Table Of ContentMultiphase Flow Analysis Using
Population Balance Modeling
Bubbles, Drops and Particles
Guan Heng Yeoh
Chi Pok Cheung
Jiyuan Tu
AMSTERDAM BOSTON HEIDELBERG LONDON
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Preface
Giventheincreasingpowerofcomputersandtheacceleratedpaceofhardwaredevelopment
ofdigitalcomputers,computermodelsaregainingsignificanttractionandincreasinglybeing
employed to investigate the fluid dynamics, heat transfer, and mass transfer of gas bubbles,
liquid drops, and solid particles affecting natural, biological, and industrial systems.
Nevertheless, the prime difficulty experienced by multiphase modelers is the modeling of
multiphase flows due to large-scale separation. The existence of large-scale flow structures
encompassing different particles within a mixture can be readily observed at the device or
macroscale. These structures are, nonetheless, influenced by the physical behavior of
particles on the microscale. Significant interactions between particles may result in local
structuralchangesduetoagglomeration/coalescenceandbreakage/breakupprocessesofgas
bubbles, liquid drops, and solid particles on the mesoscale. It is on the mesoscalewhere the
abilitytoaccuratelydeterminethesizedistributionsoftheseparticlesistheprimaryfocusof
this book. Interphase mass, momentum, and energy exchanges that appear in the transport
equations of computational multiphase fluid dynamics are usually found to be strongly
dependentonthebubble,drop,andparticlesizedistribution,whichinanycaserepresentthe
cornerstone for a fully predictive thermal and hydrodynamics in any multiphase system. In
order to aptly describe the changes in the size distribution, population balance modeling is
increasingly being adopted in predicting the representative bubble, drop, or particle size.
Thus, it is the consideration of population balance modeling in conjunction with
computational multiphase fluid dynamics which makes this book rather unique. One main
featureofpopulationbalancemodelingisitscapabilitytoaccommodatetheessentialkinetics
of particleeparticle interaction. Since it is mechanistically driven, the fusion between
computationalmultiphasefluiddynamicsandpopulationbalancemodelingwillrevolutionize
how different classifications of multiphase flows can be feasibly treated and solved.
Guan Heng Yeoh
Chi Pok Cheung
Jiyuan Tu
ix
Foreword
IamdelightedtowritetheForewordforthisbook,whichcapturestherecentadvancesinboth
analyticalandcomputationaltechniquesindescribingaccuratelymultiphaseflowphenomena
in engineering practice and complex flow systems comprising bubbles, drops, and particles.
Bubbles, drops, and particles are of fundamental importance in many natural physical
processesandinahostofindustrialactivities.Meteorologistsconstantlystudyandsurveythe
behavior of raindrops and of hailstones. Applied mathematicians and physicists are always
concernedwiththefundamentalaspectsoftheinteractionbetweenfluidsanddiscreteentities.
Chemical engineers rely on bubbles or drops for critical operations of engineering systems
associated with distillation, absorption, and spray drying while employing solid particles as
means of catalysts or chemical reactants in such systems. Mechanical engineers require the
knowledge of bubbles in electromachining and boiling. In all of these phenomena and
processes, the relative motion between bubbles, drops, and particles on the one hand and
surrounding fluid on the other hand has a major effect. The flow of these discrete entities
co-flowingwiththesurroundingfluidcanbetreatedthroughcomputationalmultiphasefluid
dynamics simulations, of which the authors of this book are prominent experts in this field.
