Fundamentals Of Incompressible Fluid Flow

208 Pages·2016·5.486 MB·English

by  V. Babu

V. Babu
Fundamentals
of Incompressible
Fluid Flow
Fundamentals of Incompressible Fluid Flow
Coverillustration:Incompressibleflowaroundasquarecylinder(showningray)ataReynolds
numberof200simulatedusingthelatticeBoltzmannmethod.ThevonKarmanvortexstreetcan
beseenclearly
V. Babu
Fundamentals
of Incompressible Fluid Flow
V.Babu
DepartmentofMechanicalEngineering
IndianInstituteofTechnologyMadras
Chennai,TamilNadu,India
ISBN978-3-030-74655-1 ISBN978-3-030-74656-8 (eBook)
https://doi.org/10.1007/978-3-030-74656-8
JointlypublishedwithANEBooksPvt.Ltd.
Inadditiontothisprintededition,thereisalocalprintededitionofthisworkavailableviaAneBooksin
SouthAsia(India,Pakistan,SriLanka,Bangladesh,NepalandBhutan)andAfrica(allcountriesinthe
Africansubcontinent).
ISBNoftheCo-Publisher’sedition:978-9-380-61816-6
©TheAuthor(s)2022
Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether
thewholeorpartofthematerialisconcerned,specificallytherightsofreprinting,reuseofillustrations,
recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor
informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublishers,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishersnortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublishersremainneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Dedicatedtomyguide
Prof.SeppoKorpelaand
hiswifeTerttuKorpela
fortheirloveand
affection
Preface
Iampleased tobring outthisrevised editionof thebook onIncompressible Fluid
Flows. Corrections that have been pointed out by readers have been incorporated.
Inaddition,thesectiononpathlinesandstreamlineshasbeencompletelyrewritten
andnowincludesmaterialonstreaklinesandtimelinesaswell.Ihavealsorewritten
Chap.6onboundarylayertheoryusingnotationconsistentwiththepreviouschap-
ters. Appropriate changes have been made in the subsequent chapters to adhere to
thisnotation.InChaps.6and7,Ihavepresentedscaleanalysisinamannerthatis
mucheasierforthereadertofollow.
I am grateful to the readers who read the book and pointed out errors and gave
suggestions.Ifthereareanymoreerrorsorifyouhaveanysuggestionsforimproving
theexpositionofanytopic,pleasefeelfreetocommunicatethemtomeviae-mail
([email protected]).
Chennai,India V.Babu
vii
Preface to the First Edition
I am pleased to bring out this book on Incompressible Fluid Flow based on my
lecturenotesofthepostgraduatecoursesthatIteachatIITMadrasonthissubject.
Theseclassesareusuallyattendedbyfinal-yearB.Tech.students,M.Tech.,M.S.and
Ph.D.studentswhohavehadapreliminaryexposuretothesubjectmatterearlier.I
haveassumedthesameaboutthereaders,whilewritingthisbook.Thishasallowed
metopresentconceptssuchasviscosityandReynoldsnumbermuchearlierthanis
usual.AbroadrangeofbasicconceptsispresentedinChap.2.Theincompressible
Navier–StokesequationsarederivedinChap.3,andthemathematicalnatureofthe
solutions to these equations is discussed in Chap. 4. In this context, the notion of
singularperturbationsolutions—outerandinner—isintroduced.Chapter5dealswith
theinviscid(outer)solutions,whiletheboundarylayer(inner)solutionsarederived
in Chap. 6. Separation of the boundary layer, its consequences and drag are also
discussedindetail.Analyticalsolutions,bothparallelandcreepingflowsolutions,
arepresentedinChap.7.TurbulentflowsarediscussedinChaps.8–10.Thenature
of turbulent flows and the importance of the turbulent mean flow are discussed in
Chap. 8. Chapters 9 and 10 build on the latter idea in the context of internal and
externalflows,respectively.Ideasofpracticalimportancesuchasdragreductionin
suchflowsarealsopresented.
Theconceptsandideasdiscussedherearenotnew,buthavemerelybeenpresented
inadifferentmannerarisingfrommyexperienceinteachingthem.Althoughthere
are many books on fluid mechanics, it is my hope that the readers might find the
arrangementandthediscussionofthetopicsinthisbooktoberefreshinglydifferent
