Computational models for polydisperse particulate and multiphase systems

548 Pages·2013·3.063 MB·English

by  Daniele L Marchisio, Rodney O Fox

more information – www.cambridge.org/9780521858489

ComputationalModelsforPolydisperseParticulateand
MultiphaseSystems
Providing a clear description of the theory of polydisperse multiphase flows,
with emphasis on the mesoscale modeling approach and its relationship
with microscale and macroscale models, this all-inclusive introduction is
ideal, whether you are working in industry or academia. Theory is linked to
practice through discussions of key real-world cases (particle/droplet/bubble
coalescence, breakup, nucleation, advection and diffusion, and physical- and
phase-space), providing valuable experience in simulating systems that can
be applied to your own applications. Practical cases of QMOM, DQMOM,
CQMOM, EQMOM, and ECQMOM are also discussed and compared, as
arerealizablefinite-volumemethods.Thisprovidesthetoolsyouneedtouse
quadrature-based moment methods, choose from the many available options,
and design high-order numerical methods that guarantee realizable moment
sets. In addition to the numerous practical examples, Matlab scripts for sev-
eralalgorithmsarealsoprovided,soyoucanapplythemethodsdescribedto
practicalproblemsstraightaway.
Daniele L. Marchisio is an Associate Professor at the Politecnico di Torino,
Italy,wherehereceivedhisPh.D.in2001.Hehasheldvisitingpositionsatthe
LaboratoiredesSciencesduGe´nieChimique,CNRS–ENSIC(Nancy,France),
IowaStateUniversity(USA),Eidgeno¨ssische Technische Hochschule Zu¨rich
(Switzerland),andUniversityCollegeLondon(UK),andhasbeenaninvited
professor at Aalborg University (Denmark) and the University of Valladolid
(Spain). He acts as a referee for the key international journals in his field of
research.Hehasauthoredmorethan60scientificpapersand5bookchapters,
andco-editedthevolumeMultiphaseReactingFlows(Springer,2007).
Rodney O. Fox is the Anson Marston Distinguished Professor of Engineering
atIowaStateUniversity(USA),anAssociateScientistattheUS-DOEAmes
Laboratory,andaSeniorResearchFellowintheEM2ClaboratoryattheEcole
Centrale Paris (France). His numerous professional awards include an NSF
Presidential Young Investigator Award in 1992 and Fellow of the American
PhysicalSocietyin2007.TheimpactofFox’sworktoucheseverytechnologi-
calareadealingwithmultiphaseflowandchemicalreactions.Hismonograph
Computational Models for Turbulent Reacting Flows (Cambridge University
Press,2003)offersanauthoritativetreatmentofthefield.
CambridgeSeriesinChemicalEngineering
SeriesEditor
ArvindVarma,PurdueUniversity
EditorialBoard
ChristopherBowman,UniversityofColorado
EdwardCussler,UniversityofMinnesota
ChaitanKhosla,StanfordUniversity
AthanassiosZ.Panagiotopoulos,PrincetonUniversity
GregoryStephanopolous,MassachusettsInstituteofTechnology
JackieYing,InstituteofBioengineeringandNanotechnology,Singapore
BooksinSeries
BaldeaandDaoutidis,DynamicsandNonlinearControlofIntegratedProcessSystems
Chau,ProcessControl:AFirstCoursewithMATLAB
Cussler,Diffusion:MassTransferinFluidSystems,ThirdEdition
CusslerandMoggridge,ChemicalProductDesign,SecondEdition
Denn,ChemicalEngineering:AnIntroduction
Denn,PolymerMeltProcessing:FoundationsinFluidMechanicsandHeatTransfer
DuncanandReimer,ChemicalEngineeringDesignandAnalysis:AnIntroduction
FanandZhu,PrinciplesofGas–SolidFlows
Fox,ComputationalModelsforTurbulentReactingFlows
Leal,AdvancedTransportPhenomena:FluidMechanicsandConvectiveTransport
LimandShin,Fed-BatchCultures:Fundamentals,Modeling,Optimization,andControlof
Semi-BatchBioreactors
MarchisioandFox,ComputationalModelsforPolydisperseParticulateandMultiphaseSystems
MewisandWagner,ColloidalSuspensionRheology
Morbidelli,Gavriilidis,andVarma,CatalystDesign:OptimalDistributionofCatalystinPellets,
Reactors,andMembranes
NobleandTerry,PrinciplesofChemicalSeparationswithEnvironmentalApplications
OrbeyandSandler,ModelingVapor–LiquidEquilibria:CubicEquationsofStateandTheir
MixingRules
Petyluk,DistillationTheoryanditsApplicationstoOptimalDesignofSeparationUnits
