Turbulence

345 Pages·1976·9.296 MB·English

by  P. Bradshaw (auth.), Peter Bradshaw (eds.)

Topics in Applied Physics Volume 12
Topics in Applied Physics Founded by Helmut K.Y. Lotsch
Volume 1 Dye Lasers Editor: F. P. Schafer
Volume 2 Laser Spectroscopy of Atoms and Molecules
Editor: H. Walther
Volume 3 Numerical and Asymptotic Techniques in Electromagnetics
Editor: R. Mittra
Volume 4 Interactions on Metal Surfaces Editor: R. Gomer
Volume 5 Mosshauer Spectroscopy Editor: U. Gonser
Volume 6 Picture Processing and Digital Filtering
Editor: T.S.Huang
Volume 7 Integrated Optics Editor: T. Tamir
Volume 8 Light Scattering in Solids Editor: M. Cardona
Volume 9 Laser Speckle and Related Phenomena
Editor: J. C. Dainty
Volume 10 Transient Electromagnetic Fields Editor: L. B. Felsen
Volume 11 Digital Picture Analysis Editor: A. Rosenfeld
Volume 12 Turbulence Editor: P. Bradshaw
Vol ume 13 High-Resolution Laser Spectroscopy Editor: K. Shimoda
Vol ume 14 Laser Monitoring of the Atmosphere
Editor: D. E. Hinkley
Volume 15 Radiationless Processes in Molecules and Crystals
Editor: F. K. Fong
Turbulence
Edited by P. Bradshaw
With Contributions by
P. Bradshaw T. Cebeci H.-H. Fernholz
J. P. Johnston B. E. Launder J. L. Lumley
W. C. Reynolds J. D. Woods
With 47 Figures
Springer-Verlag Berlin Heidelberg GmbH 1976
PETER BRADSHAW
Department of Aeronautics, Imperial College of Science and Technology,
University of London, London SW7 2BY, Great Britain
ISBN 978-3-662-22570-7 ISBN 978-3-662-22568-4 (eBook)
DOI 10.1007/978-3-662-22568-4
Library of Congress Cataloging in Publication Data. Main entry under title: Turbulence. (Topics in applied physics;
v. 12). Bibliography: p. Includes index. 1. Turbulence. I. Bradshaw. Peter. TA357.T87. 620.1'064. 76-8460.
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© by Springer-Verlag Berlin Heidelberg 1976
Originally published by Springer-Verlag Berlin Heidelberg in 1976
Softcover reprint of the hardcover 1st edition 1976
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that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Monophoto typesetting, offset printing, and bookbinding: Briihlsche Universitatsdruckerei, Giessen
Preface
Turbulent transport of momentum, heat and matter dominates many of
the fluid flows found in physics, engineering and the environmental
sciences. Complicated unsteady motions which mayor may not count as
turbulence are found in interstellar dust clouds and in the larger blood
vessels. The fascination of this nonlinear, irreversible stochastic process
for pure scientists is demonstrated by the contributions made to its
understanding by several of the most distinguished mathematical
physicists of this century, and its importance to engineers is evident
from the wide variety of industries which have contributed to, or benefit
from, our current knowledge.
Several books on turbulence have appeared in recent years. Taken
collectively, they illustrate the depth of the subject, from basic principles
accessible to undergraduates to elaborate mathematical solutions
representing many years of work, but there is no one account which
emphasizes its breadth. For this, a multi-author work is necessary. This
book is an introduction to our state of knowledge of turbulence in most
of the branches of science which have contributed to that knowledge.
It is not a Markovian sequence of unrelated essays, and we have not
simply assembled specialized accounts of turbulence problems in each
branch; this book is a unified treatment, with the material classified
according to phenomena rather than application, and freed as far as
possible from discipline-oriented detail. The approach is "applied"
rather than "pure" with the aim of helping people who need to under
stand or predict turbulence in real life.
Each chapter, especially Chapters 2 and 3, has been written as an
introduction to the literature, as well as the knowledge, of its subject.
The book is sufficiently self-contained to be used as a graduate text for
students who have attended elementary lectures on the subject, while it
should be a helpful guide for research workers. The omissions are
mostly-deliberate. Turbulent mixing is to be treated in a forthcoming
volume of this series. Noise production by turbulence is a self-contained
subject with little to offer to non-specialists, because the important
statistical properties are quite unlike those that appear in other
problems. Architectural aerodynamics and hydraulics, on the other
VI Preface
hand, have turbulence problems which are basically duplicates or
syntheses of those in other subjects.