Incomplexmultiphaseflows,thetreatmentoftheinteractionsbetweendiscreteentitiesisalso
of major importance. Consideration of the so-called population balance equations brings
anotherdimensioninthepredictionofthesizedistributionofbubbles,drops,andparticlesin
a fluid. The use of these population balance equations is considered, in addition to the
computational multiphase fluid dynamics simulations. It should be noted that population
balanceequationsarenotentirelynew.ThefamousBoltzmannequationwasfirstintroduced
in chemical physics and is now more than a century old. It can be readily seen that the
atomic and the molecular processes that are involved in solid crystal nucleation, growth,
agglomeration,andbreakage,forexample,areentirelydifferentfromthosethatoccurinthe
nucleation, coalescence, and breakup of bubbles or drops in a boiling flow, or even the
growth and reproduction of a population of microbes or animal cells. Nevertheless, certain
general concepts,suchas thoseembedded in populationbalanceequations, can be extended
todealwithalloftheaforementionedprocesses.Itisthisgenericframeworkthattheauthors
havegonetogreatlengthstopromoteinthisbookwiththespecificaimofdrawinginreaders,
whowillnotonlyunderstandthebasicconceptsaswellasspecifictechniquesofpopulation
xi
xii Foreword
balance modeling but also acquire a holistic view of a situation that involves a collection of
discrete entities with an evolving distribution of properties applicable to a wide range of
multiphase flows.
Inmyview,theauthorscanbeconfidentthattherewillbemanygratefulreaderswhowillgain
broader perspectives of computational multiphase fluid dynamics and of population balance
modelingasresultoftheirefforts.Thechallengeposedtotheauthorshasbeentoamalgamate
these two large frameworks into a single text; the authors can be proud that they have
managed to achieve such a task. The description of the complex multiphase flows is broken
down to easy-to-understand exposition beginning from first principles, and then moving
toward a thorough description of different models targeted for specific classifications of
multiphase flows. More importantly, the authors have provided useful best practice solution
methods, which are accompanied by a practical approach in solving different classifications
ofmultiphaseflows.Whetherreadersviewthistextfromeitherthecomputationalmultiphase
fluid dynamics or the population balance framework, they will discover that it has been
writteninamannertoguidethemintoaclearunderstandingofthecomprehensivetreatment
of the complicated nature of multiphase flows. This text is certainly an enthusiastic
celebrationofthreebasicelementsdtheory,modelingandpracticedinhandlingamultitude
of multiphase flows.
Goodarz Ahmadi
Clarkson University,
Potsdam, New York
13 May, 2013
Acknowledgments
GuanHengYeohwouldliketoacknowledgetheuntiringsupportandendlesstoleranceofhis
wife, Natalie, and his three daughters, Genevieve, Ellana, and Clarissa, for their enormous
understandingandunflinchingencouragementduringtheseeminglyunendinghoursspentin
preparing and writing this text.
ChiPokCheungwouldliketoexpresshisdeepgratitudetohiswife,Christine,whohasbeen
very patient during the long hours of preparing and writing this text.
Jiyuan Tu would like to acknowledge his wife, Xue, and his son, Tian, who gave their
boundless support to this project.
SpecialthanksaregiventoJonathanSimpson,wholedtheprojectintheinitialstages,andto
FionaGeraghty,whoguidedusfortherestoftheproject.Bothofthemhaveprovidedmuch
encouragement in the writing of this book. The authors are especially grateful to Elsevier
Science & Technology, and the Publisher, who have offered immense assistance both in
academic elucidation and professional skills in the publication process.
Tothosewehavefailedtomentionbuthavebeeninvolvedinonewayoranother,theauthors
extend our deepest heartfelt appreciation.
Guan Heng Yeoh
Chi Pok Cheung
Jiyuan Tu
xiii
Introduction
Multiphasesystemsdealingwithbubbles,drops, andparticlesarefrequentlyencounteredin
many natural, biological, and industrial systems. The principal objective of this book is to
provide applied scientists, practicing engineers, undergraduate and graduate students, and
researchers concerned with multiphase phenomena, with a comprehensive critical review of
the literature on particleeparticle and particleefluid interactions; a particle may be taken
more specifically to be in the form of a gas bubble, liquid drop, or solid particle. There are
importantsimilaritiesaswellassignificantdifferenceswhendealingwiththesethreetypesof
particle. Because of the parallel relevancies, this book aims to examine the different
treatments of gas bubbles, liquid drops, and solid particles in order to produce a unified text
on the subject.
