimation of aerodynamic characteristics in these regimes are then developed Attention is then turned to the aerodynamics of high speed air flows in Chapters and The laws governing the behavior of the physical properties of air are applied to the transonic and supersonic flow speeds and the aerodynamics of the abrupt changes in the flow characteristics at these speeds, shock waves, are explained Then compressible flow theories are applied to explain the significant effects on wings in transonic and supersonic flight and to develop appropriate aerodynamic characteristics Viscosity is a key physical quantity of air and its significance in aerodynamic situations is next considered in depth The powerful concept of the boundary layer and the development of properties of various flows when adjacent to solid boundaries create a body of reliable methods for estimating the fluid forces due to viscosity In aerodynamics, these forces are notably skin friction and profile drag Chapters on wing design and flow control, and propellers and propulsion, respectively, bring together disparate aspects of the previous chapters as appropriate This permits discussion of some practical and individual applications of aerodynamics Obviously aerodynamic design today relies extensively on computational methods This is reflected in part in this volume by the introduction, where appropriate, of descriptions and discussions of relevant computational techniques However, this text is aimed at providing the fundamental fluid dynamics or aerodynamics background necessary for students to move successfully into a dedicated course on computation methods or experimental methods As such, experience in computational techniques or experimental techniques are not required for a complete understanding of the aerodynamics in this book The authors urge students onward to such advanced courses and exciting careers in aerodynamics xv xvi Preface ADDITIONAL RESOURCES A set of m files for the MATLAB routines in the book are available by visiting the book’s companion site, www.elsevierdirect.com and searching on ‘houghton.’ Instructors using the text for a course may access the solutions manual and image bank by visiting www.textbooks.elsevier.com and following the online registration instructions ACKNOWLEDGEMENTS The authors thank the following faculty, who provided feedback on this project through survey responses, review of proposal, and/or review of chapters: Alina Alexeenko S Firasat Ali David Bridges Russell M Cummings Paul Dawson Simon W Evans, Ph.D Richard S Figliola Timothy W Fox Ashok Gopalarathnam Dr Mark W Johnson Brian Landrum, Ph.D Gary L Solbrekken Mohammad E Taslim Valana Wells Purdue University Tuskegee University Mississippi State University California Polytechnic State University Boise State University Worcester Polytechnic Institute Clemson University California State University Northridge North Carolina State University University of Liverpool University of Alabama in Huntsville University of Missouri Northeastern University Arizona State University Professors Collicott and Valentine are grateful for the opportunity to continue the work of Professors Houghton and Carpenter and thank Joe Hayton, Publisher, for the invitation to so In addition, the professional efforts of Mike Joyce, Editorial Program Manager, Heather Tighe, Production Manager, and Kristen Davis, Designer are instrumental in the creation of this sixth edition The products of one’s efforts are of course the culmination of all of one’s experiences with others Foremost amongst the people who are to be thanked most warmly for support are our families Collicott and Valentine thank Jennifer, Sarah, and Rachel and Mary, Clara, and Zach T., respectively, for their love and for the countless joys that they bring to us Our Professors and students over the decades are major contributors to our aerodynamics knowledge and we are thankful for them The authors share their deep gratitude for God’s boundless love and grace for all CHAPTER Basic Concepts and Definitions “To work intelligently” (Orville and Wilbur Wright) “one needs to know the effects of variations incorporated in the surfaces The pressures on squares are different from those on rectangles, circles, triangles, or ellipses The shape of the edge also makes a difference.” from The Structure of the Plane – Muriel Rukeyser LEARNING OBJECTIVES • Review the fundamental principles of fluid mechanics and thermodynamics required to investigate the aerodynamics of airfoils, wings, and airplanes • Recall the concepts of units and dimension and how they are applied to solving and understanding engineering problems • Learn about the geometric features of airfoils, wings, and airplanes and how the names for these features are used in aerodynamics communications • Explore the aerodynamic forces and moments that act on airfoils, wings, and airplanes and learn how we describe these loads quantitatively in dimensional form and as coefficients 1.1 INTRODUCTION The study of aerodynamics requires a number of basic definitions, including an unambiguous nomenclature and an understanding of the relevant physical properties, related mechanics, and appropriate mathematics Of course, these notions are common to other disciplines, and it is the purpose of this chapter to identify and explain those that are basic and pertinent to aerodynamics and that are to be used in the remainder of the volume Aerodynamics for Engineering Students DOI: 10.1016/B978-0-08-096632-8.00001-1 c 2013 Elsevier Ltd All rights reserved CHAPTER Basic Concepts and Definitions 1.1.1 Basic Concepts This text is an introductory investigation of aerodynamics for engineering students.1 Hence, we are interested in theory to the extent that it can be practically applied to solve engineering problems related to the design and analysis of aerodynamic objects The design of vehicles such as airplanes has