ascherh the dynamics and vol.1-1953

8/4/2019 AscherH The Dynamics And Vol.1-1953

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The Dynamitsand Thermodynamics ofCOMPRESSIBLE FLUID

FLOWBy

ASCHER H. SHAPIROProfessor of Mecha 'cU.'lEngineeringMassachusetts Institute of Technology

INTwo VOLUMES

VOLUME I

THE RONALD PRESS COMPANY 1 NEW YORK


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CONTENTS

VOLUME IPart I. Background

CHAPTER PAGE1 FOUNDATIONS OF FLUID DYNAMICS 3

Properties of the Continuum. Systems and Control Volumes.Conservation of Mass. Momentum Theorem. Theorem of Mo-ment of Momentum. Units and Dimensions.2FOUNDATIONS OF THERMODYNAMICS 23

The First Law of Thermodynamics. The Second Law of Thermo-dynamics. Thermodynamic Properties of the Continuum. TheFirst Law for a Control Volume. The Second Law for a ControlVolume. The Perfect Gas.

3NTRODUCTORY CONCEPTS TO COMPRESSIBLE FLOW 45The Velocity of Sound. Physical Differentes Between Incompres-sible, Subsonic, and Supersonic Flows. The Mach Number andMach Angle. Similarity Parameters. Domain of the Continuum.Classification of Compressible Flows. Optical Methods of Inves-tigation.

Part II. One-Dimensional Flow4SENTROPIC FLOW 73

General Features of Isentropic Flow. Adiabatic Flow of a PerfectGas. Isentropic Flow of a Perfect Gas. Working Charts andTables for Isentropic Flow. Choking in Isentropic Flow. Opera-tion of Nozzles Under Varying Pressure Ratios. Special Relationsfor Low Mach Numbers. Deviations from Perfect Gas Laws.Performance of Real Nozzles. Some Applications of IsentropicFlow.5NORMAL &Well WAVES 112Governing Relations of the Normal Shock. Normal Shock in aPerfect Gas. Working Formulas, Curves, and Tables. WeakShock Waves. Formation of Shock Waves. Thickness of ShockWaves. Normal Shocks in Ducts. Moving Shock Waves. Oper-ating Characteristics of Converging-Diverging Nozzle. One-Di-mensional Supersonic Diffusers. Supersonic Pitot Tube.ix


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x CONTENTSCHAFTERA G E6FLOW IN CONSTANT-AREA DUCTS WITH FRICTION59

Adiabatic, Constant-Area Flow of a Perfect Gas. Performance ofLong Ducts at Various Pressure Ratios. Isothermal Flow in LongDucts. Experimental Friction Coefficients.7FLOW IN DUCTS WITH HEATING OR COOLING90Simple-Heating Relations for a Perfect Gas. Choking Effects inSimple To-Change. Shock Waves with Changes in StagnationTemperature. The Recovery Factor. The Coefficient of HeatTransfer.8GENERALIZED ONE-DIMENSIONAL CONTINUOUS FLOW19Physical Equations and Definitions. Working Equations andTables of Influence Coefficients. Flow with Constant SpecificHeat and Molecular Weight. General Features of Flow Patterns.General Method of Solution. Simple Types of Flow. Exampleof Combined Friction and Area Change. Examples of CombinedFriction and Heat Transfer. Special Conditions at the SonicPoint.Part III. Introduction to Flow in Two and Three Dimensions9THE EQUATIONS OF MOTION FOR STEADY, IRROTATIONAL FLOW 265

The Physical Significance of Irrotational Motion. Euler's Equa-tions of Motion. Kelvin's Theorem. The Connection Betweenthe Rotation and the Thermodynamic Properties of the Flow.The Equation of Continuity. The Laws of Thermodynamics.Differential Equations in Terms of the Velocity Potential. Dif-ferential Equations in Terms of the Stream Function. RelationsBetween the Velocity Potential and the Stream Function.

