Early Developments of Modern Aerodynamics PDF
Preview Early Developments of Modern Aerodynamics
Early Developments of Modern Aerodynamics J.A.D. Ackroyd B.P. Axcell A.I. Ruban BUTTERWORTH HEINEMANN Early Developments of Modern Aerodynamics Early Developments of Modern Aerodynamics Eur. Ing. J. A. D. Ackroyd, Eur. Ing. B. P. Axcell ManchesterSchoolofEngineering and A. I. Ruban Departmentof Mathematics Universityof Manchester, Oxford Road,Manchester,UK OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 WildwoodAvenue, Woburn, MA 01801-2041 A divisionof Reed Educational and Professional PublishingLtd A member of theReed Elsevier plc group First published2001 J. A. D. Ackroyd, B. P. Axcell, A. I. Ruban 2001 All rights reserved. No part of this publication may be reproduced in any material form (including photocopyingor storing in any medium by electronic means and whetheror not transiently or incidentally to some other use of this publication)withoutthe written permission of the copyright holderexcept in accordance with the provisionsof the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London,England W1P OLP. Applicationsfor the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publishers British Library Cataloguing in Publication Data Ackroyd, J. A. D. Early developments of modern aerodynamics 1. Aerodynamics 2. Aerodynamics – History I. Title II. Axcell, B. P. III. Ruban, A. I. 629.10323 Library of Congress Cataloguing in Publication Data Ackroyd, J. A. D. Early developments of modern aerodynamics / J. A. D. Ackroyd, B. P. Axcell, and A. I. Ruban p. cm. Includes bibliographicalreferences and index. ISBN 0 7506 5133 4 1. Aerodynamics – History. I. Axcell, B. P. II. Ruban, A. I. III. Title. TL570 .A29 2001 629.1320009–dc21 2001037428 ISBN 0 7506 5133 4 Typeset in 10/12pt Times Roman by Laser Words, Madras, India Contents Introduction 1 1 A survey of the basic principles of modern aerodynamics 3 2 From antiquity to the age of Newton 14 3 From Newton to the emergence of the field theory of fluid flow 19 4 The era of the whirling arm and the invention of the aeroplane 27 5 Nineteenth-century developments in the understanding of fluid flow 42 6 Practical developments in aeronautics 51 7 Frederick William Lanchester (1868–1946) 57 8 Lift forces in flowing fluids (Kutta, 1902) 70 Commentary on Kutta (1902) 74 9 On the motion of fluids with very little friction (Prandtl, 1904) 77 Commentary on Prandtl (1904) 84 10 On annexed vortices (Zhukovskii, 1906a) 88 Commentary on Zhukovskii (1906a) 105 11 Boundary layers in fluids with small friction (Blasius, 1908) 107 Introduction 107 I Boundarylayer for the steady motion at flat plate immersed parallel to the streamlines 110 II Calculation of the separation position behind a body immersed in a steady flow 118 III Emergence of the boundary layer and the separation position with a sudden onset of motion from rest 125 IV Formation of the separation position with motion uniformly accelerating from rest 130 vi Contents V Application of the results of the separation problems to the circular cylinder 137 Commentary on Blasius (1908) 142 12 On a two-dimensional flow related to the fundamentals of the problems of flight (Kutta, 1910) 145 1 Introduction 145 2 General expression 147 3 The arched shell of circular form 149 4 The lift force on the shell 155 5 A numerical example: the rounding of the leading edge 160 6 Flat plate and shell under various angles of attack ˇ 171 7 Final considerations 180 Commentary on Kutta (1910) 183 13 On the pressure exerted by a plane-parallel flow on obstructing bodies (aeroplane theory) (Chaplygin, 1910) 186 1 Introduction 186 2 Derivation of the general formula for components of the pressure force 187 3 Pressure force in the presence of standing vortices 189 4 The pressure force on a segment of a circular cylinder 191 5 The pressure force acting on a complex wing 198 6 A wing with one cuspidal point 208 7 Other wing forms 211 8 The flow past a plate shaped into a circular arc in the presence of a vortex 213 9 Calculation of the rotating moment 218 Commentary on Chaplygin (1910) 220 14 On the contours of the aerofoils of hang gliders (Zhukovskii, 1920) 223 Commentary on Zhukovskii (1910) 229 15 Subsequent developments 232 References 234 Index 241 Introduction The modern science of aerodynamics began to emerge about one hundred years ago and it is therefore both timely and appropriate that we celebrate its inception. Rather by chance, its emergence almost coincided with the Wright brothers’ demonstration to the world that the dream of powered flight