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E-raamat: Fluid Dynamics: Part 3 Boundary Layers

Anatoly I. Ruban (Chair in Applied Mathematics and Mathematical Physics, Department of Mathematics, Imperial College London)

Formaat: PDF+DRM
Ilmumisaeg: 01-Dec-2017
Kirjastus: Oxford University Press
Keel: eng
ISBN-13: 9780191503986

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Formaat: PDF+DRM
Ilmumisaeg: 01-Dec-2017
Kirjastus: Oxford University Press
Keel: eng
ISBN-13: 9780191503986

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This is the third volume in a four-part series on Fluid Dynamics:

PART 1: Classical Fluid Dynamics
PART 2: Asymptotic Problems of Fluid Dynamics
PART 3: Boundary Layers
PART 4: Hydrodynamic Stability Theory

The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field.

The notion of the boundary layer was introduced by Prandtl (1904) to describe thin viscous layers that form on a rigid body surface in high-Reynolds-number flows. Part 3 of this series begins with the classical theory of the boundary-layer flows, including the Blasius boundary layer on a flat plate and the Falkner-Skan solutions for the boundary layer on a wedge surface. However, the main focus is on recent results of the theory that have not been presented in texbooks before. These are based on the so-called "triple-deck theory" that have proved to be invaluable in describing various fluid-dynamic phenomena, including the boundary-layer separation from a rigid body surface.

Introduction

(3)

1 Classical Boundary-Layer Theory

(139)

1.1 Flow Past a Flat Plate

(14)

1.1.1 Asymptotic analysis of the flow

(6)

1.1.2 Blasius solution

(4)

Exercises 1

(2)

1.2 Prandtl's Hierarchical Strategy

(15)

1.2.1 Outer inviscid flow region

(1)

1.2.2 Boundary layer

(4)

1.2.3 Matching procedure

(3)

1.2.4 Displacement effect of the boundary layer

(3)

Exercises 2

(3)

1.3 Solutions of Falkner and Skan

(7)

Exercises 3

(2)

1.4 Shear Layer Flows

(15)

1.4.1 Chapman's problem

(5)

1.4.2 Entrainment effect

(5)

1.4.3 Prandtl's transposition theorem

(4)

1.5 Laminar Jet

(6)

Exercises 4

(1)

1.6 Viscous Wake Behind a Rigid Body

(14)

1.6.1 Inviscid flow

(1)

1.6.2 Flow in the wake

(7)

1.6.3 Integral momentum equation

(4)

Exercises 5

(1)

1.7 Von Mises Variables

(8)

1.7.1 Boundary-layer equations in von Mises variables

(4)

1.7.2 Batchelor problem

(2)

Exercises 6

(2)

1.8 Flow Past a Rotating Cylinder

(8)

1.9 Numerical Solution of the Boundary-Layer Equations

(6)

1.9.1 Problem formulation

(1)

1.9.2 Crank--Nicolson method

(3)

1.9.3 Goldstein singularity

(2)

1.10 Compressible Boundary Layers

(13)

1.10.1 Boundary-layer equations

(2)

1.10.2 Self-similar solution

101

(4)

1.10.3 Crocco's integral

105

(3)

Exercises 7

108

(2)

1.11 Hypersonic Boundary Layers

110

(33)

1.11.1 Hypersonic flow past a body with a rounded nose

110

(4)

1.11.2 Hypersonic boundary layers on thin bodies

114

(14)

1.11.3 Upstream influence through hypersonic boundary layers

128

(10)

Exercises 8

138

(5)

2 Boundary-Layer Separation

143

(99)

2.1 Experimental Evidence

143

(6)

2.2 Self-Induced Separation of Supersonic Boundary Layer

149

(44)

2.2.1 Formulation of the problem

149

(1)

2.2.2 The flow upstream of the interaction region

150

(1)

2.2.3 Inspection analysis of the interaction process

151

(6)

2.2.4 Triple-deck model

157

(13)

2.2.5 Upstream influence

170

(4)

2.2.6 Flow behind the interaction region

174

(12)

2.2.7 Canonical form of the interaction problem

186

(3)

Exercises 9

189

(4)

2.3 Incompressible Flow Separation from a Smooth Body Surface

193

(49)

2.3.1 Problem formulation

194

(1)

2.3.2 Flow outside the interaction region

195

(7)

2.3.3 Boundary layer before the interaction region

202

(8)

2.3.4 Viscous-inviscid interaction

210

(13)

2.3.5 Flow behind the interaction region

223

(7)

2.3.6 Canonical form of the interaction problem

230

(4)

Exercises 10

234

(8)

3 Trailing-Edge Flow

242

(37)

3.1 Problem Formulation

242

(3)

3.2 Goldstein's Wake

245

(7)

3.2.1 Viscous sublayer (region 2d)

247

(3)

3.2.2 Main part of the boundary layer (region 2c)

250

(2)

3.3 Perturbations in the Inviscid Flow

252

(4)

3.4 Second-Order Perturbations in the Boundary Layer

256

(4)

3.4.1 Viscous sublayer (region 2a)

257

(3)

3.5 Triple-Deck Model

260

(19)

3.5.1 Viscous sublayer (region 3)

261

(3)

3.5.2 Middle tier (region 4)

264

(3)

3.5.3 Upper tier (region 5)

267

(2)

3.5.4 Interaction problem and numerical results

269

(3)

Exercises 11

272

(7)

4 Incipient Separation Near Corners

279

(38)

4.1 Problem Formulation

279

(1)

4.2 Subsonic Flow

280

(23)

4.2.1 Inviscid flow region

281

(2)

4.2.2 Boundary layer before the corner

283

(7)

4.2.3 Viscous-inviscid interaction region

290

(7)

4.2.4 Interaction problem

297

(6)

4.3 Supersonic Compression Ramp Flow

303

(14)

4.3.1 Linear problem

305

(5)

4.3.2 Numerical solution of the nonlinear problem

310

(2)

Exercises 12

312

(5)

5 Marginal Separation Theory

317

(62)

5.1 Experimental Observations

317

(1)

5.2 Inviscid Flow Region

318

(3)

5.3 Boundary Layer

321

(29)

5.3.1 Theoretical analysis of the boundary layer

323

(6)

5.3.2 Goldstein's singularity

329

(3)

5.3.3 Weak singularity

332

(4)

5.3.4 Formation of the singularity in the boundary layer

336

(14)

5.4 Viscous-inviscid Interaction

350

(29)

5.4.1 Upper layer (region 5)

353

(2)

5.4.2 Viscous sublayer (region 3)

355

(2)

5.4.3 Main part of the boundary layer (region 4)

357

(1)

5.4.4 Viscous-inviscid interaction problem

358

(9)

5.4.5 Numerical results

367

(5)

Exercises 13

372

(7)

References

379

(4)

Index

383

Anatoly I. Ruban is Professor and Chair in Applied Mathematics and Mathematical Physics at the Imperial College London. He was formerly Professor of Computational Fluid Dynamics in the Department of Mathematics at the University of Manchester, from 1995 to 2008. In 1991 he received the Doctor of Science degree in Physics and Mathematics. In Moscow, he served as Head of the Gas Dynamics Department in the Central Aerohydrodynamics Institute in Moscow from 1978-1995 after earning his PhD in Fluid Mechanics in 1977.

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