Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — FM-9780080966328 — 2012/2/4 — 17:25 — Page 1 — #1 Aerodynamics for Engineering Students Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — FM-9780080966328 — 2012/2/4 — 17:25 — Page 3 — #3 Aerodynamics for Engineering Students Sixth Edition E.L. Houghton P.W. Carpenter Steven H. Collicott Daniel T. Valentine AMSTERDAM•BOSTON•HEIDELBERG•LONDON NEWYORK•OXFORD•PARIS•SANDIEGO SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO Butterworth-HeinemannisanimprintofElsevier Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — FM-9780080966328 — 2012/2/4 — 17:27 — Page 4 — #4 Butterworth-HeinemannisanimprintofElsevier 225WymanStreet,Waltham,MA02451,USA TheBoulevard,LangfordLane,Kidlington,Oxford,OX51GB,UK (cid:13)c 2013Elsevier,Ltd.Allrightsreserved. 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LibraryofCongressCataloging-in-PublicationData Aerodynamicsforengineeringstudents/E.L.Houghton...[etal.].–6thed. p.cm. ISBN:978-0-08-096632-8(pbk.) 1. Aerodynamics.2. Airplanes–Designandconstruction.I. Houghton,E.L.(EdwardLewis) TL570.H642012 629.132'5–dc23 2011047033 BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ForinformationonallButterworth-Heinemannpublications visitourWebsiteatwww.elsevierdirect.com PrintedintheUnitedStates 12 13 14 15 16 17 18 10 9 8 7 6 5 4 3 2 1 Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — Preface-9780080966328 — 2012/2/8 — 2:39 — Page xv — #1 Preface This volume is intended for engineering students in introductory aerodynamics courses and as a reference useful for reviewing foundational topics for graduate courses. Thesequenceofsubjectdevelopmentinthiseditionbeginswithdefinitionsand concepts and then moves on to incompressible flow, low speed airfoil and wing theories,compressibleflow,highspeedwingtheories,viscousflow,boundarylayers, transitionandturbulence,wingdesign,andconcludeswithpropellersandpropulsion. Reinforcingorteachingfirsttheunits,dimensions,andpropertiesofthephysical quantitiesusedinaerodynamicsaddressesconceptsthatareperhapsboththesimplest and the most critical. Common aeronautical definitions are covered before lessons ontheaerodynamicforcesinvolvedandhowtheforcesdriveourdefinitionsofair- foilcharacteristics.Thefundamentalfluiddynamicsrequiredforthedevelopmentof aerodynamicstudiesandtheanalysisofflowswithinandaroundsolidboundariesfor airatsubsonicspeedsisexploredindepthinthenexttwochapters.Classicalairfoil andwingtheoriesfortheestimationofaerodynamiccharacteristicsintheseregimes arethendeveloped. AttentionisthenturnedtotheaerodynamicsofhighspeedairflowsinChapters6 and7.Thelawsgoverningthebehaviorofthephysicalpropertiesofairareapplied 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.Viscosityisakeyphysicalquantityofairanditssignificanceinaero- dynamicsituationsisnextconsideredindepth.Thepowerfulconceptoftheboundary 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, respec- tively,bringtogetherdisparateaspectsofthepreviouschaptersasappropriate.This permitsdiscussionofsomepracticalandindividualapplicationsofaerodynamics. Obviously aerodynamic design today relies extensively on computational meth- ods.Thisisreflectedinpartinthisvolumebytheintroduction,whereappropriate,of descriptionsanddiscussionsofrelevantcomputationaltechniques.However,thistext is aimed at providing the fundamental fluid dynamics or aerodynamics background necessaryforstudentstomovesuccessfullyintoadedicatedcourseoncomputation methodsorexperimentalmethods.Assuch,experienceincomputationaltechniques orexperimentaltechniquesarenotrequiredforacompleteunderstandingoftheaero- dynamicsinthisbook.Theauthorsurgestudentsonwardtosuchadvancedcourses andexcitingcareersinaerodynamics. xv Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — Preface-9780080966328 — 2012/2/8 — 2:39 — Page xvi — #2 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 throughsurveyresponses,reviewofproposal,and/orreviewofchapters: AlinaAlexeenko PurdueUniversity S.FirasatAli TuskegeeUniversity DavidBridges MississippiStateUniversity RussellM.Cummings CaliforniaPolytechnicStateUniversity PaulDawson