Turbulent Flow and Boundary Layer Theory: Selected Topics and Solved Problems

303 Pages·2021·9.522 MB·English

by  Jafar Mehdi Hassan, Riyadh S. Al-Turaihi, Salman Hussien Omran, Laith Jaafer Habeeb, Alamaslamani Ammar Fadhil Shnawa

Turbulent Flow and Boundary
Layer Theory:
Selected Topics and Solved
Problems
Authored by

Jafar Mehdi Hassan
Automotive Engineering Section, Mechanical Engineering Department,
University of Technology,
Iraq
Riyadh S. Al-Turaihi
Mechanical Engineering Department, College of Engineering/Department of Mechanical
Engineering, Babylon University,
Babil – Iraq
Salman Hussien Omran
Ministry of Higher Education & Scientific Research/Private Higher Education
Directorate,
Iraq
Laith Jaafer Habeeb
Mechanical Engineering, University of Technology,
Iraq
Alamaslamani Ammar Fadhil Shnawa
Polytechnica University of Bucharest,
Romania
Turbulent Flow and Boundary Layer Theory:
Selected Topics and Solved Problems

Authors: Jafar Mehdi Hassan, Riyadh S. Al-Turaihi, Salman Hussien Omran,
Laith Jaafer Habeeb, Alamaslamani Ammar Fadhil Shnawa

ISBN (Online): 978-1-68108-811-2

ISBN (Print): 978-1-68108-812-9

ISBN (Paperback): 978-1-68108-813-6

© 2021, Bentham Books imprint.

