P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 Low-SpeedAerodynamics,SecondEdition Low-speedaerodynamicsisimportantinthedesignandoperationofaircraftfly- ingatlowMachnumberandofgroundandmarinevehicles.Thisbookoffersa moderntreatmentofthesubject,boththetheoryofinviscid,incompressible,and irrotationalaerodynamicsandthecomputationaltechniquesnowavailabletosolve complexproblems. Auniquefeatureofthetextisthatthecomputationalapproach(fromasingle vortexelementtoathree-dimensionalpanelformulation)isinterwoventhroughout. Thus,thereadercanlearnaboutclassicalmethodsofthepast,whilealsolearning how to use numerical methods to solve real-world aerodynamic problems. This secondedition,updatesthefirsteditionwithanewchapteronthelaminarboundary layer, the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panelmethodsandadetailedpresentationofcomputationaltechniquesforthree- dimensional and unsteady flows. With extensive illustrations and examples, this bookwillbeusefulforseniorandbeginninggraduate-levelcourses,aswellasa helpfulreferencetoolforpracticingengineers. Joseph Katz is Professor of Aerospace Engineering and Engineering Mechanics atSanDiegoStateUniversity. AllenPlotkinisProfessorofAerospaceEngineeringandEngineeringMechanics atSanDiegoStateUniversity. i P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 ii P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 CambridgeAerospaceSeries Editors: MICHAEL J. RYCROFT AND WEI SHYY 1. J.M.RolfeandK.J.Staples(eds.):FlightSimulation 2. P.Berlin:TheGeostationaryApplicationsSatellite 3. M.J.T.Smith:AircraftNoise 4. N.X.Vinh:FlightMechanicsofHigh-PerformanceAircraft 5. W.A.MairandD.L.Birdsall:AircraftPerformance 6. M.J.AbzugandE.E.Larrabee:AirplaneStabilityandControl 7. M.J.Sidi:SpacecraftDynamicsandControl 8. J.D.Anderson:AHistoryofAerodynamics 9. A.M.Cruise,J.A.Bowles,C.V.Goodall,andT.J.Patrick:Principlesof SpaceInstrumentDesign 10. G.A.KhouryandJ.D.Gillett(eds.):AirshipTechnology 11. J.Fielding:IntroductiontoAircraftDesign 12. J.G.Leishman:PrinciplesofHelicopterAerodynamics 13. J.KatzandA.Plotkin:LowSpeedAerodynamics,SecondEdition iii P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 iv P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 Low-Speed Aerodynamics Second Edition JOSEPH KATZ SanDiegoStateUniversity ALLEN PLOTKIN SanDiegoStateUniversity v CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo, Mexico City Cambridge University Press 32 Avenue of the Americas, New York, NY10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521665520 © Cambridge University Press 2001 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2001 10th printing 2010 Acatalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Katz, Joseph, 1947– Low-speed aerodynamics / Joseph Katz, Allen Plotkin. – 2nd ed. p. cm. – (Cambridge aerospace series : 13) ISBN 0-521-66219-2 1. Aerodynamics. I. Plotkin, Allen. II. Title. III. Series. TL570 .K34 2000 629.132'3 – dc21 00-031270 ISBN 978-0-521-66219-2 Hardback ISBN 978-0-521-66552-0 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate. P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 Contents Preface pagexiii PrefacetotheFirstEdition xv 1 IntroductionandBackground 1 1.1 DescriptionofFluidMotion 1 1.2 ChoiceofCoordinateSystem 2 1.3 Pathlines,StreakLines,andStreamlines 3 1.4 ForcesinaFluid 4 1.5 IntegralFormoftheFluidDynamicEquations 6 1.6 