Jets, Wakes, and Cavities

1st Edition - January 1, 1957
Authors: Zarantonello Eduardo H., G. Birkhoff
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 6 2 7 1 - 5

Applied Mathematics and Mechanics, Volume 2: Jets, Wakes, and Cavities provides a systematic discussion of jets, wakes, and cavities. This book focuses on the general aspects of… Read more

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Applied Mathematics and Mechanics, Volume 2: Jets, Wakes, and Cavities provides a systematic discussion of jets, wakes, and cavities. This book focuses on the general aspects of ideal fluid theory and examines the engineering applications of fluid dynamics. Organized into 15 chapters, this volume starts with an overview of the different types of jets and explores the atomization of jets in carburetors in connection with gasoline engine design. This text then emphasizes the formal treatment of special flows and examines the flows that are bounded by flat plates and free streamlines. Other chapters consider the flows that are bounded by the cavity behind a symmetric wedge. This book discusses as well the intuitive momentum and similarity considerations. The final chapter deals with several surprising physical complications. Mathematician, physicists, engineers, and readers interested in the fields of applied mathematics, experimental physics, hydraulics, and aeronautics will find this book extremely useful.

PrefaceList of Reference AbbreviationsI. Background and Prospectus 1. Examples of Jets 2. Wakes and Cavities 3. Plan of Book 4. Dimensionless Ratios 5. Real Wakes 6. Kinds of Cavitation 7. Parallel Flow Models 8. Euler Flows 9. Free Streamlines 10. Conservation Laws and Jets 11. Applications to Cavities 12. Ideal Plane Flows 13. General Theorems 14. Applications 15. Effective Computation; Generalizations 16. Viscosity and Turbulence 17. Other Physical VariablesII. Circular Sector Hodographs 1. Introduction 2. Cavity behind Plate 3. Detailed Formulas 4. Cavity behind Wedge 5. Jet from Funnel 6. Jet against Plate 7. Réthy Flows 8. Applications; Superposition Principle 9. Partial Fractions 10. Beta FunctionsIII. Simple Flows Past Wedges 1. Introduction 2. Simple Flows; Reflection Principle 3. W-diagrams of "simple" Flows 4. Impinging Jets 5. Divided Jets 6. Physical Applications 7. Simple Flows Past Wedges 8. Reentrant Jets 9. Geometrical Classification of Simple Flows 10. Flows with Circular Sector Hodograph 11. Other ExamplesIV. General Theory 1. Singularities of W(T) 2. Reflection Principle 3. Asymptotic Geometry of Free Streamlines 4. Momentum Equations 5. Drag and Lift 6. Moment 7. Separation Curvature 8. Inflections of Free Boundaries 9. Free Stream Surfaces 10. Variational Principle 11. Extension to Infinite Stream 12. Lavrentieff's Theorem 13. Under-over Theorem 14. Uniqueness Theorem 15. Minimum Cavity DragV. Multiple Plates 1. Parametric Rectangle 2. Case of M Plates 3. Annular Sector Hodograph 4. Method of Reflection 5. Impinging Jets from Nozzles, I 6. Perpendicular Plates 7. Position Integral 8. U-shaped Obstacles II 9. Riabouchinsky Flows 10. Impinging Jets from Nozzles, II 11. General Formulas 12. Plate in Jet from Nozzle 13. Interior Sources and Vortices 14. Cusped Cavities 15. Hollow VorticesVI. Curved Obstacles 1. Semicircular Parametrization 2. The Function Ω(t) 3. Geometrical Interpretations 4. Basic Integral Equations 5. Symmetric Cavities 6. Brillouin-Villat Separation Condition 7. Asymmetric Case: Parameter Problem 8. Analogs of Réthy Flows 9. Physical Applications 10. Cusped Cavities 11. Reentrant Jets 12. Riabouchinsky Flows 13. Cascades of Airfoils 14. Other ExamplesVII. Existence and Uniqueness 1. Historical Introduction 2. Nearly Flat Obstacles 3. Leray's Use of Fixpoint Theory 4. Parameter Problem 5. Jacob's Lemma 6. Convex Obstacles 7. Method of Continuity 8. Weinstein's Function 9. Uniqueness 10. Variational Method; Symmetrization 11. The Minimizing ProfileVIII. Compressibility and Gravity 1. Hodograph Equations 2. Chaplygin Equation of State 3. Flows Past Wedges 4. Curved Obstacles 5. Polytropic Equation of State 6. General Equation of State 7. Integral Equations 8. Supersonic Jets 9. Ultra-Fast Jets 10. Potential Flows with Gravity 11. Integral Equation MethodIX. Effective Computation 1. General Remarks 2. Cavity behind a Plate 3. Jet from a Slot 4. Incomplete Beta Functions 5. Parameter Problem 6. Isobars and Isoclines 7. Related Methods 8. Curved Barriers 9. Theoretical Discussion 10. Other MethodsX. Axially Symmetric Flows 1. Typical Problems 2. Potential Theory 3. Axial Source Distributions 4. Source and Vortex Rings 5. Integral Equation Approaches 6. Approximate Methods 7. Jets from Conical Orifices 8. Impinging Jets 9. Underwater Cavities 10. Swirling Flows 11. Rising Bubbles in TubesXI. Unsteady Potential Flows 1. Vapor-Filled Spherical Bubbles 2. Cavitation in a Variable Pressure Field 3. Gas-filled Cavities 4. Transient Cavities behind Missiles 5. Bubble Migration; Laws of Bjerknes 6. Cavity Induced Mass 7. Globule Acceleration 8. Impact Forces 9. Impact of Cones and Wedges 10. Constant Acceleration Coefficient 11. Stability of Plane Interface 12. Taylor Instability 13. Spherical and Cylindrical Bubbles 14. Helmholtz Instability 15. Stability of Capillary Jets 16. Stability of other ConfigurationsXII. Steady Viscous Wakes and Jets 1. Boundary Value Problem 2. Critical Discussion 3. Wakes in Creeping Flow 4. Flow Separation 5. Asymptotic Wake Structure 6. Wake Momentum 7. Oseen Equations 8. Boundary Layer Approximation 9. Momentum Theorem 10. Similarity Hypothesis 11. Creeping Jets 12. Inertial Effects 13. Schlichting's Model 14. Laminar Plane Jets 15. Exact Self-SimilarityXIII. Periodic Wakes 1. Basic Facts 2. Karman Model 3. Shedding of Vorticity 4. Vorticity and Wake Momentum 5. Vorticity and Drag 6. Invariance Theorem 7. Karman's Stability Argument 8. Strouhal Number 9. Miscellaneous Effects 10. Plate at Zero Incidence 11. Axially Symmetric Periodic Wakes 12. Periodic Jets; Edge Tones 13. Bird TonesXIV. Turbulent Wakes and Jets 1. General Remarks 2. Flow Separation 3. Base Underpressure 4. Wake Structure 5. Wake Turbulence 6. Mixing Length Concept 7. Asymptotic Wake Behavior 8. Wakes with Hydrodynamical Self-Propulsion 9. Mixing Zone 10. Structure of Jets 11. Mixing Length "Theories" 12. Further LiteratureXV. Miscellaneous Experimental Facts 1. General Discussion 2. Bubbling and Boiling 3. Tensile Strength of Liquids 4. Bubble Dynamics 5. Acoustic Cavitation 6. Cavitation Damage 7. Propeller Cavitation 8. Scale Effects in Water Entry 9. Bubble Entrainment 10. Jet Persistence 11. Atomization of Jets 12. Other Jet ConfigurationsBibliographyPlates I-IIIndex