had become reality. Yet the new science of aerodynamics was not only providing the explanation for why flight is possible but was also indicating how it might be accomplished with far greater efficiency in the future. Indeed, the basic principles of the subject, emerging in a mere half-dozen published papers, provided the scientific wherewithal and set the stage for one of the most rapid, and dramatic, technological developments the world has seen. In popular terms, each time we take our holiday or business flight we do so by courtesy of those principles established a century ago, and in the same sense as embarkation on a sea voyage requires the support of the far older buoyancy principle of Archimedes. Clearly, then, there is much to celebrate. Our form of celebration adopted here, however,hasbeensuggestedbymorecogentreasonsthanmerelythatofritualapplause for all this scientific, technological and industrial exuberance. In the first place, those half-dozen or so publications are now not easily obtained, so that a case stands for their re-publication. Secondly, the papers are not in English, and therefore the detail of their content often remains obscure to those unfamiliar with the native language of their authors. While it is both right and proper to see citations to Kutta (1902) and Prandtl (1904) as the origins of modern lift and drag theories, such references have a tendency to become rather more ritual gestures than acknowledgements of known work.Soathirdreasonforourformofcelebrationisthatitprovidesanopportunityto present English translations of these key papers which ushered in the modern science of flight. A fourth and more general reason is that it is often informative, as well as illuminating, to be able to study the manner in which notable scientists of the past made and described their discoveries. To this point, the German polymath, Gottfried Wilhelm von Leibniz (1646–1716), provides apt justification: Itisanextremelyusefulthingtohaveknowledgeofthetrueoriginsofmemorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examplesof it. 2 EarlyDevelopmentsofModernAerodynamics Thus our subject’s noteworthy historical examples have been collected within a single volume, presented here in English translation, some for the first time, in the hope that both those familiar with the subject and also newcomers to the field may draw both instruction and inspiration from their art of revelation. To set the scene for these seminal papers, our celebration begins with a modern view of the essential features of the subject. This is followed by a historical survey of the key ideas which preceded the papers. The survey is based on material appearing in the Aeronautical Journal (Ackroyd, 1992, 2000), its use being by kind permission of the Royal Aeronautical Society. Readers familiar with the subject will realize that one paper has been omitted from the collection presented in translation here. This is Zhukovskii’s paper ‘On the fall through the air of light bodies of elongated shape, animated by a rotary movement’ (Zhukovskii, 1906b). Our reason for this omission is that the paper adds little to the discovery, announced in Zhukovskii (1906a), of what later became known as the Kutta–Zhukovskii theorem. Nonetheless, we are grateful to Dr Laurent Dala and Ms Helen Sharples for providing a translation of Zhukovskii (1906b) from the original French. A brief indication of the paper’s contents is provided in Chapter 10. A note onreferencesis appropriate,however,beforewe begin. Apartfromthe orig- inal referencing schemes retained in the papers re-published here, the system adopted is that recommended by the Royal Society. This has the advantage, particularly in matters of historical progression, of emphasizing the timing of an idea through the date of publication; thus, for example, Prandtl (1904). However, when review publi- cations are cited, these are indicated by use of italics; thus, for example, Ackroyd (1992). 