DifferentialFormoftheFluidDynamicEquations 8 1.7 DimensionalAnalysisoftheFluidDynamicEquations 14 1.8 FlowwithHighReynoldsNumber 17 1.9 SimilarityofFlows 19 2 FundamentalsofInviscid,IncompressibleFlow 21 2.1 AngularVelocity,Vorticity,andCirculation 21 2.2 RateofChangeofVorticity 24 2.3 RateofChangeofCirculation:Kelvin’sTheorem 25 2.4 IrrotationalFlowandtheVelocityPotential 26 2.5 BoundaryandInfinityConditions 27 2.6 Bernoulli’sEquationforthePressure 28 2.7 SimplyandMultiplyConnectedRegions 29 2.8 UniquenessoftheSolution 30 2.9 VortexQuantities 32 2.10 Two-DimensionalVortex 34 2.11 TheBiot–SavartLaw 36 2.12 TheVelocityInducedbyaStraightVortexSegment 38 2.13 TheStreamFunction 41 3 GeneralSolutionoftheIncompressible,PotentialFlowEquations 44 3.1 StatementofthePotentialFlowProblem 44 3.2 TheGeneralSolution,BasedonGreen’sIdentity 44 3.3 Summary:MethodologyofSolution 48 3.4 BasicSolution:PointSource 49 3.5 BasicSolution:PointDoublet 51 3.6 BasicSolution:Polynomials 54 3.7 Two-DimensionalVersionoftheBasicSolutions 56 3.8 BasicSolution:Vortex 58 3.9 PrincipleofSuperposition 60 vii P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 viii Contents 3.10 SuperpositionofSourcesandFreeStream:Rankine’sOval 60 3.11 SuperpositionofDoubletandFreeStream:FlowaroundaCylinder 62 3.12 SuperpositionofaThree-DimensionalDoubletandFreeStream: FlowaroundaSphere 67 3.13 SomeRemarksabouttheFlowovertheCylinderandtheSphere 69 3.14 SurfaceDistributionoftheBasicSolutions 70 4 Small-DisturbanceFlowoverThree-DimensionalWings: FormulationoftheProblem 75 4.1 DefinitionoftheProblem 75 4.2 TheBoundaryConditionontheWing 76 4.3 SeparationoftheThicknessandtheLiftingProblems 78 4.4 SymmetricWingwithNonzeroThicknessatZeroAngleofAttack 79 4.5 Zero-ThicknessCamberedWingatAngleofAttack–LiftingSurfaces 82 4.6 TheAerodynamicLoads 85 4.7 TheVortexWake 88 4.8 LinearizedTheoryofSmall-DisturbanceCompressibleFlow 90 5 Small-DisturbanceFlowoverTwo-DimensionalAirfoils 94 5.1 SymmetricAirfoilwithNonzeroThicknessatZeroAngleofAttack 94 5.2 Zero-ThicknessAirfoilatAngleofAttack 100 5.3 ClassicalSolutionoftheLiftingProblem 104 5.4 AerodynamicForcesandMomentsonaThinAirfoil 106 5.5 TheLumped-VortexElement 114 5.6 SummaryandConclusionsfromThinAirfoilTheory 120 6 ExactSolutionswithComplexVariables 122 6.1 SummaryofComplexVariableTheory 122 6.2 TheComplexPotential 125 6.3 SimpleExamples 126 6.3.1 UniformStreamandSingularSolutions 126 6.3.2 FlowinaCorner 127 6.4 BlasiusFormula,Kutta–JoukowskiTheorem 128 6.5 ConformalMappingandtheJoukowskiTransformation 128 6.5.1 FlatPlateAirfoil 130 6.5.2 Leading-EdgeSuction 131 6.5.3 FlowNormaltoaFlatPlate 133 6.5.4 CircularArcAirfoil 134 6.5.5 SymmetricJoukowskiAirfoil 135 6.6 AirfoilwithFiniteTrailing-EdgeAngle 137 6.7 SummaryofPressureDistributionsforExactAirfoilSolutions 138 6.8 MethodofImages 141 6.9 GeneralizedKutta–JoukowskiTheorem 146 7 PerturbationMethods 151 7.1 Thin-AirfoilProblem 151 7.2 Second-OrderSolution 154 7.3 Leading-EdgeSolution 157 P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 Contents ix 7.4 MatchedAsymptoticExpansions 160 7.5 ThinAirfoilbetweenWindTunnelWalls 163 8 Three-DimensionalSmall-DisturbanceSolutions 167 8.1 FiniteWing:TheLiftingLineModel 167 8.1.1 DefinitionoftheProblem 167 8.1.2 TheLifting-LineModel 168 8.1.3 TheAerodynamicLoads 172 8.1.4 TheEllipticLiftDistribution 173 8.1.5 GeneralSpanwiseCirculationDistribution 178 8.1.6 TwistedEllipticWing 