Introduction to Computational Fluid Dynamics Development, Application and Analysis

399 Pages·2016·38.404 MB·English

by  Atul Sharma

Introduction to
Computational
Fluid Dynamics
Development, Application and Analysis
Introduction to
Computational
Fluid Dynamics
Development, Application and Analysis
Dr. Atul Sharma
Professor, Deptt. of Mech. Engineering
IIT Bombay
Introduction to Computational Fluid Dynamics
Development, Application and Analysis
Dr. Atul Sharma
© Author, 2017
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Library Congress Cataloging-in-Publication Data
A catalogue record for this book is available from the British Library
Cover Image: The image for C, F and D in the cover page is obtained from a
Computational Fluid Dynamics simulations as follows:
C: Curvilinear-Grid and Resultant-Velocity Contours for Fluid-Flow in a C-shaped Bend
of a Pipe
F: Temperature-Contours in a Heat Conduction Problem
D: Vertical-Velocity Contours for a vertical-wall (moving upward, like a conveyor belt)
driven flow in a D shaped cavity.
Disclaimer
The contents, sources, and the information provided by the authors in different chapters are
the sole responsibility of the authors themselves, including the copyright issues. Editors and
Publishers have no liabilities whatsoever towards these in any manner.
This book is dedicated
to
Suhas V. Patankar
Dr. Suhas V. Patankar1 (born February 22, 1941) is an Indian
mechanical engineer. He is a pioneer in the (cid:28)eld of computational
(cid:29)uid dynamics (CFD) and (cid:28)nite volume method. He received his
B.E. from the University of Pune in 1962, M.Tech. from IIT Bombay
in 1964 and Ph.D. from Imperial College, London in 1967.
Dr. Patankar is currently a Professor Emeritus in the Mechanical
Engineering Department at the University of Minnesota, where he
worked for 25 years (from 1975-2000). Earlier, he held teaching and
research positions at IIT Kanpur, Imperial College, and University
of Waterloo. He is also the President of Innovative Research, Inc. He
has authored or co-authored four books, published over 150 papers,
advised 35 completed Ph.D. theses, and lectured extensively in the
USA and abroad. His 1980 book (cid:16)Numerical heat Transfer and Fluid
Flow(cid:17) is considered to be a groundbreaking contribution to CFD. He
is one of the most cited authors in science and engineering.
Forexcellenceinteaching,Dr. Patankar receivedthe1983George
TaylorDistinguishedTeachingAwardandthe1989-90Morse-Alumni
1Source (fortheBiography): PersonalCommunication
v
vi
Award for Outstanding Contributions to Undergraduate Education.
For his research contributions to computational heat transfer, he was
given the 1991 ASME Heat Transfer Memorial Award and the 1997
Classic Paper Award. He was awarded the 2008 Max Jakob Award,
whichisconsideredtobethehighestinternationalhonorinthe(cid:28)eldof
heattransfer. In2015,anInternationalConferenceonComputational
Heat Transfer (CHT-15) held at Rutgers University in New Jersey
was dedicated to Professor Patankar.
Dr. Patankar’s widespread in(cid:29)uence on research and engineering
education has been recognized in many ways. In 2007, the Editors of
the International Journal of Heat and Mass Transfer wrote, (cid:16)There is
no person who has made a more profound and enduring impact on the
theoryandpracticeofnumericalsimulationinmechanicalengineering
than Professor Patankar.(cid:17)
FOREWORD
by Prof. K. Muralidhar
Indian Institute of Technology Kanpur, INDIA
The subject of computational (cid:29)uid dynamics (CFD) emerged in the
academic context but, in the past two decades, it has developed to a
pointwhereitisextensivelyemployedasadesignandanalysistoolin
the industry. The impact of the subject is deeply felt in diverse disci-
plines ranging from the aerospace spreading all the way to the chem-
ical industry. New, compact and e(cid:30)cient designs are enabled and it
hasbecomethatmuchmoreconvenienttolocateoptimumconditions
for the operation of engineering systems. As it stands, CFD is com-
pulsorylearninginseveralbranchesofengineering. Manyuniversities
now opt to develop theoretical courses around it. The great utility of
this tool has in(cid:29)uenced adjacent disciplines and the process of solv-
ingcomplexdi(cid:27)erentialequationsbytheprocessofdiscretizationhas
become a staple for addressing engineering challenges.
For an emerging discipline, it is necessary that new books fre-
quently appear on the horizon. Students can choose from the se-
lection and will stand to gain from it. Such books should have a
perspective, of the past and the future, and it is all the more signi(cid:28)-
cant when the author has exclusive training in the subject. Dr. Atul
Sharmarepresentsacombinationofperspective, trainingandpassion
that combines well and delivers a strong text.
I have personal knowledge of the fact that Dr. Atul Sharma has
developed a whole suite of computer programs on CFD from scratch.
He has wondered and pondered over why approximations work and
conditions under which they yield meaningful solutions. His spread
vii
viii Foreword
of experience over (cid:28)fteen and odd years includes two and three di-
mensional Navier-Stokes equations, heat transfer, interfacial dynam-
ics and turbulent (cid:29)ow. He has championed the (cid:28)nite volume method
which is now the industry standard. The programming experience
