First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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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 Control Number: 2016959098
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-559-7
This short book is devoted to turbulent skin-friction control.
Reducing drag by only a few percent in transport vehicles (motor cars, aircraft, ships, etc.) would achieve a saving of tens of billions of Euros per year in fuel, and a significant reduction of the human impact on the environment. In the context of a civil or commercial transport aircraft, depending on the size, viscous or skin friction drag accounts for about 40–50% of the total drag under cruise conditions A cut in skin friction drag by 20% applied only to all commercial aircraft operating in the European Community would cut fuel consummation by about 30 million tones a year, corresponding to some 5–10% of total fuel consumption. This also corresponds to a reduction of several million tons of CO2 emissions annually. It is also important to recall the main goals of the vision 2020 launched by the European commission: a 50% cut in CO2 emissions per passenger kilometer. Environmental factors, such as noise, and impact on climate change, also have to be underlined. At present, the implementation of feasible, effective skin-friction control strategies is a long way from becoming a reality. It requires an in-depth knowledge of near-wall turbulence, which in spite of the considerable advances made during recent decades, is not yet at a sufficient level.
From a fundamental point of view, the management of the nonlinearity inherent in the Navier–Stokes equations coupled with the complexity induced by the presence of the wall is a formidable challenge for the researchers.
The aim of this book is to give a short overview of the turbulent skin-friction research conducted up until now; however, in spite of the effort invested in its preparation, it is far from being exhaustive. Only a limited part of the very broad literature on the subject could be analyzed in this book. I must say that it is difficult to avoid a certain degree of subjectivity in the presentation of the existing control approaches, although I have tried to be as objective as possible.
The book contains four chapters. A general introduction is given in Chapter 1 wherein the key elements related to the tools necessary to develop control strategies, such as numerical simulations, micro sensors and actuators, are briefly discussed. The aim of Chapter 2 is to provide the reader with a short and concentrated review of the basic structural elements of wall turbulence. Passive control strategies are discussed in Chapter 3 that concentrate only on large eddy breakup devices, riblets and superhydrophobic surfaces. Active control of skin friction drag is the subject of Chapter 4, which aims to present the huge progress achieved in the domain over the last decades.
First and foremost, I would like to extend my thanks to my former PhD students, Olivier Doche, François Bouillon, Stéphane Montesimo and Frédéric Bauer, without whom I could certainly not undertake research in the fascinating area of flow control. Writing a book requires time. My heartfelt thanks go to my wife, Carmel, for her unfailing support, and to my sons, Aran, Noah and Teoman, for their patience.
Sedat TARDU
November 2016
Cf | drag coefficient |
D/Dt | material derivative |
H | shape factor |
h | half-height of the channel |
kx | streamwise wavenumber |
kz | spanwise wavenumber |
ℓ | mixing length |
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mean pressure |
p | fluctuating pressure |
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shear velocity ![]() |
Ui | local instantaneous velocity |
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mean streamwise velocity |
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mean wall-normal velocity |
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mean spanwise velocity |
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velocity outside of the boundary layer |
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velocity at the channel centerline |
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bulk velocity |
Re | Reynolds number |
Reτ | Reynolds number based on the shear-stress rate and the outer scale (von Kárman number) |
Reθ | Reynolds number based the momentum thickness and the velocity outside of the boundary layer (or velocity in the center of a channel) |
Wc | Coles’ wake function |
u,u1 | streamwise fluctuating velocity |
v, u2 | wall-normal fluctuating velocity |
w, u3 | spanwise fluctuating velocity |
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Reynolds shear stress (for the simplicity’s sake, the correlation ![]() |
t | time |
x, x1 | streamwise coordinate |
y, x2 | wall-normal coordinate |
z, x3 | spanwise coordinate |
vko | Kolmogorov velocity scale |
( )i | velocity or vorticity component |
( )w or ( )0 | quantity at the wall |
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mean of a fluctuating physical quantity |
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Fourier transform |
( )+ | quantity rendered dimensionless by the inner scales ![]() |
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divergence |
• | scalar product |
δij | Kronecker delta |
δ | boundary-layer thickness |
δd | displacement thickness |
δv | viscous sublayer thickness |
δR | Rotta thickness |
ηK0 | Kolmogorov length scale |
κ | von Kárman constant |
Λ0 | outer length scale |
ν | kinematic viscosity |
νt | turbulent viscosity |
μ | dynamic viscosity |
ν | kinematic viscosity |
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mean vorticity component i |
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mean spanwise vorticity |
ωi | instantaneous local vorticity component i |
ωx, ωy, ωz | instantaneous local components of streamwise, wall-normal and spanwise vorticity |
Π | Coles’ wake factor |
ρ | density |
σij | stress tensor |
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mean square value of fluctuations in wall shear stress in the streamwise direction |
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mean square value of fluctuations in wall shear stress in the spanwise direction |
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mean square values of fluctuations in streamwise, wall-normal and spanwise vorticity |
θ | momentum thickness |
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mean wall shear stress |
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fluctuations of wall shear stress in the streamwise direction |
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fluctuations of wall shear stress in the spanwise direction |