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 This Edition Published by John Wiley & Sons Ltd. The Atrium, Southern Gate Chichester, West Sussex PO19 8SQ United Kingdom Tel : +44 (0)1243 779777 Fax : +44 (0)1243 775878 e-mail : [email protected] Web : www.wiley.com For distribution in rest of the world other than the Indian sub-continent and Africa. Under licence from: Athena Academic Ltd. Suite LP24700, Lower Ground Floor 145-157 St. John Street, London, ECIV 4PW. United Kingdom E-mail : [email protected] www.athenaacademic.com ISBN : 978-11-1900-299-4 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the U.K. Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. 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.