Table Of ContentSarit Kumar Das
Dhiman Chatterjee
Vapor Liquid Two
Phase Flow and
Phase Change
Vapor Liquid Two Phase Flow and Phase Change
·
Sarit Kumar Das Dhiman Chatterjee
Vapor Liquid Two Phase
Flow and Phase Change
SaritKumarDas DhimanChatterjee
DepartmentofMechanicalEngineering DepartmentofMechanicalEngineering
IndianInstituteofTechnologyMadras IndianInstituteofTechnologyMadras
Chennai,TamilNadu,India Chennai,TamilNadu,India
ISBN 978-3-031-20923-9 ISBN 978-3-031-20924-6 (eBook)
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Dedicatedto
Prof.W.Roetzel
and
Prof.V.H.Arakeri
whohaveinspiredustounderstand
two-phaseflow
Foreword
Engineers were using phase change devices even before James Watt separated the
steamengine’s condenser fromitsworking cylinder in1764.Today, phasechange
underpinsnumeroustechnologiesthateasemodernlife.Electricalpowergeneration,
foodrefrigerationandairconditioningareeachenabledbyboilingandcondensation.
Aftersomuchtime,couldanythingmorebesaidonthistopic?Indeed,yes!New
tools and growing datasets have opened new insights and opportunities. Modern
numericalmethodscansimulatecomplexbubbledynamicsfromfundamentalequa-
tions. Surface engineering and microfabrication technology have unveiled boilers
andcondenserswithpreviouslyunimaginableproperties.Andvastamountsofhigh-
quality data now support ever-improving models of the two-phase flows that cool
nuclearreactors.
Nonetheless,phasechangeembodiesacomplexitynotfoundinotherheattransfer
problems.Essentialphenomenacontinuetodefysystematicmodellingacrossconfig-
urations, despite more than 100 years of research. As a child, I often visited my
father’sboilinglaboratory.Irememberwellhis1960’sexperimentsonpoolboiling—
especiallythoseconductedinacentrifuge!Yet,eventoday,newdesignsleadustothe
samebasicquestions:whatdeterminesthecriticalheatfluxandhowcanwecontrol
it? Until we have comprehensively resolved these puzzles, engineers will need to
understandthefundamentalphysicsoftwo-phasesystems,todevelopmodelsandto
applythelatestknowledge.
IfirstmetProf.SaritDasattheISHMTconferenceinGuwahatiinJanuary2006.
There,Iwasstartledbyanaudiencememberwhoaskedanincisivequestionabout
evaporationinmyliquidjetexperiments.ItwasSarit.Sincethatday,heandIhave
beengoodfriends.Twoyearslater,IhostedSaritforaone-yearvisittoMIT.In2011,
weagainappointedhimasavisitingprofessoratMIT.Sarit’sextensiveresearchhas
touched most areas of heat transfer. And his work’s high quality resulted in his
electiontoboththeIndianNationalAcademyofSciencesandtheIndianNational
AcademyofEngineering.
Here,Profs.DasandDhimanChatterjeegiveanup-to-dateaccountofourbest
knowledgeofthesubject.Theirworkhasastrongfocusonthetwo-phaseflowsthat
vii
viii Foreword
areofthegreatestindustrialimportance.Theirapproachuniquelycoverspressure-
driven processes alongside thermally driven processes. And they discuss recent
concepts in microengineering for two-phase devices. I invite the reader to enjoy
andlearnfromthisimportantnewbook.
October2020 JohnH.LienhardV
MassachusettsInstituteofTechnology
Cambridge,USA
Preface
Before beginning to write any academic text, the authors have to come across the
centralquestion,“Whyarewewritingthisbook,what’stheneedforthisbookfor
thisareaofstudy?”Abookonphasechangeinthegas–liquidregimeisevenmore
under question because the developments in this particular area spread over more
than a century. Reputed and time-tested texts such as those by Collier and Thome
(Convectiveboilingandcondensation,1972),TongandTang(Boilingheattransfer
andtwo-phaseflow,1997)andeditedvolumeslikeMultiphaseflowhandbook(Eds,
Michaelidas, Crowe and Schwarzkopf, 2016) exist, which cover almost the entire
spectrumofstudiesinthisfield.Naturally,theneedforanothertextinthisareais
questionable. However, the authors in course of guiding the masters and doctoral
studentsfoundthattheabovetexts,althoughquitecomprehensive,arepitchedata
levelthatisinbetweenbasicphenomenologicalunderstandingandstate-of-the-art
research.Thismakesthemoverwhelmingtobeginnersintheareaoftwo-phaseheat
transfer.Personally,wehaveexperiencedevencaseswhereyoungscholarsafterthe
firstreadinghavedecidednottoventureintothisfieldbecausetheyfoundittobe
“toocomplexanddifficult”.Therearealsoscholarswhofoundthattheareais“more
empirical and observational than scientific”. In our opinion, these impressions are
duetothelackofanintroductorytextthatwillapproachthesubjectinasimpleyet
scientificwaywherethephysicalexplanationcombinedwithmathematicalanalysis
cangiveaninsighttoabeginnerwhichcankindleinterestinhim/her.