is important because it brings in the precision needed for assembling
the jigsaw puzzle. The sprinkling of computer programs in the book
is no coincidence.
Atul knows the conventional method of discretizing di(cid:27)erential
equations but has never been satis(cid:28)ed with it. He has felt an ele-
ment of discomfort going away from a physical reality into a world
of numbers connected by arithmetic operations. As a result, he has
developed a principle that physical laws that characterize the di(cid:27)er-
ential equations should be re(cid:29)ected at every stage of discretization
and every stage of approximation, indeed at every scale (cid:21) whether a
single tetrahedron or the sub-domain or the region as a whole. This
idea permeates the book where it is shown that discretized versions
must provide reasonable answers because they continue to represent
the laws of nature.
This new CFD book is comprehensive and has a stamp of origi-
nality of the author. It will bring students closer to the subject and
enable them to contribute to it.
Kanpur
August, 2016 K. Muralidhar
PREFACE
As a Post-Graduate (PG) student in 1997, I got introduced to a
course on CFD at Indian Institute of Science (IISc) Bangalore. Dur-
ing the (cid:16)introductory(cid:17) course on CFD, although I struggled hard
in the physical understanding and computer-programming, it didn’t
stop my interest and enthusiasm to do research, teaching, and writ-
ing a text-book on a (cid:16)introductory(cid:17) course in CFD. Since then, I did
my Masters project work on CFD (1997-98); introduced and taught
this course to Under-Graduate (UG) students at National Institute
ofTechnology, Hamirpur, H.P.(1999-2000); didmyDoctoralworkon
this subject at Indian Institute of Technology (IIT) Kanpur (2000-
2004); and co-authored a Chapter on (cid:16)(cid:28)nite volume method(cid:17) in a re-
vised edition of an edited book on computational (cid:29)uid (cid:29)ow and heat
transfer, during my Ph.D. in 2003. After joining as a faculty in 2004,
I taught this course to UG as well as PG students of di(cid:27)erent depart-
mentsatIITBombayaswellastothestudentsofdi(cid:27)erentcollagesin
IndiathroughCDEEP(CenterforDistanceEngineeringProgramme)
IIT Bombay; from 2007-2010. Furthermore, I gave series of lecture
on CFD at various collages and industries in India. More recently,
in 2012, I delivered a (cid:28)ve-days lecture and lab-session on CFD (to
around 1400 collage teachers from di(cid:27)erent parts of India) as a part
ofaprojectfundedbyministryofhumanresourcedevelopmentunder
NMEICT (National Mission on Education through information and
communication technology).
The increasing need for the development of the customized CFD
software (app), and wide spread CFD application as well as analysis
for the design, optimization, and innovation of various types of engi-
neering systems always motivated me to write this book. Due to the
increasing importance of CFD, another motivation is to present CFD
ix
x Preface
simple enough to introduce the (cid:28)rst-course at early under-graduate
curriculum; rather than the post-graduate curriculum. The moti-
vation got strengthened by my own as well as other’s (students,
teachers, researchers, and practitioners) struggle on physical under-
standing of the mathematics involved during the Partial Di(cid:27)erential
Equation(PDE)basedalgebraic-formulation((cid:28)nitevolumemethod),
along with the continuous frustrating pursuit to e(cid:27)ectively convert
the theory of CFD into the computer-program.
This led me to come up with an alternate physical-law (PDE-
free) based (cid:28)nite volume method as well as solution methodol-
ogy, which are much easier to comprehend. Mostly, the success of
the programming e(cid:27)ort is decided by the perfect execution of the
implementations-detailswhichrarelyappearsin-print(existingbooks
and journal articles). The physical law based CFD development
approach and the implementations-details are the novelties in the
present book. Furthermore, using an open-source software for nu-
merical computations (Scilab), computer programs are given in this
book on the basic modules of conduction, advection, and convection.
Indeed, the reader can generalize and extend these codes for the de-
velopmentofNavier-Stokessolver; andgeneratetheresultspresented
in the chapters towards the end of this book.
I have limited the scope of this book to the numerical-techniques
whichIwishtorecommendforthebook,althoughtherearenumerous
other advanced and better methods in the published literature. I do
notclaimthattheprogramming-practicepresentedherearethemost
e(cid:30)cient − they are presented here more for the ease in programming
(understand as your program) than for the computational e(cid:30)ciency.
Furthermore, although I am enthusiastic about my presentation of
the physical law based CFD approach, it may not be more e(cid:30)cient
than the alternate mathematics based CFD approach. The emphasis
in this book is on the ease of understanding of the formulations and
programming-practice; for the introductory course on CFD.
I would hereby acknowledge that I owe my greatest debt to Prof.
J. Srinivasan (my M.E. Project supervisor at IISc Bangalore) who
did a hand-holding and wonderful job in patiently introducing me to
the fascinating world of research in (cid:29)uid-dynamics and heat trans-
fer. I would also acknowledge the excellent training from Prof. V.