advanced to the level where we require the wealth of experience gained in the investigation of flight over the past 100 years We plan to investigate the clever approximations made by the few who learned how to apply mathematical ideas that led to productive methods and useful formulas to predict the dynamical behavior of “aerodynamic” shapes We need to learn the strengths and, more important, the limitations of the methodologies and discoveries that came before us Although we have extensive archives of recorded experience in aeronautics, there are still many opportunities for advancement For example, significant advancements can be achieved in the state of the art in design analysis As we develop ideas related to the physics of flight and the engineering of flight vehicles, we will learn the strengths and limitations of existing procedures and existing computational tools (commercially available or otherwise) We will learn how airfoils and wings perform and how we approach the designs of these objects by analytical procedures The fluid of primary interest is air, which is a gas at standard atmospheric conditions We assume that air’s dynamics can be effectively modeled in terms of the continuum fluid dynamics of an incompressible or simple-compressible fluid Air is a fluid whose local thermodynamic state we assume is described either by its mass density ρ = constant, or by the ideal gas law In other words, we assume air behaves as either an incompressible or a simple-compressible medium, respectively The concepts of a continuum, an incompressible substance, and a simple-compressible gas will be elaborated on in Chapter The equation of state, known as the ideal gas law, relates two thermodynamic properties to other properties and, in particular, the pressure It is p = ρ RT where p is the thermodynamic pressure, ρ is mass density, T is absolute (thermodynamic) temperature, and R = 287 J/(kg K) or R = 1716 ft-lb (slug◦ R)−1 Pressure and temperature are relatively easy to measure For example, “standard” barometric pressure at sea level is p = 101,325 Pascals, where a Pascal (Pa) is 1N/m2 In Imperial units this is 14.675 psi, where psi is lb/in2 and psi is equal to 6895 Pa (note that It has long been common in engineering schools for an elementary, macroscopic thermodynamics course to be completed prior to a compressible-flow course The portions of this text that discuss compressible flow assume that such a course precedes this one, and thus the discussions assume some elementary experience with concepts such as internal energy and enthalpy 1.1 Introduction 14.675 psi is equal to 2113.2 lb/ft2 ) The standard temperature is 288.15 K (or 15◦ C, where absolute zero equal to −273.15◦ C is used) In Imperial units this is 519◦ R (or 59◦ F, where absolute zero equal to −459.67◦ F is used) Substituting into the ideal gas law, we get for the standard density ρ = 1.225 kg/m3 in SI units (and ρ = 0.00237 slugs/ft3 in Imperial units) This is the density of air at sea level given in the table of data for atmospheric air; the table for standard atmospheric conditions is provided in Appendix B The thermodynamic properties of pressure, temperature, and density are assumed to be the properties of a mass-point particle of air at a location x = (x, y, z) in space at a particular instant in time, t We assume the measurement volume to be sufficiently small to be considered a mathematical point We also assume that it is sufficiently large so that these properties have meaning from the perspective of equilibrium thermodynamics And we further assume that the properties are the same as those described in a course on classical equilibrium thermodynamics Therefore, we assume that local thermodynamic equilibrium prevails within the mass-point particle at x and t regardless of how fast the thermodynamic state changes as the particle moves from one location in space to another This is an acceptable assumption for our macroscopic purposes because molecular processes are typically faster than changes in the flow field we are interested in from a macroscopic point of view In addition, we invoke the continuum hypothesis, which states that we can define all flow properties as continuous functions of position and time and that these functions are smooth, that is, their derivatives are continuous This allows us to apply differential integral calculus to solve partial differential equations that successfully model the flow fields of interest in this course In other words, predictions based on the theory reported in this text have been experimentally verified To develop the theory, the fundamental principles of classical mechanics are assumed They are • • • • Conservation of mass Newton’s second law of motion First law of thermodynamics Second law of thermodynamics The principle of conservation of mass defines a mass-point particle, which is a fixedmass particle Thus the principle also defines mass density ρ, which is mass per unit volume If a mass-point particle conserves mass, as we have postulated, then density changes can only occur if the volume of the particle changes, because the dimension of mass density is M/L3 , where M is mass and L is length The SI unit of density is thus kg/m3 Newton’s second law defines the concept of force in terms of acceleration (“F = ma”) The acceleration of a mass-point particle is the change in its velocity with respect to a change in time Let the velocity vector u = (u, v, w); this is the velocity of a mass-point particle at a point in space, x = (x, y, z), at a particular instant in time t CHAPTER Basic Concepts and Definitions The acceleration of this mass-point particle is a= Du ∂u = + u · ∇u Dt ∂t This is known as the substantial derivative of the velocity vector Since we are interested in the properties at fixed points in space in a coordinate system attached to the object of interest (i.e., the “laboratory” coordinates), there