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CONTENTS
FOREWORD ................................................................................................................................................ i
PREFACE ..................................................................................................................................................... ii
PART 1 TURBULENT FLOW
CHAPTER 1 FUNDAMENTALS OF TURBULENT FLOW ....................................................... 1
1. INTRODUCTION TO TURBULENT FLOW ........................................................................ 1
1.1. Nature of Turbulent .............................................................................................................. 2
1.1.1. Irregularity or Randomness ...................................................................................... 2
1.1.2. Diffusivity ................................................................................................................... 2
1.1.3. Large Reynolds Numbers ............................................................................................ 3
1.1.4. Three – dim. Vorticity Fluctuations ............................................................................ 3
1.1.5. Dissipation ................................................................................................................. 4
1.1.6. Continuum .................................................................................................................. 5
1.1.7. Turbulent Flow are Flows ...........................................................................................5
1.2. Methods of Analysis ............................................................................................................... 5
1.3. The Origin of Turbulent ......................................................................................................... 6
1.4. Diffusion of Turbulent ............................................................................................................ 7
1.5. Length Scales in Turbulent Flows .......................................................................................... 14
CHAPTER 2 TURBULENT TRANSPORT OF MOMENTUM ............................................................. 23
1. INTRODUCTION ..................................................................................................................... 23
2. THE REYNOLDS EQUATIONS ............................................................................................. 24
2.1. Correlated Variables .............................................................................................................. 26
2.2. Equation for the Mean Flow .................................................................................................. 27
2.3. The Reynolds Stress .............................................................................................................. 29
3. ESTIMATE OF THE REYNOLDS STRESS .......................................................................... 30
4. REYNOLDS STRESS AND VORTEX STRETCHING ......................................................... 32
5. PRANDTL MIXING LENGTH THEORY ............................................................................. 34
6. THE LOGARITHMIC – OVERLAP LAW ............................................................................ 38
7. TURBULENT VELOCITY PROFILE .................................................................................... 41
8. TURBULENT FLOW SOLUTION ......................................................................................... 42
8.1. Flow in Pipes ......................................................................................................................... 42
8.2. Flow between Parallel Plates ................................................................................................. 44
9. EFFECT OF ROUGH WALLS ................................................................................................ 45
10. DERIVATION OF REYNOLDS STRESS EQUATION OF MOTION FOR
TURBULENT FLOW ............................................................................................................... 47
CHAPTER 3 THE DYNAMICS OF TURBULENCE .............................................................................. 52
1. INTRODUCTION ..................................................................................................................... 52
2. TURBULENT KINETIC ENERGY (TKE) ............................................................................ 52
3. SOLUTION OF TKE ................................................................................................................ 55
CHAPTER 4 TRANSIENT FLOW ............................................................................................................ 63
1. DEFINITIONS ........................................................................................................................... 63
2. PRESSURE CHANGES CAUSED BY AN INSTANTANEOUS VELOCITY CHANGE 64
3. WAVE PROPAGATION AND REFLECTION IN A SINGLE PIPELINE ......................... 68
4. CLASSIFICATION OF HYDRAULIC TRANSIENTS ......................................................... 71
5. CAUSES OF TRANSIENTS..................................................................................................... 71
6. EQUATIONS OF UNSTEADY FLOW THROUGH CLOSED CONDUITS ...................... 72
6.1. Assumptions .......................................................................................................................... 72
6.2. Dynamic Equation ................................................................................................................. 72
6.3. Continuity Equation ............................................................................................................... 75
7. VELOCITY OF WATERHAMMER WAVES ....................................................................... 78
8. METHODS FOR CONTROLLING TRANSIENTS .............................................................. 83
8.1. General .................................................................................................................................. 83
8.2. Available Device and Methods for Controlling Transients .................................................... 84
8.3. Surge Tanks ................................................................................................................................. 84
8.4. Types of Surge Tanks .................................................................................................................. 86
8.5. Air Chambers............................................................................................................................... 87
8.6. Valves .......................................................................................................................................... 88
SOLVED PROBLEMS ........................................................................................................................ 92
PART 2 TURBULENT BOUNDARY LAYER
CHAPTER 5 BOUNDARY LAYER .......................................................................................................... 151
1. INTRODUCTION ..................................................................................................................... 151
2. DEFINITIONS ........................................................................................................................... 154
2.1. Displacement Thickness ................................................................................................ 154
2.2. Momentum Thickness θ ................................................................................................. 155
2.3. Kinetic Energy Factor .................................................................................................... 155
2.4. Shape Factor .................................................................................................................. 155
3. THE SEPARATION OF A B.L. ............................................................................................... 155
4. PRESSURE DRAG .................................................................................................................... 157
5. BOUNDARY LAYER THEORIES .......................................................................................... 158
5.1. Motivation ..................................................................................................................... 158
5.2. A Concise Result for Separately Quasinearly Subharmonic Functions .......................... 162
5.2.1. Laminar B.L ............................................................................................................ 163
5.2.2. Turbulent B.L .......................................................................................................... 163
5.3. Simulation Solution for Steady 2D. Flow ...................................................................... 165
5.4. The Blasius Solution for Flat – Plate Flow .................................................................... 166
5.5. The Falkner – Skan Wedge Flows (General Solution) ................................................... 168
5.6. Thwaites Method (Steady Flow) .................................................................................... 172
CHAPTER 6 TURBULENT BOUNDARY LAYER ................................................................................. 176
1. TURBULENT B.L. EQUATION .............................................................................................. 176
2. THE RELATIONS BETWEEN STRESSES AND PRESSURE GRADIENTS ................... 179
2.1. Laminar Sub – Layer .......................................................................................................... 181
2.2. The Inner Region of the Turbulent Layer ........................................................................... 183
3. THE SKIN FRICTION COEFFICIENT Cf (x) .............................................................. 185
CHAPTER 7 TRANSITION ZONE OF BOUNDARY LAYER .............................................................. 188
1. TRANSITION AND TURBLANCE ........................................................................................ 188
2. STABILITY ANALYSIS .......................................................................................................... 189
3. TRANSITION ZONE ................................................................................................................ 191
3.1. Conditions at Transition .................................................................................................. 191
3.2. Mixed B.L. Flow on a Flat Plate with Zero Pressure Gradient........................................ 191
4. METHODS OF BOUNDARY – LAYER CONTROL ............................................................ 195
4.1. Method of the Solid Wall ................................................................................................ 195
4.2. Acceleration of the Boundary Layer (Blowing) .............................................................. 196
4.3. Suction ............................................................................................................................ 196
4.4. Injection of Different Gas ............................................................................................... 197
4.5. Prevention of Transition by the Provision of Suitable Shapes ........................................ 197
4.6. Cooling of the Wall ......................................................................................................... 197
SOLVED PROBLEMS ................................................................................................................. 199
REFERENCES ............................................................................................................................................ 283
SUBJECT INDEX ....................................................................................................................................... 284
i
FOREWORD
Most flows encountered in engineering practice are turbulent, and thus it is
important to understand how turbulence affects wall shear. However, turbulent
flow is a complex mechanism dominated by fluctuation, and despite tremendous
amounts of work done in this area by researchers, turbulent flow still is not fully
understood. Therefore, we must rely on experiment and the empirical or semi-
empirical correlation developed for various situations. In laminar flow, fluid
particles flow in an orderly manner along path lines, and momentum and energy
are transferred across streamlines by molecular diffusion. In turbulent flow, the
swirling eddies transport mass, momentum, and energy to other regions of flow
much more rapidly than molecular diffusion, greatly enhancing mass, momentum
and heat transfer. As a result, turbulent flow is associated with much higher values
of friction, heat transfer, and mass transfer coefficients. The author with his
collaboration has been teaching the subject of turbulent flow and the boundary
layer for the past twenty years. In addition, this monograph is essential based on
the lectures delivered. The lecture notes were prepared to be utilized by the
postgraduate student as a part of their research work in the field of mechanical
engineering (power generation). Also including about a hundred solved problems
that have been given during the courses and examinations. From the experience
gained throng useful class discussion and feedback, the notes were revised to
improve the clarity and necessary explanatory nots were added during each
teaching semester. The subject matter has thus been thoroughly tested in the
classroom and found suitable. This book is a compilation and no claim is made of
its originality. Acknowledgments are due and hereby made to all the authors
whose work has been used in the preparation of this text. Finally, this book
emphasizes the need for postgraduate engineers to acquire great efficiency in
using the tool of the study and researches in the field of turbulent flow, boundary
layers, etc.