181 8.1.7 ConclusionsfromLifting-LineTheory 183 8.2 SlenderWingTheory 184 8.2.1 DefinitionoftheProblem 184 8.2.2 SolutionoftheFlowoverSlenderPointedWings 186 8.2.3 TheMethodofR.T.Jones 192 8.2.4 ConclusionsfromSlenderWingTheory 194 8.3 SlenderBodyTheory 195 8.3.1 AxisymmetricLongitudinalFlowPastaSlender BodyofRevolution 196 8.3.2 TransverseFlowPastaSlenderBodyof Revolution 198 8.3.3 PressureandForceInformation 199 8.3.4 ConclusionsfromSlenderBodyTheory 201 8.4 FarFieldCalculationofInducedDrag 201 9 Numerical(Panel)Methods 206 9.1 BasicFormulation 206 9.2 TheBoundaryConditions 207 9.3 PhysicalConsiderations 209 9.4 ReductionoftheProblemtoaSetofLinearAlgebraicEquations 213 9.5 AerodynamicLoads 216 9.6 PreliminaryConsiderations,PriortoEstablishingNumericalSolutions 217 9.7 StepstowardConstructingaNumericalSolution 220 9.8 Example:SolutionofThinAirfoilwiththeLumped-VortexElement 222 9.9 AccountingforEffectsofCompressibilityandViscosity 226 10 SingularityElementsandInfluenceCoefficients 230 10.1 Two-DimensionalPointSingularityElements 230 10.1.1 Two-DimensionalPointSource 230 10.1.2 Two-DimensionalPointDoublet 231 10.1.3 Two-DimensionalPointVortex 231 10.2 Two-DimensionalConstant-StrengthSingularityElements 232 10.2.1 Constant-StrengthSourceDistribution 233 10.2.2 Constant-StrengthDoubletDistribution 235 10.2.3 Constant-StrengthVortexDistribution 236 10.3 Two-DimensionalLinear-StrengthSingularityElements 237 10.3.1 LinearSourceDistribution 238 P1:JSN/FIO P2:JSN/UKS QC:JSN/UKS T1:JSN CB329-FM CB329/Katz October3,2000 15:18 CharCount=0 x Contents 10.3.2 LinearDoubletDistribution 239 10.3.3 LinearVortexDistribution 241 10.3.4 QuadraticDoubletDistribution 242 10.4 Three-DimensionalConstant-StrengthSingularityElements 244 10.4.1 QuadrilateralSource 245 10.4.2 QuadrilateralDoublet 247 10.4.3 ConstantDoubletPanelEquivalencetoVortex Ring 250 10.4.4 ComparisonofNearandFarFieldFormulas 251 10.4.5 Constant-StrengthVortexLineSegment 251 10.4.6 VortexRing 255 10.4.7 HorseshoeVortex 256 10.5 Three-DimensionalHigherOrderElements 258 11 Two-DimensionalNumericalSolutions 262 11.1 PointSingularitySolutions 262 11.1.1 DiscreteVortexMethod 263 11.1.2 DiscreteSourceMethod 272 11.2 Constant-StrengthSingularitySolutions(UsingtheNeumannB.C.) 276 11.2.1 ConstantStrengthSourceMethod 276 11.2.2 Constant-StrengthDoubletMethod 280 11.2.3 Constant-StrengthVortexMethod 284 11.3 Constant-Potential(DirichletBoundaryCondition)Methods 288 11.3.1 CombinedSourceandDoubletMethod 290 11.3.2 Constant-StrengthDoubletMethod 294 11.4 LinearlyVaryingSingularityStrengthMethods (UsingtheNeumannB.C.) 298 11.4.1 Linear-StrengthSourceMethod 299 11.4.2 Linear-StrengthVortexMethod 303 11.5 LinearlyVaryingSingularityStrengthMethods (UsingtheDirichletB.C.) 306 11.5.1 LinearSource/DoubletMethod 306 11.5.2 LinearDoubletMethod 312 11.6 MethodsBasedonQuadraticDoubletDistribution (UsingtheDirichletB.C.) 315 11.6.1 LinearSource/QuadraticDoubletMethod 315 11.6.2 QuadraticDoubletMethod 320 11.7 SomeConclusionsaboutPanelMethods 323 12 Three-DimensionalNumericalSolutions 331 12.1 Lifting-LineSolutionbyHorseshoeElements 331 12.2 ModelingofSymmetryandReflectionsfromSolidBoundaries 338 12.3 Lifting-SurfaceSolutionbyVortexRingElements 340 12.4 IntroductiontoPanelCodes:ABriefHistory 351 12.5 First-OrderPotential-BasedPanelMethods 353 12.6 HigherOrderPanelMethods 358 12.7 SampleSolutionswithPanelCodes 360