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Theory and Modeling of Dispersed Multiphase Turbulent Reacting Flows Theory and Modeling of Dispersed Multiphase Turbulent Reacting Flows Lixing Zhou TsinghuaUniversity, Beijing, China Butterworth-HeinemannisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyrightr2018ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without permissioninwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthe Publisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearance CenterandtheCopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher (otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingand usinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationor methodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomthey haveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliability foranyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,or fromanyuseoroperationofanymethods,products,instructions,orideascontainedinthematerialherein. BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress ISBN:978-0-12-813465-8 ForInformationonallButterworth-Heinemannpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionEditor:GlynJones EditorialProjectManager:NaomiRobertson ProductionProjectManager:VijayarajPurushothaman CoverDesigner:MilesHitchen TypesetbyMPSLimited,Chennai,India Preface Multiphase, turbulent, and reacting flows are widely encountered in engineering and the natural environment. The basic theory, phenomena, mathe- matical models, numerical simulations, and applications of multiphase (gas or liquid flows with particles/droplets or bubbles), turbulent reacting flows are presented in this book. The special feature of this book is in combining the multiphase fluid dynamics with the turbulence modeling theory and reacting fluid dynamics (combustion theory). There are nine chapters in this book, namely: “Fundamentals of Dispersed Multiphase Flows”; “Basic Concepts and Description of Turbulence”; “Fundamentals of Combustion Theory”; “Basic Equations of Multiphase Turbulent Reacting Flows”; “Modeling of Single-Phase Turbulent Flows”; “Modeling of Dispersed Multiphase Turbulent Flows”; “Modeling of Turbulent Combustion”; “The Solution Procedure for Modeling Multiphase Turbulent Reacting Flows”; and “Simulation of Flows and Combustion in Practical Fluid Machines, Combustors and Furnaces.” The main difference between this book and pre- vious books written by the author is that more much better descriptions of basic equations and closure models of multiphase turbulent reacting flows are introduced, and recent advances made by the author and other investiga- torsbetween 1994 and2016 are included. This book serves as a reference book for teaching, research, and engineering design for faculty members, students, and research engineers in the fields of fluid dynamics, thermal science and engineering, aeronautical, astronautical, chemical, metallurgical, petroleum, nuclear, and hydraulic engineering. The author wishes to thank Prof. F.G. Zhuang, H.X. Zhang, and C.K. Wu for their valuable comments and suggestions. Thanks also go to colleagues and former students: Prof. W.Y. Lin, R.X. Li, X.L. Wang, J. Zhang, B. Zhou, Y.C. Guo, H.Q. Zhang, L.Y. Hu, Y. Yu, F. Wang, Z.X. Zeng, K. Li, Y. Zhang; Drs. Gene X.Q. Huang, T. Hong, C.M. Liao, W.W. Luo, K.M. Sun, Y. Li, T. Chen, Y. Xu, G. Luo, M. Yang, L. Li, H.X. Gu, X.L. Chen, X.Zhang,andY.Liu.Theirresearch resultsunderthedirectionandcoopera- tion of the author contributed tothe context ofthis book. xi xii Preface Finally, the author’s gratitude is given to the editors from Elsevier and the Executive Editor, Dr. Qiang Li from the Tsinghua University Press for their hard work inthe final editing and publishing ofthis book. Any comments and suggestions from the experts and readers would be highly appreciated. LixingZhou TsinghuaUniversity,Beijing,China February,2017 Nomenclature A area B preexponentialfactor c empirialconstants,specificheat c dragcoefficient d d diameter D diffusivity E activationenergy e internalenergy F force f mixturefraction G productionterm g gravitationalacceleration;meansquirevalueofconcentrationfluctuation H stagnationenthalpy h enthalpy J diffusionfux k turbulentkineticenergy;reaction-ratecoefficient l turbulentscale;length M molecularweight m mass N totalparticlenumberflux;particlenumberdensity n fluctuationofparticlenumberdensity;exponentinparticle-sizedistribution function;reactionorder;molenumberdensity Nu Nusseltnumber p pressure;probabilitydensitydistributionfunction Pr Prandtlnumber Q heat;heatingeffect q heatflux R universalgasconstant;weightfractioninparticle-sizedistribution r radius;radialcoordinate Re Reynoldsnumber R fluxRichardsonnumber f S sourceterm Sc Schmidtnumber Sh Sherwoodnumber T temperature t time u,v,w velocitycomponents V volume;driftvelocity xiii xiv Nomenclature w reactionrate x,y,z coordinates X combinedmassfraction;molefraction Y massfraction GREEK ALPHABETS α volumefraction μ dynamicviscosity ν kinematicviscosity λ heatconductivity ε dissipationrateofturbulentkineticenergy;emissivity φ generalizeddependentvariable θ dimensionlesstemperature τ shearstress σ Stefan-Boltzmannconstant;generalizedPrandtlnumber SUBSCRIPTS A,a air c rawcoal,reaction ch reaction;char d diffusion e effective;exit F,fu fuel f flame;fluid g gas h char;heterogeneous hr heterogeneous i,in initial;inlet i,j,k coordinatedirections k k-thparticlegroup l liquid m mixture Introduction Dispersed multiphase turbulent