RaoandNott,AnIntroductiontoGranularFlow
Russell,Robinson,andWagner,MassandHeatTransfer:AnalysisofMassContactorsandHeat
Exchangers
Schobert,ChemistryofFossilFuelsandBiofuels
Slattery,AdvancedTransportPhenomena
Varma,Morbidelli,andWu,ParametricSensitivityinChemicalSystems
Computational Models for
Polydisperse Particulate and
Multiphase Systems
DANIELE L. MARCHISIO
PolitecnicodiTorino
RODNEY O. FOX
IowaStateUniversity
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Computationalmodelsforpolydisperseparticulateandmultiphasesystems/DanieleL.
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pages cm.–(Cambridgeseriesinchemicalengineering)
ISBN978-0-521-85848-9
1. Multiphaseflow–Mathematicalmodels. 2. Chemicalreactions–Mathematicalmodels.
3. Transporttheory. 4. Dispersion–Mathematicalmodels. I. Fox,RodneyO.,1959–
II. Title.
TA357.5.M84M37 2013
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2012044073
ISBN978-0-521-85848-9Hardback
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Contents
Preface pagexiii
Notation xvii
1 Introduction 1
1.1 Dispersemultiphaseflows 1
1.2 Twoexamplesystems 3
1.2.1 Thepopulation-balanceequationforfineparticles 3
1.2.2 Thekineticequationforgas–particleflow 8
1.3 Themesoscalemodelingapproach 14
1.3.1 Relationtomicroscalemodels 16
1.3.2 Number-densityfunctions 18
1.3.3 Thekineticequationforthedispersephase 19
1.3.4 Closureatthemesoscalelevel 20
1.3.5 Relationtomacroscalemodels 20
1.4 Closuremethodsformoment-transportequations 23
1.4.1 Hydrodynamicmodels 23
1.4.2 Momentmethods 25
1.5 AroadmaptoChapters2–8 27
2 Mesoscaledescriptionofpolydispersesystems 30
2.1 Number-densityfunctions(NDF) 30
2.1.1 Length-basedNDF 32
2.1.2 Volume-basedNDF 33
2.1.3 Mass-basedNDF 33
2.1.4 Velocity-basedNDF 34
2.2 TheNDFtransportequation 35
2.2.1 Thepopulation-balanceequation(PBE) 35
2.2.2 Thegeneralizedpopulation-balanceequation(GPBE) 37
2.2.3 Theclosureproblem 37
2.3 Moment-transportequations 38
2.3.1 Moment-transportequationsforaPBE 38
2.3.2 Moment-transportequationsforaGPBE 40
2.4 FlowregimesforthePBE 43
2.4.1 LaminarPBE 43
2.4.2 TurbulentPBE 44
2.5 Themoment-closureproblem 45
vii
viii Contents
3 Quadrature-basedmomentmethods 47
3.1 Univariatedistributions 47
3.1.1 Gaussianquadrature 49
3.1.2 Theproduct–difference(PD)algorithm 51
3.1.3 TheWheeleralgorithm 53
3.1.4 Consistencyofamomentset 55
3.2 Multivariatedistributions 62
3.2.1 Brute-forceQMOM 63
3.2.2 Tensor-productQMOM 68
3.2.3 ConditionalQMOM 74
3.3 Theextendedquadraturemethodofmoments(EQMOM) 82
3.3.1 Relationshiptoorthogonalpolynomials 83
3.3.2 UnivariateEQMOM 84
3.3.3 EvaluationofintegralswiththeEQMOM 91
3.3.4 MultivariateEQMOM 93
3.4 Thedirectquadraturemethodofmoments(DQMOM) 99
4 Thegeneralizedpopulation-balanceequation 102
4.1 Particle-baseddefinitionoftheNDF 102
4.1.1 DefinitionoftheNDFforgranularsystems 102
4.1.2 NDFestimationmethods 105
4.1.3 DefinitionoftheNDFforfluid–particlesystems 107
4.2 Fromthemulti-particle–fluidjointPDFtotheGPBE 110
4.2.1 Thetransportequationforthemulti-particlejointPDF 111
4.2.2 Thetransportequationforthesingle-particlejointPDF 112
4.2.3 ThetransportequationfortheNDF 112
4.2.4 Theclosureproblem 113
4.3 Moment-transportequations 114
4.3.1 Afewwordsaboutphase-spaceintegration 114
4.3.2 Disperse-phasenumbertransport 116
4.3.3 Disperse-phasevolumetransport 116
4.3.4 Fluid-phasevolumetransport 117
4.3.5 Disperse-phasemasstransport 118
4.3.6 Fluid-phasemasstransport 121
4.3.7 Disperse-phasemomentumtransport 123
4.3.8 Fluid-phasemomentumtransport 124
4.3.9 Higher-ordermomenttransport 127
4.4 MomentclosuresfortheGPBE 130
5 Mesoscalemodelsforphysicalandchemicalprocesses 136
5.1 Anoverviewofmesoscalemodeling 136
5.1.1 MesoscalemodelsintheGPBE 137
5.1.2 Formulationofmesoscalemodels 141
5.1.3 Relationtomacroscalemodels 145
5.2 Phase-spaceadvection:massandheattransfer 147
5.2.1 Mesoscalevariablesforparticlesize 149
5.2.2 Sizechangeforcrystallineandamorphousparticles 152
5.2.3 Non-isothermalsystems 155
5.2.4 Masstransfertogasbubbles 156