Statistical Approach to Wall Turbulence E-Book

Sedat Tardu

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 323

Veröffentlichungsjahr: 2013

Beschreibung

Wall turbulence is encountered in many technological applications as well as in the atmosphere, and a detailed understanding leading to its management would have considerable beneficial consequences in many areas. A lot of inspired work by experimenters, theoreticians, engineers and mathematicians has been accomplished over recent decades on this important topic and Statistical Approach to Wall Turbulence provides an updated and integrated view on the progress made in this area.

Wall turbulence is a complex phenomenon that has several industrial applications, such as in aerodynamics, turbomachinery, geophysical flows, internal engines, etc. Several books exist on fluid turbulence, but Statistical Approach to Wall Turbulence is original in the sense that it focuses solely on the turbulent flows bounded by solid boundaries. The book covers the different physical aspects of wall turbulence, beginning with classical phenomenological aspects before advancing to recent research in the effects of the Reynolds numbers, near wall coherent structures, and wall turbulent transport process.

This book would be of interest to postgraduate and undergraduate students in mechanical, chemical, and aerospace engineering, as well as researchers in aerodynamics, combustion, and all applications of wall turbulence.

Leseprobe

Table of Contents

Foreword

Introduction

Chapter 1: Basic Concepts

1.1. Introduction

1.2. Fundamental equations

1.3. Notation

1.4. Reynolds averaged Navier-Stokes equations

1.5. Basic concepts of turbulent transport mechanisms

1.6. Correlation tensor dynamics

1.7. Homogeneous turbulence

1.8. Isotropic homogeneous turbulence

1.9. Axisymmetric homogeneous turbulence

1.10. Turbulence scales

1.11. Taylor hypothesis

1.12. Approaches to modeling wall turbulence

Chapter 2: Preliminary Concepts: Phenomenology, Closures and Fine Structure

2.1. Introduction

2.2. Hydrodynamic stability and origins of wall turbulence

2.3. Reynolds equations in internal turbulent flows

2.4. Scales in turbulent wall flow

2.5. Eddy viscosity closures

2.6. Exact equations for fully developed channel flow

2.7. Algebraic closures for the mixing length in internal flows

2.8. Some illustrations using direct numerical simulations at low Reynolds numbers

2.9. Transition to turbulence in a boundary layer on a flat plate

2.10. Equations for the turbulent boundary layer

2.11. Mean vorticity

2.12. Integral equations

2.13. Scales in a turbulent boundary layer

2.14. Power law distributions and simplified integral approach

2.15. Outer layer

2.16. Izakson-Millikan-von Mises overlap

2.17. Integral quantities

2.18. Wake region

2.19. Drag coefficient in external turbulent flows

2.20. Asymptotic behavior close to the wall

2.21. Coherent wall structures – a brief introduction

Chapter 3: Inner and Outer Scales: Spectral Behavior

3.1. Introduction

3.2. Townsend-Perry analysis in the fully-developed turbulent sublayer

3.3. Spectral densities

3.4. Clues to the kx−1 behavior, and discussion

3.5. Spectral density Evv and cospectral density Euv

3.6. Two-dimensional spectral densities

Chapter 4: Reynolds Number-Based Effects

4.1. Introduction

4.2. The von Karman constant and the renormalization group

4.3. Complete and incomplete similarity

4.4. Symmetries and their consequences

4.5. Principle of asymptotic invariance. Approach of W.K. George

4.6. Mean velocity distribution. Summary

4.7. Townsend’s attached eddies

4.8. Overlap region in internal flows

4.9. Two-point correlations

4.10. Active and passive Townsend eddies

4.11. Fine structure

Chapter 5: Vorticity

5.1. Introduction

5.2. General characteristics of vorticity

5.3. Reynolds shear stress and vorticity transport

5.4. Characteristics of the vorticity field close to the wall

5.5. Statistics and fine structure

5.6. Vorticity transport

5.7. Estimating the importance of non-linearity close to the wall

5.8. Measurements

Notations Used

Bibliography

Index

First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKJohn Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.iste.co.ukwww.wiley.com

© ISTE Ltd 2011

The rights of Sedat Tardu to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Tardu, Sedat, 1959-

Statistical approach in wall turbulence / Sedat Tardu.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-262-6

1. Fluid-structure interaction--Statistcal methods. 2. Turbulence--Statistical methods. 3. Boundary value problems. I. Title.