The book begins with a general introduction, containing most of the
equations, theoretical results and literature references which are
common to two or more of the subsequent chapters. Chapters 2 to 4
describe the behavior of turbulent flows with the wide variety of
boundary conditions found in practice. Chapter 2 deals with the simplest
situation, a shear layer beneath a nominally non-turbulent stream: it
differs from most short reviews of turbulent boundary layers in
emphasizing the effect of perturbations on the flow. Chapter 3 treats
internal flows; some shear-layer phenomena which appear in a more
crucial form in internal flows are introduced in Chapter 2 and discussed
in detail in Chapter 3. Chapter 4 is a brief review of the effects of
buoyancy on turbulent flow, intended to supplement rather than replace
the many recent reviews of geophysical problems and to introduce the
existing literature on laboratory-scale buoyancy problems.
Chapters 5 to 7 consider the solution of the equations of Chapter 1
in the situations described in Chapters 2 to 4. Chapter 5 begins with a
survey of the rapidly developing subject of turbulent transport mod
elling; this is an extended synopsis of an article by Prof. W. C. REYNOLDS
in Volume 8 of Annual Review of Fluid Mechanics. An account of the
older, simpler methods follows. Chapter 6 discusses the prediction of
heat-or pollutant-transfer, which is the primary interest in many
turbulence problems although prediction of the velocity field must come
first. Although turbulence in Newtonian fluids is complicated enough,
practical problems frequently involve two-phase flow (fluid-solid or
gas-liquid), and Chapter 7 is a summary of theoretical results together
with an introduction to the behavior of turbulence in long-chain
polymer solutions.
To some, the study of turbulence is a branch of mathematics or
numerical analysis, to others a branch of engineering, while for present
purposes it is a branch of applied physics. Turbulence is a phenomenon
that transcends man-made boundaries and we hope that this book will
help to diffuse knowledge across those boundaries.
Sir GEOFFREY (G.I.) TAYLOR died while this book was being written.
Without being so planned, the book is a record of the application, to
many different subjects, of the statistical theory of turbulence which he
created. We dedicate it to the memory of a man held in unique affection
by the applied physics community.
London, March 1976 PETER BRADSHAW
Contents
1. Introduction. By P. BRADSHAW (With 6 Figures)
1.1 Equations of Motion . . . . . . . . .
1.2 Shear-Layer Instability and the Development of
Turbulence ... . . . . . . . . . . . . . 7
1.3 Statistical Averages . . . . . . . . . . . . . 13
1.4 Two-Point Statistics and Spectral Representation 15
1.5 Local Isotropy . . . . . . . . . . . . . 21
1.6 Inhomogeneous Turbulence . . . . . . . 24
1. 7 Turbulence Flows in Practice: Shear Layers 28
1.8 Turbulent Flow Near a Solid Surface 34
1.9 Conditions Near a Turbulent/Non-Turbulent Interface 39
1.1 0 The Eddy Structure of Shear Layers 41
References . . . . . . . . . . . . . . . . . . . . .. 43
2. External Flows. By H.-H. FERNHOLZ (With 7 Figures)
2.1 Introduction 45
2.2 Flow Configurations and Boundary Conditions 47
2.3 Two-Dimensional Boundary Layers at Small Mach
Numbers. 50
2.3.1 The Multi-Layer Model of Turbulent Boundary
Layers. 50
The Inner Layer . 53
The Outer Layer 56
2.3.2 Self-Preserving Shear Layers. 60
2.3.3 Upstream History, Relaxation Effects and
Downstream Stability 63
2.3.4 The Effect of Free-Stream Turbulence 65
2.3.5 The Effect of Streamwise Pressure Gradient 66