Part I Subsonic Flow10 TWO-DIMENSIONAL, SUBSONIC FLOW WITH SMALL PERTURBA-

TIONSLinearization of the Potential Equation. Linearization of thePressure Coefficient. Flow Past a Wave-Shaped Wall. Gothert'sRule. The Prandtl-Glauert Rule. Experimental Results for ThinProfiles. Wind Tunnel Corrections. Flow Inside Two-Dimen-sional P assages.

11 HODOGRAPH METHOD FOR TWO-DIMENSIONAL, STIBSONICFLOW

Derivation of the Hodograph Equations. The Tangent-Gas Ap-proximation. The Karman-Tsien Pressure Correction Formula.Calculation of Profile Shape Correction. Extension of Karman-Tsien Method. Miscellaneous Examples.

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CONTENTS xiCHAPTER P A G E12 MISCELLANEOUS METHODS AND RESULTS FOR TWO-DIMEN-SIONAL, SUBSONIC FLOW 364

The Rayleigh-Janzen Method of Expansion in Series of the MachNumber. The Prandtl-Glauert Method of Expansion in Series ofa Shape Parameter. Relaxation Method. Some Measured Effectsof Compressibility in Subsonic Flow. The Streamline CurvatureMethod.13 THREE-DIMENSIONAL, SUBSONIC FLOW 39 3

Gothert's Rule for Uniform Flow with Small Perturbations. FlowPast Ellipsoids. Bodies of Revolution. Spheres. Wings of FiniteSpan. Sweptback Wings. Sweptback Wings of Finite Span.

Part V. Supersonic Flow14 TWO-DIMENSIONAL, STJPERSONIC FLOW WITII SMALL PER-

TURBATIONS 427Linearization of the Equations. The General Solution for Linear-ized Supersonic Flow. Geometrical Interpretation of the GeneralSolution. Flow Past a Wave-Shaped Wall. Supersonic Airfoils.Refiection and Interseetion of Waves.

15 METHOD OF CHARACTERISTICS FOR TWO-DIMENSIONAL, SU-PERSONIC FLOW 462

Flow with Waves of One Family by Extension of Linear Theory.Flow w ith Wave s of Both Families by E xtension of Linear T heory.Application of Theory of Characteristics. Simple Waves byTheory of Characteristics. Field Method Versus Lattice-PointMethod. Unit Processes. Graphical Versus Numerical Method.Some Special Features of Supersonic Flow. Applications ofMethod of Characteristics. Design of Supersonic Wind TunnelNozzles. Adiabatic, Nonviscous Flow with Rotation.16 OBLIQUE SHOCKS 529Oblique Shock Equations. Shock Geometry. Shock Polars.Some Special Aspects of Oblique Shocks. Very Weak Shocks.Refiection and Interaction of Shocks. Curved Shocks. ExplicitSolutions by Series Expansions. Examples of Two-DimensionalFlows Containing Shocks. Two-Dimensional Profiles. Interac-tion of Shock Waves with Boundary Layer.

AppendixATHEORY OF CHARACTERISTICS 595The Characteristic Curves. Method of Constructing Character-

istic Curves. Simple Waves.BTABLES OF COMPRESSIBLE-FLOW FUNCTIONS 61 0

INDEX 635


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VOLUME IIPart V. Supersonic Flow (Continued )

CHAFTER17AXIALLY SYMMETRIC SUPERSONIC FLOW

Exact Solution for Flow Past a Cone. Linear Theory for SlenderBodies of Revolution. Method of Characteristics. MiscellaneousExperimental Results.18 SUPERSONIC FLOW PAST WINGS OF FINITE SPAN

Preliminary Considerations of Finite Wings. Sweptback Wings.Similarity Rule for Supersonic Wings. The Method of Super-sonic Source and Doublet Distributions. The Method of ConicalFields. Typical Theoretical Results for Finite Wings. Compari-son of Theory with Experiment.19HYPERSONIC FLOWSimilarity Laws for Hypersonic Flow. Oblique Shock Relationsfor Hypersonic Flow. Simple-Wave Expansion Relations for Hy-personic Flow. Hypersonic Performance of Two-DimensionalProfiles. Hypersonic Performance of Bodies of Revolution. Ex-perimental Results.

