Table Of ContentTuncer Cebeci Jean Cousteix
Modeling and Computation of Boundary-Layer Flows
Second Edition
HORIZONS
PUBLISHING
Long Beach, California
Heidelberg, Germany
Tuncer Cebeci Jean Cousteix
Modeling
and Computation
of Boundary-Layer
Flows
Laminar, Turbulent and Transitional
Boundary Layers in Incompressible
and Compressible Flows
Second Revised and Extended Edition
With 224 Figures, 15 Tables, 168 Problems
and a CD-ROM
^ Sprmi] ger
HORIZONS '
PUBLISHING
Tuncer Cebeci
The Boeing Company
Long Beach, CA 90807-5309, USA
and
810 Rancho Drive
Long Beach, CA 90815, USA
TuncerC @ aol.com
Jean Cousteix
ONERA/DMAE and SUPAERO
2, Avenue Edouard Belin
31055 Toulouse Cedex, France
[email protected]
ISBN 0-9668461-9-2 Horizons PubUshing Inc., Long Beach
ISBN 0-9668461-0-9 1st edition Horizons Publishing Inc., Long Beach
ISBN 3-540-24459-X Springer Beriin Heidelberg New York
ISBN 3-540-65010-5 1st edition Springer BerHn Heidelberg New York
Library of Congress Control Number: 2005923827
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Horizons Publishing Inc., 810 Rancho Drive, Long Beach,
CA 90815, USA) except for brief excerpts in connection with reviews or scholarly analysis. Use
in connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
© Horizons Pubhshing Inc., Long Beach, California 1999, 2005
Printed in Germany
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the
former are not especially identified, is not to be taken as a sign that such names, as understood by
the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
Please note: All rights pertaining to the Computer Programs are owned exclusively by the authors
and Horizons Publishing Inc. The publisher and the authors accept no legal responsibility for any
damage caused by improper use of the programs. Although the programs have been tested with
extreme care, errors cannot be excluded.
Typeset in lArgX by the authors. Edited and reformatted by Kurt Mattes, Heidelberg, Germany.
Printing and binding: Strauss GmbH, Morlenbach, Germany
Cover design: Erich Kirchner, Heidelberg, Germany
Printed on acid-free paper 5 4 3 210
Preface
This second edition of the book, Modeling and Computation of Boundary-Layer
Flows^ extends the topic to include compressible flows. This implies the inclusion
of the energy equation and non-constant fluid properties in the continuity and
momentum equations. The necessary additions are included in new chapters,
leaving the first nine chapters to serve as an introduction to incompressible
flows and, therefore, as a platform for the extension. This part of the book can
be used for a one semester course as described below.
Improvements to the incompressible flows portion of the book include the
removal of listings of computer programs and their description, and their incor
poration in two CD-ROMs. A listing of the topics incorporated in the CD-ROM
is provided before the index. In Chapter 7 there is a more extended discussion
of initial conditions for three-dimensional flows, application of the characteristic
box to a model problem and discussion of flow separation in three-dimensional
laminar flows. There are also changes to Chapter 8, which now includes new
sections on Tollmien-Schlichting and cross-flow instabilities and on the predic
tion of transition with parabolised stability equations, and Chapter 9 provides
a description of the rational behind interactive boundary-layer procedures.
Chapters 10 to 14 deal with compressible flows and consider, respectively,
the boundary layer equations, two-dimensional laminar and turbulent flows,
three-dimensional laminar and turbulent flows and stability and transition. A
computer program for two-dimensional laminar and turbulent flows without
separation and a computer program for three-dimensional laminar and turbulent
flows, including those with separation, and related software to predict transition
in three-dimensional flows are described in CD-ROMs and is available from the
first author.
The above implies that the sequence of chapters is as follows. The Intro
duction of Chapter 1 presents two examples to demonstrate the use of invis-
cid and boundary-layer equations for solving engineering problems. Chapter 2
presents the conservation equations for incompressible flows, and is compara-
VI Preface
tively brief since detailed derivations are available elsewhere. The third Chapter
discusses the boundary-layer equations. The calculation of laminar and turbu
lent boundary-layers and the prediction of transition in two-dimensional flows
are addressed in Chapters 4 through 6. Chapter 4 considers incompressible lam
inar boundary-layers and their solution and includes computer programs that
solve the boundary-layer equations and that are provided in two CD-ROMs
(Appendices A and B).