are two parts to masspoint particle acceleration The first is the local change in velocity with respect to time The second takes into account the convective acceleration associated with a change in velocity of the mass-point particle from its location upstream of the point of interest to the observation point x at time t We will also be interested in the spatial and temporal changes in any property f of a mass-point particle of fluid These changes are described by the substantial derivative as follows: Df ∂f = + u · ∇f Dt ∂t This equation describes the changes in any material property f of a mass point at a particular location in space at a particular instant in time This is in a laboratory reference frame, the so-called Eulerian viewpoint The next step in conceptual development of a theory is to connect the changes in flow properties with the forces, moments, and energy exchange that cause these changes to happen We this by first adopting the Newtonian simple-compressible viscous fluid model for real fluids (e.g., water and air), which is described in detail in Chapter Moreover, we will apply the simpler, yet quite useful, Euler’s perfect fluid model, also described in Chapter It is quite fortunate that the latter model has significant practical use in the design analysis of aerodynamic objects Before we proceed to Chapter and look at the development of the equations of motion and the simplifications we will apply to potential flows in Chapters 3, and 5, we review some useful mathematical tools, define the geometry of the wing, and provide an overview of wing performance in the next three sections, respectively 1.1.2 Measures of Dynamical Properties The mathematical concepts presented in this section and applied in this text describe the dynamic behavior of a thermo-mechanical fluid In other words, we neglect electromagnetic, relativistic, and quantum effects on dynamics Also, as already pointed out, we take the view that the properties are continuous functions of location in space and time The discussion of units and dimensions here are thus limited to the measures of flow properties of fluids (liquids and gases) near the surface of the Earth under standard conditions The units and dimensions of all physical properties and the relevant properties of fluids are recalled, and after a review of the aeronautical definitions of 1.2 Units and Dimensions wing and airfoil geometry, the remainder of the chapter discusses aerodynamic force The origins of aerodynamic force and how it is manifest on wings and other aeronautical bodies, and the theories that permit its evaluation and design, are to be found in the following chapters In this chapter the lift, drag, side-wind components, and associated moments of aerodynamic force are conventionally identified, the application of dimensional theory establishing their coefficient form The significance of the pressure distribution around an aerodynamic body and the estimation of lift, drag, and pitching moment on the body in flight completes the basic concepts and definitions 1.2 UNITS AND DIMENSIONS Measurement and calculation require a system of units in which quantities are measured and expressed Aerospace is a global industry, and to be best prepared for a global career, engineers need to be able to work in both systems in use today Even when one works for a company with a strict standard for use of one set of units, customers, suppliers, and contractors may be better versed in another, and it is the engineer’s job to efficiently reconcile the various documents or specifications without introducing conversion errors Consider, too, the physics behind the units That is, one knows that for linear motion, force equals the product of mass and acceleration The units one uses not change the physics but change only our quantitative descriptions of the physics When confused about units, focus on the process or state being described and step through the analysis, tracking units the entire way In the United States, “Imperial” or “English” units remain common Distance (within the scale of an aerodynamic design) is described in inches or feet Mass is described by either the slug or the pound-mass (lbm) Weight is described by pounds (lb) or by the equivalent unit with a redundant name, the pound-force (lbf) Large distances—for example, the range of an aircraft—are described in miles or nautical miles Speed is feet per second, miles per hour, or knots, where one knot is one nautical mile per hour Multimillion dollar aircraft are still marketed and sold using knots and nautical miles (try a web search on “777 range”), so these units are not obsolete In other parts of the world, and in K-12 education in the United States, the dominant system of units is the Syste` me International d’Unite´ s, commonly abbreviated as “SI units.” It is used throughout this book, except in a very few places as specially noted It is essential to distinguish between “dimension” and “unit.” For example, the dimension “length” expresses the qualitative concept of linear displacement, or distance between two points, as an abstract idea, without reference to actual quantitative measurement The term “unit” indicates a specified amount of a quantity Thus a meter is a unit of length, being an actual “amount” of linear displacement, and so is ... Congress Cataloging-in-Publication Data Aerodynamics for engineering students / E.L Houghton [et al.] – 6th ed p cm ISBN: 978-0-08-096632-8 (pbk.) Aerodynamics Airplanes–Design and construction... 10 Preface This volume is intended for engineering students in introductory aerodynamics courses and as a reference useful for reviewing foundational topics for graduate courses The sequence of... kg—kilogram, slugs for slugs, and lbm for pound-mass m—meter and ft for feet s—second ◦ C—degree Celsius and ◦ F for degree Fahrenheit K—Kelvin and R for Rankine (but also for the gas constant)