BoiseStateUniversity SimonW.Evans,Ph.D WorcesterPolytechnicInstitute RichardS.Figliola ClemsonUniversity TimothyW.Fox CaliforniaStateUniversityNorthridge AshokGopalarathnam NorthCarolinaStateUniversity Dr.MarkW.Johnson UniversityofLiverpool BrianLandrum,Ph.D UniversityofAlabamainHuntsville GaryL.Solbrekken UniversityofMissouri MohammadE.Taslim NortheasternUniversity ValanaWells ArizonaStateUniversity ProfessorsCollicottandValentinearegratefulfortheopportunitytocontinuethe work of Professors Houghton and Carpenter and thank Joe Hayton, Publisher, for theinvitationtodoso.Inaddition,theprofessionaleffortsofMikeJoyce,Editorial ProgramManager,HeatherTighe,ProductionManager,andKristenDavis,Designer areinstrumentalinthecreationofthissixthedition. Theproductsofone’seffortsareofcoursetheculminationofallofone’sexperi- enceswithothers.Foremostamongstthepeoplewhoaretobethankedmostwarmly forsupportareourfamilies.CollicottandValentinethankJennifer,Sarah,andRachel andMary,Clara,andZachT.,respectively,fortheirloveandforthecountlessjoys that they bring to us. Our Professors and students over the decades are major con- tributorstoouraerodynamicsknowledgeandwearethankfulforthem.Theauthors sharetheirdeepgratitudeforGod’sboundlessloveandgraceforall. Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — Ch01-9780080966328 — 2012/2/3 — 21:13 — Page 1 — #1 CHAPTER 1 Basic Concepts and Definitions “Toworkintelligently”(OrvilleandWilburWright) “oneneedstoknowtheeffectsofvariations incorporatedinthesurfaces....Thepressuresonsquares aredifferentfromthoseonrectangles,circles,triangles,or ellipses.... Theshapeoftheedgealsomakesadifference.” fromTheStructureofthePlane–MurielRukeyser LEARNING OBJECTIVES • Reviewthefundamentalprinciplesoffluidmechanicsandthermodynamics requiredtoinvestigatetheaerodynamicsofairfoils,wings,andairplanes. • Recalltheconceptsofunitsanddimensionandhowtheyareappliedtosolving andunderstandingengineeringproblems. • Learnaboutthegeometricfeaturesofairfoils,wings,andairplanesandhowthe namesforthesefeaturesareusedinaerodynamicscommunications. • Exploretheaerodynamicforcesandmomentsthatactonairfoils,wings,and airplanesandlearnhowwedescribetheseloadsquantitativelyindimensional formandascoefficients. 1.1 INTRODUCTION The study of aerodynamics requires a number of basic definitions, including an unambiguous nomenclature and an understanding of the relevant physical proper- ties, 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 explainthosethatarebasicandpertinenttoaerodynamicsandthataretobeusedin theremainderofthevolume. AerodynamicsforEngineeringStudents.DOI:10.1016/B978-0-08-096632-8.00001-1 1 (cid:13)c 2013ElsevierLtd.Allrightsreserved. Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — Ch01-9780080966328 — 2012/2/3 — 21:13 — Page 2 — #2 2 CHAPTER 1 Basic Concepts and Definitions 1.1.1 Basic Concepts Thistextisanintroductoryinvestigationofaerodynamicsforengineeringstudents.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 discoveriesthatcamebeforeus. Althoughwehaveextensivearchivesofrecordedexperienceinaeronautics,there arestillmanyopportunitiesforadvancement.Forexample,significantadvancements 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 thestrengthsandlimitationsofexistingproceduresandexistingcomputationaltools (commerciallyavailableorotherwise).Wewilllearnhowairfoilsandwingsperform andhowweapproachthedesignsoftheseobjectsbyanalyticalprocedures. The fluid of primary interest is air, which is a gas at standard atmospheric con- ditions. We assume that air’s dynamics can be effectively modeled in terms of the continuumfluiddynamicsofanincompressibleorsimple-compressiblefluid.Airis a fluid whose local thermodynamic state we assume is described either by its mass densityρ=constant,orbytheidealgaslaw.Inotherwords,weassumeairbehaves aseitheranincompressibleorasimple-compressiblemedium,respectively.Thecon- cepts of a continuum, an incompressible substance, and a simple-compressible gas willbeelaboratedoninChapter2. The equation of state, known as the ideal gas law, relates two thermodynamic propertiestootherpropertiesand,inparticular,thepressure.Itis p=ρRT