Introduction to Interactive Boundary Layer Theory

Introduction to Interactive Boundary Layer Theory

by Ian John Sobey, I. J. Sobey
     
 

ISBN-10: 0198506759

ISBN-13: 9780198506751

Pub. Date: 02/28/2001

Publisher: Oxford University Press, USA

One of the major achievements in fluid mechanics in the last quarter of the twentieth century has been the development of an asymptotic description of perturbations to boundary layers known generally as 'triple deck theory'. These developments have had a major impact on our understanding of laminar fluid flow, particularly laminar separation. It is also true that the…  See more details below

Overview

One of the major achievements in fluid mechanics in the last quarter of the twentieth century has been the development of an asymptotic description of perturbations to boundary layers known generally as 'triple deck theory'. These developments have had a major impact on our understanding of laminar fluid flow, particularly laminar separation. It is also true that the theory rests on three quarters of a century of development of boundary layer theory which involves analysis, experimentation and computation. All these parts go together, and to understand the triple deck it is necessary to understand which problems the triple deck resolves and which computational techniques have been applied. This book presents a unified account of the development of laminar boundary layer theory as a historical study together with a description of the application of the ideas of triple deck theory to flow past a plate, to separation from a cylinder and to flow in channels. The book is intended to provide a graduate level teaching resource as well as a mathematically oriented account for a general reader in applied mathematics, engineering, physics or scientific computation.

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Product Details

ISBN-13:
9780198506751
Publisher:
Oxford University Press, USA
Publication date:
02/28/2001
Series:
Oxford Texts in Applied and Engineering Mathematics Series, #3
Edition description:
New Edition
Pages:
352
Product dimensions:
6.10(w) x 9.00(h) x 1.00(d)

Table of Contents

1Mathematical and Fluid Mechanical Introduction1
1.1Introduction1
1.2The Navier-Stokes equations3
1.3Boundary conditions5
1.4Asymptotic methods5
1.5The Euler equations and potential flow9
1.6Stokes flow10
1.7Oseen's approximation11
1.8Basic boundary layer theory13
1.9Drag17
1.10Summary and overview20
IThe Triple Deck
2The Boundary Layer on a Flat Plate25
2.1Introduction25
2.2Semi-infinite plate--Rectangular coordinates26
2.3Semi-infinite plate - Parabolic coordinates36
2.4The drag on a section of semi-infinite plate45
2.5The wake behind a finite length plate49
2.6Near wake region50
2.7Far wake expansion59
2.8The drag on a finite plate69
2.9Summary74
3The Triple Deck76
3.1Introduction76
3.2Formulation82
3.3The middle deck83
3.4The outer deck85
3.5The inner deck86
3.6Computed results88
3.7Drag90
3.8Numerical solution of the Navier-Stokes equations91
3.9Summary96
4Numerical Solution of Triple Deck Equations97
4.1Introduction97
4.2Numerical solution in rectangular coordinates98
4.3Solution using sublayer coordinates103
4.4A spectral method104
4.5Channel flow106
IISeparation
5Introduction to Separation111
6Separated Flow about a Cylinder115
6.1Observation at moderate Reynolds number115
6.2Free streamline theory122
6.3Boundary layer with a variable pressure gradient149
6.4Combined boundary layer--free streamline models164
6.5Goldstein's hypothesis of a boundary layer singularity169
6.6Direct numerical solution of boundary layer equations176
6.7Reprise183
6.8Numerical solution of Navier-Stokes equations184
6.9Attempts to resolve Goldstein's singularity194
6.10Summary198
7Prediction of Separation from a Cylinder199
7.1Introduction199
7.2Sychev's hypothesis for separation204
7.3Smith's solution near separation206
7.4Separation from a cylinder208
7.5Comparison with numerical solutions210
7.6Prandtl-Batchelor flow212
7.7Summary218
IIIChannel Flow
8Introduction to Channel Flow223
8.1Introduction223
8.2Asymmetric channels: R[superscript -1] [double less-than sign] [Set membership] [double less-than sign] R[superscript -1/7]228
8.3Symmetric channels: R[superscript -1] [double less-than sign] [Set membership] [double less-than sign] 1233
8.4Free streamline theory234
8.5Computed examples246
8.6Numerical solution of the Navier-Stokes equations250
8.7Flow near a corner252
8.8Summary261
9Upstream Influence263
9.1Introduction263
9.2Asymmetric channels: [Set membership] [similar] R[superscript -1/7]263
9.3Upstream influence266
9.4A numerical example276
9.5Symmetric channels277
9.6Prandtl-Batchelor flow in channels282
9.7Summary282
10Coanda Effect284
10.1Introduction284
10.2Symmetry and bifurcation284
10.3Bifurcation solutions from Navier-Stokes equations290
10.4Application of interactive boundary layer theory292
10.5Summary298
Appendix AProblems and Computer Programs299
A.1Chapter 1--Introduction299
A.2Chapter 2--Flat plate300
A.3Chapter 3 & 4--Triple deck300
A.4Chapter 5 & 6--Separation301
A.5Chapter 7--Prediction of separation from a cylinder303
A.6Chapter 8--Channel flow303
A.7Chapter 9--Upstream influence304
A.8Chapter 10--Coanda effect306
Bibliography307
Author Index323
Subject Index327

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