Low-Speed Aerodynamics

629 Pages·2001·7.42 MB·English

by  Joseph Katz

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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.
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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
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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.
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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
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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
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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
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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