where p is the thermodynamic pressure, ρ is mass density, T is absolute (thermo- dynamic)temperature,andR=287J/(kgK)orR=1716ft-lb(slug◦R)−1.Pressure andtemperaturearerelativelyeasytomeasure.Forexample,“standard”barometric pressureatsealevelisp=101,325Pascals,whereaPascal(Pa)is1N/m2.InImpe- rialunitsthisis14.675psi,wherepsiislb/in2and1psiisequalto6895Pa(notethat 1It has long been common in engineering schools for an elementary, macroscopic thermodynamics coursetobecompletedpriortoacompressible-flowcourse.Theportionsofthistextthatdiscusscom- pressible flow assume that such a course precedes this one, and thus the discussions assume some elementaryexperiencewithconceptssuchasinternalenergyandenthalpy. Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — Ch01-9780080966328 — 2012/2/3 — 21:13 — Page 3 — #3 1.1 Introduction 3 14.675psiisequalto2113.2lb/ft2).Thestandardtemperatureis288.15K(or15◦C, whereabsolutezeroequalto−273.15◦Cisused).InImperialunitsthisis519◦R(or 59◦F,whereabsolutezeroequalto−459.67◦Fisused).Substitutingintotheidealgas law, we get for the standard density ρ=1.225 kg/m3 in SI units (and ρ=0.00237 slugs/ft3 inImperialunits).Thisisthedensityofairatsealevelgiveninthetableof dataforatmosphericair;thetableforstandardatmosphericconditionsisprovidedin AppendixB. Thethermodynamicpropertiesofpressure,temperature,anddensityareassumed tobethepropertiesofamass-pointparticleofairatalocationx=(x,y,z)inspace at a particular instant in time, t. We assume the measurement volume to be suf- ficiently small to be considered a mathematical point. We also assume that it is sufficientlylargesothatthesepropertieshavemeaningfromtheperspectiveofequi- libriumthermodynamics.Andwefurtherassumethatthepropertiesarethesameas thosedescribedinacourseonclassicalequilibriumthermodynamics.Therefore,we assume that local thermodynamic equilibrium prevails within the mass-point parti- cleatxandtregardlessofhowfastthethermodynamicstatechangesastheparticle movesfromonelocationinspacetoanother.Thisisanacceptableassumptionforour macroscopicpurposesbecausemolecularprocessesaretypicallyfasterthanchanges intheflowfieldweareinterestedinfromamacroscopicpointofview.Inaddition, weinvokethecontinuumhypothesis,whichstatesthatwecandefineallflowproper- tiesascontinuousfunctionsofpositionandtimeandthatthesefunctionsaresmooth, thatis,theirderivativesarecontinuous.Thisallowsustoapplydifferentialintegral calculustosolvepartialdifferentialequationsthatsuccessfullymodeltheflowfields ofinterestinthiscourse.Inotherwords,predictionsbasedonthetheoryreportedin thistexthavebeenexperimentallyverified. To develop the theory, the fundamental principles of classical mechanics are assumed.Theyare • Conservationofmass • Newton’ssecondlawofmotion • Firstlawofthermodynamics • Secondlawofthermodynamics Theprincipleofconservationofmassdefinesamass-pointparticle,whichisafixed- massparticle.Thustheprinciplealsodefinesmassdensityρ,whichismassperunit volume.Ifamass-pointparticleconservesmass,aswehavepostulated,thendensity changescanonlyoccurifthevolumeoftheparticlechanges,becausethedimension ofmassdensityisM/L3,whereMismassandLislength.TheSIunitofdensityis thuskg/m3. Newton’ssecondlawdefinestheconceptofforceintermsofacceleration(“F= ma”). The acceleration of a mass-point particle is the change in its velocity with respecttoachangeintime.Letthevelocityvectoru=(u,v,w);thisisthevelocityof amass-pointparticleatapointinspace,x=(x,y,z),ataparticularinstantintimet. Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — Ch01-9780080966328 — 2012/2/3 — 21:13 — Page 4 — #4 4 CHAPTER 1 Basic Concepts and Definitions Theaccelerationofthismass-pointparticleis Du ∂u a= = +u·∇u Dt ∂t Thisisknownasthesubstantialderivativeofthevelocityvector.Sinceweareinter- ested in the properties at fixed points in space in a coordinate system attached to theobjectofinterest(i.e.,the“laboratory”coordinates),therearetwopartstomass- point 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 changeinvelocityofthemass-pointparticlefromitslocationupstreamofthepoint ofinteresttotheobservationpointxattimet. 