Jets, Wakes, and Cavities
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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.
Table of Contents
Preface
List of Reference Abbreviations
I. 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 Variables
II. 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 Functions
III. 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 Examples
IV. 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 Drag
V. 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 Vortices
VI. 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 Examples
VII. 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 Profile
VIII. 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 Method
IX. 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 Methods
X. 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 Tubes
XI. 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 Configurations
XII. 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-Similarity
XIII. 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 Tones
XIV. 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 Literature
XV. 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 Configurations
Bibliography
Plates I-II
Index
Product details
- No. of pages: 366
- Language: English
- Copyright: © Academic Press 1957
- Published: January 1, 1957
- Imprint: Academic Press
- eBook ISBN: 9780323162715