1 A survey of the basic principles of modern aerodynamics The briefest trawl through the contents of this book will reveal that our subject here, in a broad sense, is fluid flow. The term ‘fluid’ here embraces both gases and liquids which, in simple terms, differ only in the magnitudes of their material properties such as density and viscosity. Our stress on viscosity will no doubt surprise newcomers to the subject. However, it must be emphasized at the outset that, without viscosity, all flight,eveninnature,wouldbeimpossiblesincewingswouldproducenolift.Fromthis itfollows thatboth marineandaircraftpropellers – essentiallyrotatingwings – would be useless, while ships driven since antiquity by sails – flexible wings – would have suffered an extremely short history. Moreover, without viscosity we would all be in severe danger of asphyxiating in our own exhalations. Thus an understanding of the role of viscosity emerges as not only vital to any explanation of flight but also vital, quite literally, to life itself. As a material property, viscosity acts so as to transmit shearing effectsthroughout a fluid. Its action can be understood from the situation shown in Fig. 1.1. This figure is takenfromLanchester(1907),oneofthefirsttograspviscosity’sroleinflightandwho, himself, drew the figure from Maxwell (1870) who was the first to measure its prop- erties. Fig. 1.1 shows a fluid sandwiched between two long parallel solid plates. The upper plate moves at constant speed, as shown, whereas the lower plate is stationary. The fluid sticks to the surface of each plate, that is the fluid has the same velocity as thatofthesolidsurfacewithwhichitisincontact.Thisphenomenonisnowknownas the no-slip condition. It occurs because of interaction on the molecular scale between the fluid and the solid. Because of the imposition of this condition, there is a contin- uousvelocityvariationinthefluidbetweentheplates.Thisvariationisdepictedbythe lines ab in the figure. If we imagine that we can draw a rectangle in the fluid at one instant,andthenwatchthisshapeastimeprogresses,thenwhatwewouldseeisshown in Fig. 1.2. Our rectangular element distorts, its angles change, it suffers increasing angularstrainastimeprogresses.Andthiscontinuousstrainingiscausedbytheviscous shearing forces shown, which act around the periphery of our rectangle. The action is akin to shearinga thick book lying on a table by pushing sideways acrossits cover.In thefluidcase,however,asthekinetictheoryofMaxwell(1860)revealsforgases,these viscous shearing forces are the consequence of the random motion of fluid molecules. Those from a higher speed fluid layer randomly collide with molecules in a layer of lower speed, or vice versa, thereby exchanging momentum between layers. Such momentum changes on the molecular scale thus create at the macroscopic level the viscous forces between layers. These viscous forces not only act upon each and every 4 EarlyDevelopmentsofModernAerodynamics V C D a b a b a b h a b ab A B Fig.1.1 Theviscousflowbetweentwolongparallelplates(adaptedfromLanchester,1907). fluidelementbutalso, asitturnsout, aredirectlyrelatedtothecontinuous strainingof theelement.Andthesedistortions,inturn,arerelateddirectlytothevelocityvariations within the flow, specifically combinations of the flow’s velocity gradients which have been imposed by the no-slip condition. At this point we need to be rather more specific about the form of these viscous forces, by stating that they turn out to be calculable as the simple multiple of a flow’s continuous straining and the fluid’s coefficient of viscosity. This coefficient, like density, is a property of the fluid itself, not the flow. Depending on the fluid, the numerical value of this coefficient varies enormously. Air and water, for example, possessextremelysmallviscosityvalueswhereasthoseforfluidssuchasoilandtreacle are verylarge. Here,however, we are interested predominantly in airflows. The essen- tial point in such cases is that, even though the air’s viscosity coefficient is extremely small, the viscous forceswithin its flows are appreciablewhereverthe flow’s straining becomes intense. Now suppose that our rectangular element of Fig. 1.2 is replaced by one which is circular. If you wish, you can think of the fluid now as being composed of thousands of tiny ball bearings. One of these is shown in Fig. 1.3, again subject to the viscous shearingforcesdescribedearlier.Clearly,the actionof suchshearingforceswill cause the balls to spin about their own centres. In other words, a further action of viscosity is to cause rotation, or vorticity, within each tiny element of the fluid. One other force shown actinginFig. 1.3is that dueto pressure.Butsuchforces,actingalwaysnormal to the ball’s surface so that their lines of action therefore pass always through its centre, cannot alone change whatever angular momentum the ball possesses because suchpressureforcescancreatenomomentsabouttheball’scentre.Similarly,theball’s ownweight,alsoactingthroughitscentre,isequallyunproductiveinchangingangular momentum. Viscous shearing force Fig.1.2 TheangulardistortionastimeprogressesofafluidelementshowninFig.1.1.
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