Guan Heng Yeoh
Chi Pok Cheung
Jiyuan Tu
xv
CHAPTER 1
Introduction
1.1 Classification and Application of Multiphase Flows
Multiphaseflowscanbeviewedasafluidflowsystemcomprisingtwoormoredistinctphases
simultaneously co-flowing in a mixturewhere the level of separation between phases is at a
scale well above the molecular level. In principle, multiphase flows can be classified on the
basis of numberof phases, types of phases, size of phases and interaction between phases.
Dependingonthecombinationofdifferentphases,multiphaseflowscanbefurtherclassified
according to: dispersed phase flows, separated phase flows, gaseliquid flows, liquideliquid
flows, gaseparticle flows, liquideparticle flows, and three-phase flows.
Dispersedphaseflowscanbeconsideredasflowswherebyoneofthephasesexistsasdiscrete
particles.Twoclassicalexamplesarethemotionofbubblesinaliquidflowandthemotionof
liquid droplets in a gas. In such flows, there is no connection between these discrete fluid
particlesintheliquid.Itisthustakenasamixtureofdifferentsizedbubblesordropletsthat
are being dispersed in a continuous medium.
Separated phase flows are different from dispersed phase flows due to the prevalence of a
distinct line of contact separating two phases. One example is annular flow where there is a
liquidlayeralongthepipewallandagaseousinnercore.Categorically,onephaseinthistype
of flow is distinctly separated from another in the same medium.
Gaseliquid flows having one phase being in gaseous form and the other in liquid state can
assumemanyforms.Sincethegasphaseispermittedtofreelydeformwithintheliquidphase,
several different geometrical shapes are possible, which include spherical, elliptical,
distorted,toroidalandcap.Suchflowsalsooftenexhibitothercomplexinterfacialstructures,
namely, mixed or transitional flows that depict the transition between the dispersed phase
flows and separated phase flows. Change of interfacial structures occurs through the
occurrence of bubbleebubble or dropletedroplet interactions due to coalescence and break
up and the presence of any phase change process.
Liquideliquidflowsbelongtothespecialcategorywheretwoimmisciblefluidsareco-flowing
withinthemedium.Onetypicalexampleisthepresenceofoildropletsinwaterorviceversa.
Gaseparticleflowsareconcernedwiththemotionofsuspendedsolidparticlesinthegasphase.
Forsmallparticlenumberdensity,thegasflowexertsthemaineffectontheparticles.Dilute
gaseparticleflowsarepredominantlygovernedbythesurfaceandbodyforcesactingonthe
MultiphaseFlowAnalysisUsingPopulationBalanceModeling.
http://dx.doi.org/10.1016/B978-0-08-098229-8.00001-2
Copyright(cid:1)2014ElsevierLtd.Allrightsreserved. 1
2 Chapter 1
particles.Forverydilutegaseparticleflows,thesolidparticlesaretreatedaspassivetracers,
whichdonothaveaneffectonthegasflow.Forlargeparticlenumberdensity,particleeparticle
interactionsbecomemoreimportantthantheforcesduetointerstitialgas.Suchtwo-phaseflows
arereferredtoasdensegaseparticleflows.Collisionsinherentlyexistbetweenthesolid
particlesandsignificantlyinfluencetheirmovementandmigrationinthegasphase.For
substantiallybiggerparticles,suchflowsarecategoricallyknownasgranularflows.
Liquideparticle flows, in contrast to gaseparticles flows, consist of the transport of solid
particles in liquid flow instead. Here, the solid particles do not have a distinct velocity field
but generally follow the liquid velocity field. Also known as slurry flows, they fall into the
same category as dispersed phase flows in which the liquid now represents the continuous
medium. The different liquid and solid phases are mainly driven by, and largely respond to,
thepresenceofpressuregradientssincethedensityratiobetweenphasesislowandthedrag
between phases is generally rather high in such flows.
Three-phase flows are encountered in a number of engineering applications of technical
relevance,for example, bubbles in slurry flowsresulting in three phases co-flowing together
inthesamemedium.Inthisparticularcategory,solidparticlesandgasbubblesco-flowwith
the continuous liquid phase. The coexistence of three phases considerably complicates the
computational modeling of the flow physics due to the required understanding associated
with the phenomena of particleeparticle, bubbleebubble, particleebubble, particleefluid,
and bubbleefluid interactions.