M. I. Abu-Tabikh
Mechanical Engineering Department
University of Technology
Baghdad - Iraq
E-mails: [email protected]
[email protected]
ii
PREFACE

The present book is focused on fundamental concepts of turbulent flow with
boundary layer analysis. It is the outgrowth of our several years of teaching
postgraduate courses in mechanical engineering department at University of
Technology. A general introduction to turbulent flow is provided discussing flows
turbulent that occurring in nature and engineering application. Also transient flow,
methods for controlling transients, turbulent models and dynamic equations are
explained for unsteady flow through closed conduits. In this book, all the basic
concepts in turbulent flow are clearly identiifed and presented in a simple manner.
with illustrative and practical examples. We have also attempted to make this
book self-contained as much as possible; for example, materials needed from
previous courses, such as equations, theory and engineering mechanics, are
presented. Each chapter also has a set of questions and problems to test the
student’s power of comprehending the topics. Many of our colleagues and
academic friends helped us by giving valuable suggestions on the structure and
content of this text and these were instrumental in improving the quality and
presentation of this book. We wish to express our profound gratitude and
appreciation to all of them.

It is expected that the book will be a useful reference/text for
professionals/students of engineering and including dynamic research and project
consultants undertaking turbulent flow and boundary layer methods analysis. We
have tried not only to give a comprehensive coverage of the various aspects of
turbulent flow analysis but provided an exhaustive appendix on interest examples .
These examples, along with the topics discussed, will, we believe, help both
students and teachers in carrying out turbulent flow analysis and solving
problems. In this book, all the basic concepts in turbulent flow are clearly
identiifed and presented in a simple manner with illustrative and practical
examples.

Any suggestions for improving the contents would be warmly appreciated.

CONSENT FOR PUBLICATION
Not applicable.
iii
CONFLICT OF INTEREST
The author declares no conflict of interest, financial or otherwise.
ACKNOWLEDGEMENTS
Declared none.

Jafar Mehdi Hassan
Automotive Engineering Section
Mechanical Engineering Department
University of Technology
Iraq
E-mail: [email protected]

Riyadh S. Al-Turaihi
Mechanical Engineering Department
College of Engineering/Department of Mechanical Engineering, Babylon
University, Babil
Iraq
E-mail: [email protected]

Salman Hussien Omran
Ministry of Higher Education & Scientific Research/Private Higher Education
Directorate
Iraq
E-mail: [email protected]

Laith Jaafer Habeeb
Mechanical Engineering
University of Technology
Iraq
E-mail: [email protected]

&

Alamaslamani Ammar Fadhil Shnawa
Polytechnica University of Bucharest
Romania
E-mail: [email protected]