andinsightful.Ifthereareanyerrorsorifyouhaveanysuggestionsforimproving
theexpositionofanytopic,pleasefeelfreetocommunicatethemtomeviae-mail
([email protected]).Aswithmyotherbooks,myintentionwasnottowriteabook
thatwasexam-orientedbutonethatwillhelpstudentsimprovetheirunderstandingof
thesubjectmatter.Toalargeextent,theexamplesandexerciseproblemsaredrawn
frompracticalapplicationstoenablethestudenttoappreciatetheusefulnessofthe
conceptsdiscussedhereininsuchsituations.Ihavesuggestedalistofbooksatthe
end(inalphabeticalorder)forthestudentstoconsult.Thesebooksalsohavealarge
collectionofexerciseproblemsthatthestudentscan(andshould)practice.
ix
x PrefacetotheFirstEdition
Some parts of this book were written when I was at the Ohio State University
onlongleave.IwishtothanktheChairmanoftheDepartmentofMechanicalEngi-
neering, Prof. K. Srinivasan, for the hospitality and support that I received during
mystaythere.Onthepersonalside,IwishtothankDr.PrasadMokashiandhiswife
Janhavifortreatingmeasamemberoftheirfamilyandmakingmystaysopleasant
andmemorable.
Asalways,IwouldliketothankmyteachersSri.S.Sundaresan,Prof.R.Bodonyi,
Prof.M.FosterandProf.T.Scheick,who,asteachers,inspiredmetoagreatextent.
OnepersontowhomIowethemostisProf.S.KorpelaoftheOhioStateUniversity.
I learnt from him not only how to be a good academic researcher, but also, more
importantly,howtobeagoodhumanbeingaswell.Thekindnessandaffectionthat
heandhiswifeTepashowedduringmystayinColumbuslastyearwereincredible.
Ihavemadeanattempttoshowthemmygratitudebydedicatingthisbooktothem.
Icannotadequatelyexpressinwordsmygratitudeforthelove,affection,support
andencouragementthatIhavereceivedfrommywifeChitraandsonAravindhover
theyears.Iamfortunateindeed.
IwishtoexpressmyheartfeltgratitudetomygrandfatherSri.V.Gopalanandmy
parents who endeavored somuch to give me a good education. They have given a
lottomebutreceivedverylittleinreturn.
Finally,IwouldliketothankmystudentsS.Somasundaram,V.G.Ramanathan
andDr.P.S.Tidefortheirhelpinworkingouttheexamplesandexerciseproblems
andmywifeChitraforproof-readingthemanuscript.
Chennai,India V.Babu
Contents
1 Introduction .................................................. 1
1.1 CompressibilityofFluids .................................. 1
1.2 CompressibleandIncompressibleFlows ..................... 2
1.3 LaminarandTurbulentFlows .............................. 4
2 BasicConceptsinIncompressibleFlows ......................... 5
2.1 DefinitionofaFluid ...................................... 5
2.2 SteadyandUnsteadyFlows ................................ 5
2.3 Pathlines,StreaklinesandStreamlines ....................... 9
2.4 StreamFunction,VorticityandCirculation ................... 13
2.5 EulerianandLagrangianFormulations ...................... 21
2.6 MaterialDerivative ....................................... 23
Exercises ..................................................... 23
3 TheIncompressibleNavier–StokesEquations .................... 25
3.1 ContinuityEquation—EulerianFormulation ................. 25
3.2 MomentumEquation—LagrangianFormulation .............. 29
3.2.1 ForcesActingonaFluidElementandtheStress
Tensor .......................................... 30
3.3 StrainingofaFluidElementandtheStrainRateTensor ........ 35
3.4 Relation Between the Deviatoric Stress Tensor
andtheStrainRateTensor ................................. 40
3.4.1 Stokes’Hypothesis ................................ 40
3.5 IncompressibleNavier–StokesEquations .................... 41
3.6 NewtonianandNon-NewtonianFluids ...................... 42
3.7 ContinuityEquation—Revisited ............................ 44
Exercises ..................................................... 45
4 SolutionstotheIncompressibleNavier–StokesEquations ......... 47
4.1 MathematicalNatureoftheIncompressibleNavier–Stokes
Equations ............................................... 47
4.2 BoundaryConditions ..................................... 48
4.3 AnIllustrativeExample ................................... 49
xi