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 derivativeasfollows: 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 referenceframe,theso-calledEulerianviewpoint. 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 changestohappen.WedothisbyfirstadoptingtheNewtoniansimple-compressible viscous fluid model for real fluids (e.g., water and air), which is described in detail in Chapter 2. Moreover, we will apply the simpler, yet quite useful, Euler’s perfect fluidmodel,alsodescribedinChapter2.Itisquitefortunatethatthelattermodelhas significantpracticaluseinthedesignanalysisofaerodynamicobjects. Before we proceed to Chapter 2 and look at the development of the equations of motion and the simplifications we will apply to potential flows in Chapters 3, 4 and5,wereviewsomeusefulmathematicaltools,definethegeometryofthewing, andprovideanoverviewofwingperformanceinthenextthreesections,respectively. 1.1.2 Measures of Dynamical Properties Themathematicalconceptspresentedinthissectionandappliedinthistextdescribe thedynamicbehaviorofathermo-mechanicalfluid.Inotherwords,weneglectelec- tromagnetic,relativistic,andquantumeffectsondynamics.Also,asalreadypointed out,wetaketheviewthatthepropertiesarecontinuousfunctionsoflocationinspace and time. The discussion of units and dimensions here are thus limited to the mea- sures of flow properties of fluids (liquids and gases) near the surface of the Earth understandardconditions. The units and dimensions of all physical properties and the relevant proper- ties of fluids are recalled, and after a review of the aeronautical definitions of Toprotecttherightsoftheauthor(s)andpublisherweinformyouthatthisPDFisanuncorrectedproofforinternalbusinessuseonlybytheauthor(s),editor(s), reviewer(s),ElsevierandtypesetterdiacriTech.Itisnotallowedtopublishthisproofonlineorinprint.Thisproofcopyisthecopyrightpropertyofthepublisher andisconfidentialuntilformalpublication. Houghton — Ch01-9780080966328 — 2012/2/3 — 21:13 — Page 5 — #5 1.2 Units and Dimensions 5 wing and airfoil geometry, the remainder of the chapter discusses aerodynamic force. Theoriginsofaerodynamicforceandhowitismanifestonwingsandotheraero- nauticalbodies,andthetheoriesthatpermititsevaluationanddesign,aretobefound in the following chapters. In this chapter the lift, drag, side-wind components, and associatedmomentsofaerodynamicforceareconventionallyidentified,theapplica- tion 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 Measurementandcalculationrequireasystemofunitsinwhichquantitiesaremea- sured and expressed. Aerospace is a global industry, and to be best prepared for a globalcareer,engineersneedtobeabletoworkinbothsystemsinusetoday.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’sjobtoefficientlyreconcilethevariousdocumentsorspecificationswith- out introducing conversion errors. Consider, too, the physics behind the units. That is,oneknowsthatforlinearmotion,forceequalstheproductofmassandaccelera- tion.Theunitsoneusesdonotchangethephysicsbutchangeonlyourquantitative descriptionsofthephysics.Whenconfusedaboutunits,focusontheprocessorstate beingdescribedandstepthroughtheanalysis,trackingunitstheentireway. 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 describedbyeithertheslugorthepound-mass(lbm).Weightisdescribedbypounds (lb) or by the equivalent unit with a redundant name, the pound-force (lbf). Large distances—forexample,therangeofanaircraft—aredescribedinmilesornautical miles. Speed is feet per second, miles per hour, or knots, where one knot is one nauticalmileperhour.Multimilliondollaraircraftarestillmarketedandsoldusing knots and nautical miles (try a web search on “777 range”), so these units are not obsolete. Inotherpartsoftheworld,andinK-12educationintheUnitedStates,thedomi- nantsystemofunitsistheSyste`meInternationald’Unite´s,commonlyabbreviatedas “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”expressesthequalitativeconceptoflineardisplacement,ordis- tancebetweentwopoints,asanabstractidea,withoutreferencetoactualquantitative measurement. The term “unit” indicates a specified amount of a quantity. Thus a meterisaunitoflength,beinganactual“amount”oflineardisplacement,andsois