Asymptotic Theory of Separated Flows

Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.

Preface

vii

(3)

Preface to the English Edition

x

1 The Theory of Separation from a Smooth Surface

1

(34)

1.1 Boundary-Layer Theory

1

(5)

1.2 The Problem of Boundary-Layer Separation

6

(3)

1.3 Self-Induced Separation

9

(5)

1.4 The Preseparation Flow

14

(5)

1.5 The Interaction Region

19

(4)

1.6 The Flow in the Separation Region

23

(5)

1.7 The Numerical Solution of the Problem

28

(4)

1.8 The Effect of Surface Curvature

32

(3)

2 Flow Separation from Corners of a Body Contour

35

(65)

2.1 Separation from a Corner with the Formation of an Extensive Stagnation Zone

36

(25)

2.2 Flows with Small Values of the Parameter k

61

(10)

2.3 The Onset of Separation near a Corner of a Body Contour with Small Turning Angle

71

(19)

2.4 Other Aspects of Multistructured Boundary-Layer Theory

90

(10)

3 Flow in the Vicinity of the Trailing Edge of a Thin Airfoil

100

(35)

3.1 The Boundary Layer in the Vicinity of the Trailing Edge of a Flat Plate

100

(12)

3.2 The Influence of Profile Thickness

112

(13)

3.3 The Influence of Angle of Attack

125

(10)

4 Separation at the Leading Edge of a Thin Airfoil

135

(41)

4.1 Experimental Observations

135

(2)

4.2 Statement of the Problem. Inviscid-Flow Region

137

(2)

4.3 The Boundary Layer

139

(17)

4.4 The Interaction Region

156

(10)

4.5 Numerical Solution of the Fundamental Equation

166

(10)

5 The Theory of Unsteady Separation

176

(57)

5.1 The Analogy between Unsteady Separation and Separation from a Moving Surface

176

(4)

5.2 Singular Solutions of the Boundary-Layer Equations

180

(9)

5.3 Self-Induced Separation on a Moving Surface

189

(28)

5.4 Unsteady Boundary-Layer Separation

217

(16)

6 The Asymptotic Theory of Flow Past Blunt Bodies

233

(33)

6.1 The Background of the Problem

233

(6)

6.2 Formulation of the Problem. Initial Assumptions and Estimates

239

(4)

6.3 The Flow in the Mixing Layer and the Separation Zone

243

(6)

6.4 Drag of the Body and Parameters of the Separation Zone

249

(4)

6.5 Separation-Zone Closure and Unsteadiness

253

(2)

6.6 On the Zero-Drag Theory

255

(3)

6.7 The Transition to a Thin Body

258

(8)

7 Numerical Methods for Solving the Equations of Interaction

266

(48)

7.1 Statement of the Problem

267

(5)

7.2 Marching and Inverse Methods

272

(12)

7.3 Fast Iteration Methods

284

(11)

7.4 Direct Methods of Solving Interaction Problems

295

(19)

References

314

(17)

Index

331

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Asymptotic Theory of Separated Flows

Summary

Table of Contents

Supplemental Materials