Theoretical and Computational Aerodynamics

517 Pages·2014·17.39 MB·English

by  Tapan K Sengupta

Tapan K. Sengupta
Theoretical and
Computational
Aerodynamics
Aerospace Series
Editors Peter Belobaba, Jonathan Cooper
and Allan Seabridge

THEORETICAL AND
COMPUTATIONAL
AERODYNAMICS
AerospaceSeriesList
TheoreticalandComputationalAerodynamics Sengupta September2014
AerospacePropulsion Lee October2013
AircraftFlightDynamicsandControl Durham August2013
CivilAvionicsSystems,2ndEdition Moir,SeabridgeandJukes August2013
ModellingandManagingAirportPerformance Zografos,AndreattaandOdoni July2013
AdvancedAircraftDesign: Torenbeek June2013
ConceptualDesign,Analysisand
OptimizationofSubsonicCivilAirplanes
DesignandAnalysisofComposite Kassapoglou April2013
Structures:WithApplicationsto
AerospaceStructures,2ndEdition
AircraftSystemsIntegrationof Rigby April2013
Air-LaunchedWeapons
DesignandDevelopmentof Moirand November2012
AircraftSystems,2ndEdition Seabridge
UnderstandingAerodynamics: McLean November2012
ArguingfromtheRealPhysics
AircraftDesign:ASystems Sadraey October2012
EngineeringApproach
IntroductiontoUAVSystems4e FahlstromandGleason August2012
TheoryofLift:Introductory McBain August2012
ComputationalAerodynamicswith
MATLABandOctave
SenseandAvoidinUAS:Research Angelov April2012
andApplications
MorphingAerospaceVehicles Valasek April2012
andStructures
GasTurbinePropulsionSystems MacIsaacandLangton July2011
BasicHelicopterAerodynamics,3rdEdition SeddonandNewman July2011
AdvancedControlofAircraft,SpacecraftandRockets Tewari July2011
CooperativePathPlanningofUnmanned
AerialVehicles Tsourdosetal November2010
PrinciplesofFlightforPilots Swatton October2010
AirTravelandHealth:ASystems Seabridgeetal September2010
Perspective
DesignandAnalysisofComposite Kassapoglou September2010
Structures:Withapplicationstoaerospace
Structures
UnmannedAircraftSystems:UAVS
Design,DevelopmentandDeployment Austin April2010
IntroductiontoAntennaPlacement&Installations Macnamara April2010
PrinciplesofFlightSimulation Allerton October2009
AircraftFuelSystems Langtonetal May2009
TheGlobalAirlineIndustry Belobaba April2009
ComputationalModellingandSimulationof
AircraftandtheEnvironment:
Volume1--PlatformKinematicsand
SyntheticEnvironment Diston April2009
HandbookofSpaceTechnology Ley,WittmannHallmann April2009
AircraftPerformanceTheoryandPracticeforPilots Swatton August2008
AircraftSystems,3rdEdition Moir&Seabridge March2008
IntroductiontoAircraftAeroelasticityAndLoads Wright&Cooper December2007
StabilityandControlofAircraftSystems Langton September2006
MilitaryAvionicsSystems Moir&Seabridge February2006
DesignandDevelopmentofAircraftSystems Moir&Seabridge June2004
AircraftLoadingandStructuralLayout Howe May2004
AircraftDisplaySystems Jukes December2003
CivilAvionicsSystems Moir&Seabridge December2002
THEORETICAL AND
COMPUTATIONAL
AERODYNAMICS
TapanK.Sengupta
IITKanpur,India
Thiseditionfirstpublished2015
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Contents
SeriesPreface xv