Part VI. Mixed Flow20THE HODOGRAPH METHOD FOR MIXED SUBSONIC-SUPERSONIC

FLOWEquations of the Hodograph Method. Source-Vortex Flow.Compressible Flow with 180 Turn. The Limit Line. Solutionof Hodograph Equations by Hypergeometric Functions.

21TRANSONIC FLOWThe Transonic Similarity Law. Applications of the TransonicSimilarity Law. Flow in Throat of Converging-Diverging Nozzle.Relaxation Method. Transonic Flow Past a Wavy Wall. Flowat Mach Number Unity. Slopes of Force Coefficients at M. = 1.T ransonic Flow P ast We dge Nose.

22DRAG AND LIFT AT TRANSONIC SPEEDSExperimental Validity of Transonic Similarity Law. Character-istics of Wing Profiles. Characteristics of Wings. TransonicDrag of Bodies of Revolution. Detached Shocks. TheoreticalConsideration of Transonic Flow Without Shocks. InteractionBetween Boundary Layer and Shock Wave.xii


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C O N T E N T SiiiPart VII. Unsteady Motion in One DimensionCHAPTER23UNSTEADY WAVE MOTION OF SMALL AMPLITUDE

Equations of Motion. Waves of Small Amplitude. SimplifiedPhysical Analysis of Pressure Pulse. Characteristic Curves.Application of Theory. Development of Wave Form. Effectsof Gradual Changes in Area.24UNSTEADY, ONE-DIMENSIONAL, CONTINUOUS FLOW

Extension of Linearized Theory. Method of Characteristics.Simple Waves. Waves of Both Families. Unit Operations andBoundary Conditions. Unsteady, One-Dimensional Flow. Re-marks on Details of Working Out the Method of Characteristics.Some Examples.2NSTEADY, ONE-DIMENSIONAL SHOCK WAVESAnalysis in Terms of Stationary Shock Formulas. Analysis ofMoving Shocks. The Shock TubeRiemann's Problem. WeakShock Waves. Modified Calculation Procedure for Weak Shocks.End Conditions and Interaction Effects for Strong Shocks. Com-parison Between Experimental and Theoretical Results.Part VIII. Flow of Real Gases with Viscosity andHeat Co nductivity

26THE LAMINAR BOUNDARY LAYERDifferential Equations of the Laminar Boundary Layer. FlowWith Prandtl Number Unity. Flow With Arbitrary PrandtlNumber. Integral Equations of the Laminar Boundary Layer.Laminar Boundary Layer for Axi-Symmetric Flow. ExperimentalResults for Laminar Boundary Layers. Stability of the LaminarBoundary Layer.

27THE TURBULENT BOUNDARY LAYERDifferential Equations of the Turbulent Boundary Layer. Inte-gral Equations of the Turbulent Boundary Layer. Analyses ofRecovery Factor, Skin Friction, and Heat Transfer for TurbulentFlow Fast a Flat Plate with Turbulent Prandtl Number of Unity.Theoretical and Experimental Results for Skin Friction on FlatPlates. Recovery Factor for Turbulent Flow. Turbulent Boun-dary Layer on Bodies of Revolution.

28 B O U ND A R Y L A Y ER S IN TU B ES A ND IN TH E P R ESENCE O F S H O C KWAVES

Flow in Tubes. Shock-Boundary Layer Interactions in Super-sonic Flow. Shock-Boundary Layer Interactions in TransonicFlow. Normal Shocks in Ducts. Boundary-Layer SeparationProduced by Shock Waves.INDEX FOR VOLUMES I AND II

ascherh the dynamics and vol.1-1953

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