Basedontheaboveclassifications,multiphaseflowsarealsowidelyfeaturedinmanydiverse
natural, biological, and industrial systems. Some examples of multiphase flows that can be
distinguished in these three different systems are illustrated in Table 1.1. It should be noted
that the list of examples presented in this table is by no means exhaustive but is intended to
providethereaderabroadoverviewoftherangeofapplicationsandtypesofmultiphaseflows
that can be found in these systems.
Multiphase flows are inherently complex. The physical understanding of flows where
more than one phase is involved offers problems of complexity that are immeasurably far
greater than in single-phase flows. This is because the phases do not, in general, uniformly
mix and because small-scale interactions between the phases can have profound effects on
the macroscopic properties of the fluid flow. This clearly reflects the ubiquitous challenges
that still exist when dealing with the complex nature of multiphase flows.
1.2 Complexity of Multiphase Flows
Dispersedflowsofgasbubbles,liquiddropsandsolidparticlesarecentralto theanalysisof
multiphaseflowsanddevelopmentofgenericcomputationalapproaches.Themotionofthese
Introduction 3
Table 1.1: Examples of multiphaseflows innatural,biological and industrialsystems.
Multiphaseflows
Gaseliquid Liquideliquid Gaseparticle Liquideparticle Three-phase
Natural Raindroplets, Oilewater Sandstorms, Sedimentation Oilewatere
oceanwaves,mist mixture,liquid volcanoes, ofsandinrivers sandmixture
formation bridges avalanches andsea,soil
erosion,mud
slides,debris
flows
Biological Aerosols Waterand Dustparticles, Nanoparticles Plasma,red
hydrophobic smoke(soot inbloodflow bloodcellsand
phases(lipids particles) leukocytesin
ormembranes) bloodflow
Industrial Boilingwaterand Emulsifiers, Pneumatic Slurry Airliftpumps,
pressurizedwater fuel-cell conveyers,dust transportation, airlift
nuclearreactors, systems, collectors, flotation, bio-reactors,
boilers, micro-channel fluidizedbeds, fluidizedbeds, fluidizedbeds
heatexchangers, applications pulverizedsolid waterjet
chemicalreactor particles,spray cutting,sewage
desalination drying treatment
systems plants
particles is strongly affected by the relative motion of the phases within the mixture. As the
relative motion becomes large enough, inertial instabilities can give rise to mesoscale
structures (Agrawal et al., 2001). The complex nature of such flows is manifested by the
appearance of clusters of bubbles, drops or particles (Serizawa, 2003).
In dispersed flows of bubbles or drops, the existence of dynamically changing interface can
causeindividualgasbubblesorliquiddropstodeform,coalescethroughthebreakingdownof
the interfaces between the phases to form larger bubbles or drops, and break up into two
smallerbubblesordropsduetotheshearingofthefluid.Asthevolumeflowofgasesordrops
increases,coalescencecausestheappearanceofcaplikegasbubblesorliquiddrops.Forsmall
diameter tubes, a pattern is exhibited whereby slugs of highly aerated liquid fill the whole
tube.Theseso-calledTaylorbubblesordropshavecharacteristicsofasphericalcapnoseand
are somewhat abruptly terminated at the bottom edge. With increasing volume fractions of
gases or drops, a churn pattern persists resulting in a haphazard flow of gaseliquid or
liquideliquidmixture.Incontrasttosmalldiametertubes,churnflowcanberatherdifferent
in large diameter pipes where Taylor bubbles are not formed. At very high velocities of the
dispersedphase,anannularpatternisobservedwherebypartoftheliquidflowsalongthewall
andtheremainderisthedispersedphase.Thecomplexityofflowregimetransitionsremains
an important problem whereby an improved physical understanding of one flow regime to
anotherisrequiredtoestablishasoundphysicaltheoryforthepredictionofthedifferentflow
patterns.