Apartfromtheabovenoveltyinapproach,thebookcontainsanumberofunique
features.Usually,liquid–vapourphasechangetextsarelimitedtoboilingandconden-
sation alone, stressing on the thermal aspects of these phenomena. However, the
pressure-dominated phase change like cavitation is usually not included in such
books.Wefeelthatfromnucleationtobubbledynamics,therearealotofcommon
groundsbetweenboilingandcavitationandhencedecidedtomakeitapartofthe
presenttext(Chap.5).
The other unique feature of this book is the inclusion of the materials which
happentobethefocusofresearchintwo-phaseheattransfertoday.Boilinginmini
and microchannels (Chap. 16) is one such chapter. The other one is an elaborated
chapter on numerical modelling of two-phase flow and heat transfer (Chap. 14).
ix
x Preface
It goes without saying that these are included for the readers interested in these
areasonlyandcanbeleftoutbyothers.Chapter15isdevotedtotheequipmentfor
boilingandcondensation.Wefeltthatitisnecessarytofamiliarizethereaderwith
thedevicesusedindifferentpracticalapplicationsasthesetopicsmaybeusefulfor
theirprofessionalcareer.
Wetakethisopportunitytothankalargenumberofpeoplewhohelpedustobring
out this text. First, we express our gratitude to Prof. B. Premachandran of Indian
InstituteofTechnologyDelhiwhohelpedustocompletelyreframeandevenwrite
partsofthechapteronnumericalmodellingoftwo-phaseheattransfer(Chap.14).
Thanks are also due to Dr. S. V. Diwakar of JNCASR for contributing the portion
onQUASIalgorithminthesamechapter.WealsothankDr.M.Venkatesanforhis
contributionstowardsaportiononboilinginmicrochannelsandrewritingpartsof
Chap. 16. Next, we must thank our students in general and Mr. Allwyn Blessing
Johnson,inparticular,whohavecontributedinvariouswaysfromconceptualization
to execution of this book writing project. Special thanks are due to Ms. Anitha
and Ms. Maninder Kaur who prepared the manuscript along with the figures with
utmost dedication. We also thank our collaborators who have enhanced our own
understandingofthesubject.TomentionafewofthemareProf.A.R.Balakrishnan
(IITMadras)andProf.KausikSarkar(UniversityofDelaware).Wethankprofoundly
thepublisherAneBookfortheirpatienceinwaitinglongforthecompletionofthis
bookandthetechnicalsupporttheyprovidedus.Lastbutnottheleastisthesacrifices
madebyourfamilieswhonevercomplainedtofindthatthisbookwritingactivityis
furthershrinkingthealreadyscarcelyavailabletimeforthem.
Finally, the proof of the pudding is in the eating. It is the readers, scholars and
studentswhowilldecidetheworthofthisbook.Iftheyfeelthatthisbookhashelped
them anyway to grasp this rather complex yet interesting subject, the authors will
considertheireffortstohavebeenrewarded.
Chennai,India SaritKumarDas
DhimanChatterjee
Contents
1 IntroductiontoTwo-PhaseFlow—FlowPatternsandMaps ....... 1
1.1 DefinitionsRelatedtoTwo-PhaseFlow ...................... 1
1.2 Two-PhaseFlowPatternsandMaps ......................... 6
1.2.1 AdiabaticFlowRegimesandPatterns ................ 7
1.2.2 Non-adiabaticFlowRegimesandPatterns ............ 9
1.2.3 FlowPatternMaps ................................ 12
Examples ..................................................... 17
Exercises ..................................................... 20
References .................................................... 22
2 Two-PhaseFlow—PressureDropandFlowFriction .............. 23
2.1 MomentumBalanceinanInclinedTubeandPressureDrop .... 24
2.1.1 Single-PhaseFlow ................................ 25
2.1.2 Two-PhaseFlow .................................. 26
2.2 FrictionalPressureDropandTwo-PhaseMultiplier ........... 28
2.2.1 HomogeneousFlow ............................... 31
2.2.2 SeparatedFlow—Lockhart–MartinelliModel ......... 35
2.2.3 Martinelli–NelsonMethodforDiabaticSeparated
Flow ............................................ 38
2.2.4 BarcozyandChisolmModel ....................... 42
2.3 DriftFluxModel ......................................... 44
2.3.1 One-dimensionalDriftFluxModel .................. 46
2.3.2 ApplicationtoBubblyFlow ........................ 47
2.3.3 Two-dimensionalDriftFluxModel .................. 48
Examples ..................................................... 49
Exercises ..................................................... 58
References .................................................... 59
3 ThermodynamicsofPhaseChange .............................. 61
3.1 PureSubstanceandStatePrinciple .......................... 62
3.2 PropertiesofLiquid–VapourSysteminThermodynamic
Equilibrium ............................................. 64
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