2.3.6 Separation, Separation Bubbles and Reattachment
Flow 68
Separation Bubbles 70
Reattachment of Turbulent Shear Flow 71
VIII Contents
2.3.7 The Effect of Changing Wall Geometry 72
Wall Roughness. . . . . . 72
Wavy Walls. . . . . . . . . . . . . 75
2.3.8 The Effect of Wall Curvature . . . . . 76
2.3.9 The Effect of Heat Transfer at the Wall 77
2.3.10 Transition from Laminar to Turbulent Flow 79
2.3.11 Relaminarization and Reverse Transition . . 82
2.4 Three-Dimensional Boundary Layers. . . . . . . 83
2.4.1 Classification of Three-Dimensional Flows 83
2.4.2 Three-Dimensional Thin Shear Layers . . 85
2.4.3 Separation in Three-Dimensional Flow 90
2.5 Two-Dimensional Boundary Layers at High Mach
Numbers. 90
References . . . . . . . . . . . . . . . . . . 98
3. Internal Flows. By J. P. JOHNSTON (With 15 Figures)
3.1 Zones of Flow and Basic Phenomena . . . . 109
3.1.1 Longitudinal Curvature and System Rotation 113
3.1.2 Secondary Flows. . . . . . 118
3.1.3 Interactions in Duct Flows . . . . 126
3.1.4 Separation and Reattachment 130
3.2 Fully Developed Flow in Pipes and Ducts 133
3.3 Flow in Diverging Ducts 139
3.4 Fully Separated Flows . . . . . . . . 144
3.4.1 Sudden Expansion in a Pipe 148
3.4.2 Two-Dimensional Step Expansions 152
3.4.3 Confined Jet Mixing (Ejectors) 154
3.5 Turbomachinery. . . . . . . . . . . 157
3.5.1 Profile Boundary Layers in Axial Flow 158
3.5.2 End-Wall Boundary Layers . . . . . 161
3.5.3 Periodic Flow, Turbulence and Blade Wakes 163
References . . . . . . . . . . . . . . . . . . . . 165
4. Geophysical Turbulence and Buoyant Flows.
By P. BRADSHAW and J. D. WOODS
4.1 Geophysical Boundary Layers. . . . 173
4.1.1 The Atmospheric Boundary Layer 173
4.1.2 The Ocean Surface Layer 179
4.1.3 Pollutant Plume Dispersion in the Surface Layer 185
4.2 Laboratory-Scale Buoyant Flows. . . . . . . . .. 186
4.2.1 Buoyant Free Convection from Horizontal Surfaces 186
4.2.2 Density Interfaces ... . . . . . . . . . .. 187
Contents IX
4.2.3 Convection from Inclined or Vertical Surfaces 188
4.2.4 Turbulent Convection in Confined Spaces 189
References . . . . . . . . . . . . . . . . . . . . 191
5. Calculation of Turbulent Flows. By W. C. REYNOLDS and T. CEBECI
(With 3 Figures)
5.1 Strategy and Recent Developments 193
5.1.1 Background . . . . . 193
5.1.2 One-Equation Models. 195
5.1.3 Two-Equation Models. 197
5.1.4 Stress-Equation Models · 201
5.1.5 Large-Eddy Simulations. 204
5.2 Simpler Methods . . . · 206
5.2.1 Discussion. . . . · 206
5.2.2 Integral Methods . · 208
Head's Method .208
Green's "Lag-Entrainment" Method · 210
Myring's Method ..... · 212
5.2.3 Differential Methods . . · 216
Zero-Equation Methods . · 216
One-Equation Methods . · 222
5.2.4 Short-Cut Methods. . . · 222
Incompressible Flow on a Smooth Flat Plate · 222
Prediction of Flow Separation in Two-Dimensional
Incompressible Flows . . . . . . . . .224
Similarity Solutions for Free Shear Flows · 225
References . . . . . . . . . . . . . . . . . . · 228
6. Heat and Mass Transport. By B. E. LAUNDER (With 7 Figures)
6.1 Background . . . . . . . . . . . . . 232
6.1.1 Areas of Importance . . . . . . . . . . 232
6.1.2 Models for Heat and Mass Transport . . . 233
6.2 Scalar Fluxes in Flows Near Local Equilibrium 236
6.2.1 Some Proposals for Closing the Scalar Flux Equations 236
6.2.2 Near-Wall Turbulence and the Turbulent Prandtl
Number .................... 244
6.2.3 Streamwise and Lateral Heat Transport in Near-Wall
Turbulence . . . . . . . . . . . . . . .. 247
6.2.4 Buoyant Influences on Local-Equilibrium Flows 250
6.3 Inhomogeneous Flows . . . . . . . . . . 259
6.3.1 Closure of the Scalar Flux Equations in
Inhomogeneous Flows . . . . . . . 259