The prediction of the onset of transition from laminar to turbulent flow has
traditionally been achieved by correlations, which are known to have limited
ranges of applicability. The use of the e^-method based on solutions of the lin
ear stability equations has been proposed as a more general approach. Thus,
Chapter 5 describes the solution of the linear stability equations for incompress
ible flows and the prediction of transition by the e^-method with the numerical
method of Chapter 4, and a CD-ROM (Appendix B) provides a computer pro
gram that solves the Orr-Sommerfeld equation and computes transition.
Chapter 6 addresses two-dimensional incompressible turbulent boundary-
layers. It begins with a physical description of turbulent boundary-layers and
the empirical laws that govern them and is followed by a brief discussion of a
few popular turbulence models as well as a discussion of methods for computing
two-dimensional turbulent boundary-layers. Chapters 7 and 8 extend the discus
sions of Chapters 4 through 6 from two-dimensional flows to three-dimensional
flows. Chapter 7 discusses three-dimensional laminar and turbulent boundary-
layers and a CD-ROM (Appendix B) presents a computer program to solve the
boundary-layer equations.
Chapter 8 extends the discussion of Chapter 5 from two- to three-dimensional
flows. Unlike the occurrence of transition in two-dimensional flows, transition
in three-dimensional flows can occur by different mechanisms as discussed here.
The chapter also describes the solution of the linear stability equations with
the numerical method of Chapter 5 as well as predicting transition with the
e^-method.
Chapter 9 provides a brief description of interactive boundary-layer theory,
in which the solutions of the inviscid flow equations are coupled to those of the
boundary-layer equations with an interaction approach. The viscous effects are
neglected in the inviscid flow solutions, and are re-introduced with the help of
the solutions of the boundary-layer equations. Applications of this approach are
demonstrated for laminar and turbulent flows on a flat plate and for single and
multi-element airfoils.
Chapter 10 is similar to Chapters 2 and 3 and presents the conservation
equations and their reduced forms for compressible flows while Chapters 11 and
12 address the calculation of laminar und turbulent boundary layers for two-
dimensional and compressible flows and a CD-ROM (Appendix B) provides a
computer program that solves the boundary-layer equations for compressible
Preface VII
flows. Chapter 13 extends the discussions of Chapters 11 and 12 from two-
dimensional to three-dimensional flows, and Chapter 14 extends the discussion
of Chapter 8 from three-dimensional incompressible flows to compressible flows.
A one semester course on Modeling and Calculation of Boundary-Layer
Flows for senior undergraduate students, would include a brief reading of Chap
ter 1 followed by Chapters 2 and 3, Sections 4.1 to 4.4 in Chapter 4, Sections 5.1
to 5.5 in Chapter 5, Sections 6.1 to 6.5 and Section 6.7 in Chapter 6. For first
year graduate students, the above material might be extended to include Sec
tions 4.5, 5.6, 6.6 that deal with the numerical methods and computer programs
in Chapters 4 and 5.
A list of related and current books and solution manuals, published by Hori
zons and Springer-Verlag, is available on the Horizons Web site,
http://hometown.aol.com/tuncerc
This book is an outgrowth of work done by the authors as employees of
the Boeing Company and ONER A. Their teaching responsibilities at the Cal
ifornia State University at Long Beach (CSULB) and at the Ecole Nationale
Superieure de L'Aeronautique et de L'Espace (SUPAERO) have contributed to
its organization.
The authors would like to express their appreciation to several people who
have given thoughts and time to the development of this book and to people
who have given encouragements and moral support. In particular, we want to
thank the late A. M. O. Smith of Douglas Aircraft Company, Herb Keller of the
California Institute of Technology, the late Keith Stewartson of University Col
lege, Jim Whitelaw of Imperial College, Peter Bradshaw of Stanford University
and D. Arnal, B. Aupoix and R. Houdeville of ONERA. We also wish to thank
Hsun H. Chen, K. C. Chang and J. P. Shao for proof reading the manuscript
and making many helpful suggestions. In addition, we are indebted to many of
our students who have contributed to many of the new material included in this
book.
Finally, the authors wish to thank their wives, Sylvia Cebeci and Claudine
Cousteix for their understanding and encouragement. Only authors of books
can fully understand their contribution.