Preface xvii
Acknowledgements xxi
1 IntroductiontoAerodynamicsandAtmosphere 1
1.1 MotivationandScopeofAerodynamics 1
1.2 ConservationPrinciples 4
1.2.1 ConservationLawsandReynoldsTransportTheorem(RTT) 4
1.2.2 ApplicationofRTT:ConservationofLinearMomentum 6
1.3 OriginofAerodynamicForces 6
1.3.1 MomentumIntegralTheory:RealFluidFlow 8
1.4 FlowinAcceleratingControlVolumes:ApplicationofRTT 9
1.5 AtmosphereandItsRoleinAerodynamics 11
1.5.1 VonKa´rma´nLine 11
1.5.2 StructureofAtmosphere 11
1.5.3 ArmstrongLineorLimit 12
1.5.4 InternationalStandardAtmosphere(ISA)andOtherAtmosphericDetails 13
1.5.5 PropertyVariationsinTroposphereandStratosphere 15
1.6 StaticStabilityofAtmosphere 17
Bibliography 20
2 BasicEquationsofMotion 21
2.1 Introduction 21
2.1.1 CompressibilityofFluidFlow 22
2.2 ConservationPrinciples 23
2.2.1 FlowDescriptionMethod:EulerianandLagrangianApproaches 23
2.2.2 TheContinuityEquation:MassConservation 24
2.3 ConservationofLinearMomentum:IntegralForm 25
2.4 ConservationofLinearMomentum:DifferentialForm 26
2.4.1 GeneralStressSysteminaDeformableBody 26
2.5 StrainRateofFluidElementinFlows 28
2.5.1 KinematicInterpretationofStrainTensor 29
viii Contents
2.6 RelationbetweenStressandRateofStrainTensorsinFluidFlow 32
2.7 CirculationandRotationalityinFlows 35
2.8 IrrotationalFlowsandVelocityPotential 36
2.9 StreamFunctionandVectorPotential 37
2.10 GoverningEquationforIrrotationalFlows 38
2.11 Kelvin’sTheoremandIrrotationality 40
2.12 Bernoulli’sEquation:RelationofPressureandVelocity 41
2.13 ApplicationsofBernoulli’sEquation:AirSpeedIndicator 42
2.13.1 AircraftSpeedMeasurement 43
2.13.2 ThePressureCoefficient 44
2.13.3 CompressibilityCorrectionforAirSpeedIndicator 44
2.14 ViscousEffectsandBoundaryLayers 46
2.15 ThermodynamicsandReynoldsTransportTheorem 47
2.16 ReynoldsTransportTheorem 48
2.17 TheEnergyEquation 49
2.17.1 TheSteadyFlowEnergyEquation 51
2.18 EnergyConservationEquation 52
2.19 AlternateFormsofEnergyEquation 54
2.20 TheEnergyEquationinConservationForm 55
2.21 StrongConservationandWeakConservationForms 55
2.22 SecondLawofThermodynamicsandEntropy 56
2.23 PropagationofSoundandMachNumber 60
2.24 One-DimensionalSteadyFlow 61
2.25 NormalShockRelationforSteadyFlow 62
2.26 Rankine--HugoniotRelation 64
2.27 PrandtlorMeyerRelation 65
2.28 ObliqueShockWaves 69
2.29 WeakObliqueShock 71
2.30 ExpansionofSupersonicFlows 74
Bibliography 76
3 TheoreticalAerodynamicsofPotentialFlows 77
3.1 Introduction 77
3.2 PreliminariesofComplexAnalysisfor2DIrrotationalFlows:
Cauchy--RiemannRelations 78
3.2.1 Cauchy’sResidueTheorem 81
3.2.2 ComplexPotentialandComplexVelocity 81
3.3 ElementarySingularitiesinFluidFlows 81
3.3.1 SuperposingSolutionsofIrrotationalFlows 83
3.4 Blasius’Theorem:ForcesandMomentforPotentialFlows 90
3.4.1 ForceActingonaVortexinaUniformFlow 92
3.4.2 FlowPastaTranslatingandRotatingCylinder:LiftGeneration
Mechanism 94
3.4.3 Prandtl’sLimitonMaximumCirculationanditsViolation 97
3.4.4 PressureDistributiononSpinningandTranslatingCylinder 98
3.5 MethodofImages 99