TA357.5.F58T37 2011

620.1'064--dc23

2011018476

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-262-6

Foreword

Turbulent fluid motions are at the core of many key processes in nature and engineering systems. These motions involve turbulent flow over a surface or an interface in a vast majority of applications. Such wall-bounded turbulent flows are ubiquitous in our environment, particularly in the atmospheric surface layer or in benthic boundary layers in aquatic systems. The flux of water vapor and carbon dioxide from the ocean’s surface, or the movement of nutrients to and from a riverbed, are largely controlled by wall turbulence. Similarly in engineering applications, heat and mass transfer from a surface are mainly caused by turbulent flow, as is the skin friction drag on aircraft and ships, and the hydraulic resistance in rivers and canals.

These important applications rely on fundamental knowledge and quantitative characterization of the turbulence, and thus justifiably the field of wall turbulence has remained an active and important area of research. These flows are particularly challenging, as the presence of the wall imposes at least one additional length scale on the problem, and results in extremely high gradients across the wall-normal direction of the flow with high levels of anisotropy. Understandably, these challenges have experienced a large number of different theories developed over many decades. This field continues to evolve, as new measurement techniques are being developed and larger computational resources are made available for studying the complex interactions in this rich, non-linear system.

In this book, Professor Tardu presents a detailed, clear and deep perception of wall-bounded turbulence from a statistical perspective. No single book can cover all the developments reported in the literature, and it would be wrong for any book to try. Even so, Professor Tardu presents a comprehensive account of the field, and chooses the topics carefully, so as to present a consistent and thorough account of the statistical descriptions of wall turbulence. This is complemented by a review of the classical literature, particularly as it relates to the new material. He also does not shy away from discussing topics relating to ongoing controversies in the field, and provides a valuable synthesis of the study material, making clear where further advances are required and draws broad conclusions, where possible. This renders the book most interesting to researchers in the field, both experienced and those who are new to the field. At the same time, the discussion and the manner in which it deals with numerical methods, render the book extremely valuable for engineers who would like to be provided with an in-depth appreciation of wall-bounded turbulent flows.

The book would also be invaluable for graduate students, and advanced undergraduates interested in the field. The subject material has been presented with detailed steps of analysis where necessary, and provides valuable references for further investigation. The coverage of material is purposefully broad and includes topics such as Townsend’s attached eddy hypothesis (in a notably accessible form) and Lie group analysis. The discussion has been reinforced with the presentation of experimental and direct numerical simulation data where appropriate.

It has been several decades since a comprehensive book on the statistical description of wall-bounded turbulence has emerged. This work fills that void and would be of value to students, researchers or engineers who would like to have a thorough account of this rich and complex subject.

Ivan MARUSIC

Professor and ARC Federation FellowDepartment of Mechanical EngineeringUniversity of Melbourne

June 2011 Australia

Introduction

One of the key references on turbulent shear flows is undoubtedly the work by Townsend entitled Turbulent Shear Flows. The second edition of his book dates back to 1976. It was Townsend who had introduced a number of original concepts in wall turbulence such as passive and active attached eddies. Significant progress in terms of our physical understanding of wall turbulence has been achieved since the reference [TOW 76] was published, and this has led to tangible applications such as the management of turbulent drag or turbulent mixing. When I started to write this book, my ambition was to disseminate an appreciation of this progress to a wider audience. It did not take me long to realize the gravity and difficulty of this task. In writing this book my intention was to achieve a text that was as up-to-date as possible, while at the same time attempting to keep it at an accessible pedagogical level.

This book is mostly aimed at Masters and doctoral PhD students, but would also be of interest to researchers. The first two chapters may also be useful in Masters-level teaching.

Above all I must thank my colleagues and friends Julien Baerenzung and Lyazid Djenidi, who were kind enough to read through the manuscript, along with Jean Paul Bonnet who honored me by writing the preface to the French edition of this work. Eric Lamballais has reviewed every chapter in great detail and his efforts have improved the work to a great extent. I am particularly thankful to him. I warmly thank my colleague Ivan Marusic who honored me by agreeing to write the preface for this book. I also thank my wife Carmel for her support, as well as my sons Aran, Noah and Teoman for their patience.