Indian Wells, California, USA Tuncer Cebeci
Toulouse, France Jean Cousteix
April 2005
iXf9Sgi0s0mS. :iWms&&9MiM^M^M
m
Contents
1. Introduction 1
1.1 Skin-Friction Drag Reduction 3
1.1.1 Laminar Flow Control 4
1.1.2 Calculations for NLF and HLFC Wings 7
1.2 Prediction of the Maximum Lift Coefficient
of Multielement Wings 11
References 16
2. Conservation Equations for Mass and Momentum
for Incompressible Flows 17
2.1 Introduction 17
2.2 Navier-Stokes Equations 18
2.3 Reynolds-Averaged Navier-Stokes Equations 20
2.4 Inviscid Flow Equations 22
References 23
Problems 24
3. Boundary-Layer Equations for Incompressible Flows 27
3.1 Two-Dimensional Flows 27
3.1.1 Laminar Flows 27
3.1.2 Turbulent Flows 29
3.2 Axisymmetric Flows 30
3.3 Momentum Integral Equation 31
3.3.1 Two-Dimensional Flows 32
3.3.2 Axisymmetric Flows 33
3.4 Boundary and Initial Conditions 34
References 36
Problems 36
X Contents
4. Two-Dimensional Incompressible Laminar Flows 43
4.1 Introduction 43
4.2 Similar Flows: External Flows 44
4.2.1 Similarity Concept 44
4.2.2 Falkner-Skan Equation 44
4.2.3 Solutions of the Falkner-Skan Equation 48
4.3 Similar Flows: Free-Shear Flows 53
4.3.1 Axisymmetric Jet 53
4.3.2 Two-Dimensional Wake 56
4.3.3 Mixing Layer Between Two Uniform Streams 59
4.3.4 Power Laws for the Width and for the Centerline Velocity
of Similar Free Shear Layers 61
4.4 Numerical Solution of the Boundary-Layer Equations:
Integral Form 62
4.4.1 Pohlhausen Method 62
4.4.2 Thwaites' Method 64
4.5 Numerical Solution of the Boundary-Layer Equations:
Differential Form 66
4.5.1 Numerical Formulation 69
4.5.2 Newton's Method 70
4.5.3 Block-Elimination Method 72
4.6 Applications of BLP2 to External Flows 73
4.6.1 Airfoil Flow 74
4.6.2 Ellipse Flow 75
4.6.3 Prolate Spheroid Flow 77
References 79
Problems 80
5. Transition in Two-Dimensional Incompressible Flows 105
5.1 Introduction 105
5.2 Transition Process 106
5.3 Linear Stability Theory 109
5.3.1 Boundary Conditions 112
5.3.2 Properties of the Orr-Sommerfeld Equation
for Two-Dimensional Flows 113
5.4 Prediction of Transition 117
5.4.1 Empirical Correlations 117
5.4.2 e^-Method 119
5.4.3 H-R:, Method 121
5.5 Factors that Influence Transition 122
5.5.1 Effects of Freestream Turbulence and Noise 122
5.5.2 Effects of Pressure Gradient 124
Contents XI
5.5.3 Effects of Heat Transfer 127
5.5.4 Effects of Suction 130
5.5.5 Effects of Surface Roughness 133
5.5.6 Effects of Surface Curvature 135
5.6 Numerical Solution of the Orr-Sommerfeld Equation 136
5.6.1 Eigenvalue Procedure for Two-Dimensional Flows 139
5.6.2 Eigenvalue Procedure for Transition 143
5.7 Applications of STP 144
5.7.1 Stability Diagrams for Blasius Flow 145
5.7.2 Transition Prediction 146
References 149
Problems 151
6. Two-Dimensional Incompressible Turbulent Flows 163
6.1 Introduction 163
6.2 Composite Nature of a Turbulent Boundary-Layer 163
6.2.1 The Inner Layer: Smooth Surface 164
6.2.2 The Inner Layer: Rough Surface 166
6.2.3 The Outer Layer 169
6.2.4 Summary - 171
6.2.5 The Whole Layer 171
6.3 Turbulence Models 175
6.3.1 Zero-Equation Models 176
6.3.2 Turbulence Models Based on Transport Equations 179
6.4 Turbulent Boundary-Layers on Smooth and Rough Surfaces
with Zero Pressure Gradient 186
6.4.1 Smooth Flat Plate 187
6.4.2 Rough Flat Plate 190
6.5 Turbulent Boundary-Layers with Pressure Gradient:
Integral Methods 192
6.6 Turbulent Boundary-Layers with Pressure Gradient:
Differential Methods 195
6.7 Free Shear Layers 196
6.7.1 Axisymmetric Jet 196
6.7.2 Two-Dimensional Wake 199
6.7.3 Power Laws for the Width and the Centerline Velocity
of Similar Free Shear Layers 201
References 201
Problems 203
7. Three-Dimensional Incompressible Laminar
and Turbulent Flows 209
7.1 Introduction 209