reacting flows are widely encountered in thermal, aeronautical, astronautical, nuclear, chemical, metallurgical, petroleum, and hydraulic engineering, and in water and atmosphere environments. As early as the 1950s, Von Karman and H.S. Tsien suggested using continuum mechanics to study laminar gas reacting flows and combustion, called “aerothermochemistry” or “dynamics of chemically reacting fluids.” Multiphase fluid dynamics was first proposed by S.L. Soo in the 1960s for studying nonreacting multiphase flows. The classical reacting fluid dynamics and multiphase fluid dynamics do not include the theory of turbulence modeling. On the other hand, the theory of turbulence modeling was first proposed by P.Y. Chou in the 1950s, and was fully realized by B.E. Launder and D.B. Spalding in the 1970s. Within the last 40 years, through worldwide study and application, it has become the only reasonable and economical method to solve complex turbulent flows in engineering problems. However, up until the 1980s, the theory of turbulence modeling was limited to only single-phasefluidflows themselves, anddidnotconcernthe dispersedphase, i.e., particles/droplets/bubbles inmultiphase flows. Since the 1980s, the author has combined multiphase fluid dynamics with the theory of turbulence modeling, and proposed the concept of multiphase (two-phase) turbulence models, in particular the turbulence models of the dispersed phase, i.e., particles/droplets/bubbles. Furthermore, we developed the turbulence-chemistry models for single-phase and two-phase combustion using a method similar to turbulence modeling. Hence, the dynamics of multiphase turbulent reacting flows was developed, where the modeling theory, numerical simulation, measurements, and their application in combustion systems were systematically studied. The comprehensive models, basic con- servation equations, the relationships between slip and diffusion, the energy distribution between the continuum and dispersed phases, the fluid-particle/ droplet/bubble turbulence interactions, the interactions between particle turbulence and particle reaction, the gas-phase turbulence-chemistry interaction, and the particle(cid:1)wall interaction were thoroughly studied. A series of new closure models were proposed, many 2-D and 3-D computer codes were developed based on the proposed models and some of the simulation results xv xvi Introduction were validated using the laser Doppler velocimeter (LDV), phase Doppler particle anemometer (PDPA), and particle imaging velocimeter (PIV) measurements and direct numerical simulation (DNS). The research results were applied to develop innovative swirl combustors, cement kilns, oil(cid:1)water hydrocyclones, gas(cid:1)solid cyclone separators, and innovative cyclone coal combustors. This book is written based on the research results of the author, aswellasthoseobtainedbyotherinvestigatorsinrecentyears.Inthefollow- ing sections some basic definitions and descriptionsare discussed. TURBULENT DISPERSED MULTIPHASE FLOWS Gas/liquid flows containing a vast amount of particles/droplets/bubbles are called dispersed multiphase flows. This terminology is widely accepted by the academic and engineering communities in the fields of fluid dynamics, thermal science and engineering, aeronautical, astronautical, metallurgical, chemical, petroleum, nuclear, and hydraulic engineering. Frequently, the concept of “phase” is considered as a thermodynamic state, so multiphase flows are divided into gas(cid:1)solid (gas(cid:1)particle), liquid(cid:1)solid (liquid(cid:1)particle), gas(cid:1)liquid (gas(cid:1)spray or bubble(cid:1)liquid), liquid(cid:1)liquid (oil(cid:1)water) two-phase flows and gas(cid:1)solid(cid:1)liquid, oil(cid:1)water(cid:1)gas three-phase flows. Also, sometimes the terminologies “suspension flows” and “dispersed flows” are adopted. Besides, there are nondispersed two-phase flows, such as stratified and annular gas(cid:1)liquid flows. However, from the multiphase fluid dynamic point of view, in particular in multifluid models, particles/droplets/bubbles with differentsizes,velocities,andtemperaturesmayconstitutedifferentphases.This is the reason why the terminology “multiphase fluid dynamics” was first proposed by S.L. Soo in the 1960s. In short, although different academic and engineering communities have different understanding of the above-listed terminologies, nowadays “multiphase flow” as a general concept of a branch of scienceandtechnologyiswidelyacceptedwithoutdisagreement. Most practical fluid flows, maybe more than 99% of flows in the natural environment and engineering, are laden with particles, droplets, or gas bubbles.Puresingle-phaseflowsexist onlyinafewcases such asflowsinartifi- cial ultraclean environment. There are a variety of multiphase flows, such as cosmic dust in cosmic space, cloud and fog (rain droplets), dusty-air flow, sandyrivers,blood flowsinbiologicalbodies,pneumatic/hydraulicconveying, dust separation and collection, spray coating, drying and cooling, spray/ pulverized-coal combustion, plasma chemistry, fluidized bed, flows in gun barrels, solid-rocket exhaust, steam-droplet flows in turbines and gas-fiber flows, steam-water flows in boilers and nuclear reactors, oil(cid:1)water and gas(cid:1)oil(cid:1)water flows in petroleum pipes, and gas(cid:1)liquid(cid:1)solid flows in steel making furnaces. Most fluid flows in engineering facilities, such as flows in hydraulic channels, gas pipes, heat exchangers, fluid machines, chemical reactors,