Jets, Wakes, and Cavities

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.

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