Asymptotic Theory of Separated Flows

by Vladimir V. Sychev , Anatoly I. Ruban , Victor V. Sychev , Georgi L. Korolev , Translated by Elena V. Maroko

• ISBN13: 9780521455305
• ISBN10: 0521455308
• Format: Hardcover
• Copyright: 1998-08-28
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

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