Chapter 18. Introduction to Modeling Multiphase …

1 Chapter 18. Introduction to ModelingMultiphase FlowsA large number of flows encountered in nature and technology are a mix-ture of phases. Physical phases of matter are gas, liquid, and solid, butthe concept of phase in a Multiphase flow system is applied in a broadersense. In Multiphase flow, a phase can be de ned as an identi able classof material that has a particular inertial response to and interaction withthe flow and the potential eld in which it is immersed. For example,di erent-sized solid particles of the same material can be treated as dif-ferent phases because each collection of particles with the same size willhave a similar dynamical response to the flow Chapter provides an overview of Multiphase Modeling inFLUENT,and Chapters 19 and 20 provide details about the Multiphase modelsmentioned here. Chapter 21 provides information about melting andsolidi in this Chapter is presented in the following sections: Section : Multiphase Flow Regimes Section : Examples of Multiphase Systems Section : Approaches to Multiphase Modeling Section : Choosing a Multiphase Modelc Fluent Inc.

2 November 28, 200118-1 Introduction to Modeling Multiphase Multiphase Flow RegimesMultiphase flow can be classi ed by the following regimes, grouped intofour categories: gas-liquid or liquid-liquid flows{bubbly flow: discrete gaseous or fluid bubbles in a continuousfluid{droplet flow: discrete fluid droplets in a continuous gas{slug flow: large bubbles in a continuous fluid{strati ed/free-surface flow: immiscible fluids separated by aclearly-de ned interface gas-solid flows{particle-laden flow: discrete solid particles in a continuous gas{pneumatic transport: flow pattern depends on factors suchas solid loading, Reynolds numbers, and particle patterns are dune flow, slug flow, packed beds, andhomogeneous flow.{fluidized beds: consist of a vertical cylinder containing parti-cles where gas is introduced through a distributor. The gasrising through the bed suspends the particles.}}}}}}}

3 Depending onthe gas flow rate, bubbles appear and rise through the bed,intensifying the mixing within the bed. liquid-solid flows{slurry flow: transport of particles in liquids. The fundamentalbehavior of liquid-solid flows varies with the properties of thesolid particles relative to those of the liquid. In slurry flows,the Stokes number (see Equation ) is normally less than1. When the Stokes number is larger than 1, the characteristicof the flow is liquid-solid fluidization.{hydrotransport: densely-distributed solid particles in a con-tinuous liquid18-2c Fluent Inc. November 28, Examples of Multiphase Systems{sedimentation: a tall column initially containing a uniformdispersed mixture of particles. At the bottom, the particleswill slow down and form a sludge layer. At the top, a clearinterface will appear, and in the middle a constant settlingzone will exist. three-phase flows (combinations of the others listed above)Each of these flow regimes is illustrated in Figure Examples of Multiphase SystemsSpeci c examples of each regime described in Section are listedbelow: Bubbly flow examples: absorbers, aeration, air lift pumps, cavita-tion, evaporators, flotation, scrubbers Droplet flow examples: absorbers, atomizers, combustors, cryo-genic pumping, dryers, evaporation, gas cooling, scrubbers Slug flow examples: large bubble motion in pipes or tanks Strati ed/free-surface flow examples: sloshing in o shore separatordevices, boiling and condensation in nuclear reactors Particle-laden flow examples: cyclone separators, air classi ers,dust collectors, and dust-laden environmental flows Pneumatic transport examples: transport of cement, grains, andmetal powders Fluidized bed examples.}}}

4 Fluidized bed reactors, circulating flu-idized beds Slurry flow examples: slurry transport, mineral processing Hydrotransport examples: mineral processing, biomedical and phys-iochemical fluid systems Sedimentation examples: mineral processingc Fluent Inc. November 28, 200118-3 Introduction to Modeling Multiphase Flowsslug flowbubbly, droplet, orparticle-laden flowstratified/free-surface flowpneumatic transport, hydrotransport, or slurry flowsedimentationfluidized bedFigure : Multiphase Flow Regimes18-4c Fluent Inc. November 28, Approaches to Multiphase Approaches to Multiphase ModelingAdvances in computational fluid mechanics have provided the basis forfurther insight into the dynamics of Multiphase flows. Currently thereare two approaches for the numerical calculation of Multiphase flows: theEuler-Lagrange approach and the Euler-Euler The Euler-Lagrange ApproachThe Lagrangian discrete phase model inFLUENT(described in Chap-ter 19) follows the Euler-Lagrange approach.

5 The fluid phase is treatedas a continuum by solving the time-averaged Navier-Stokes equations,while the dispersed phase is solved by tracking a large number of parti-cles, bubbles, or droplets through the calculated flow eld. The dispersedphase can exchange momentum, mass, and energy with the fluid fundamental assumption made in this model is that the dispersed sec-ond phase occupies a low volume fraction, even though high mass loading(_mparticles _mfluid) is acceptable. The particle or droplet trajectories arecomputed individually at speci ed intervals during the fluid phase cal-culation. This makes the model appropriate for the Modeling of spraydryers, coal and liquid fuel combustion, and some particle-laden flows,but inappropriate for the Modeling of liquid-liquid mixtures, fluidizedbeds, or any application where the volume fraction of the second phaseis not The Euler-Euler ApproachIn the Euler-Euler approach, the di erent phases are treated mathemat-ically as interpenetrating continua.

6 Since the volume of a phase cannotbe occupied by the other phases, the concept of phasic volume fractionis introduced. These volume fractions are assumed to be continuousfunctions of space and time and their sum is equal to one. Conserva-tion equations for each phase are derived to obtain a set of equations,which have similar structure for all phases. These equations are closedby providing constitutive relations that are obtained from empirical in-formation, or, in the case of granular flows, by application of Fluent Inc. November 28, 200118-5 Introduction to Modeling Multiphase FlowsInFLUENT, three di erent Euler-Euler Multiphase models are available:the volume of fluid (VOF) model, the mixture model, and the VOF ModelThe VOF model (described in Section ) is a surface-tracking tech-nique applied to a xed Eulerian mesh. It is designed for two or moreimmiscible fluids where the position of the interface between the fluidsis of interest.

7 In the VOF model, a single set of momentum equations isshared by the fluids, and the volume fraction of each of the fluids in eachcomputational cell is tracked throughout the domain. Applications ofthe VOF model include strati ed flows, free-surface flows, lling, slosh-ing, the motion of large bubbles in a liquid, the motion of liquid aftera dam break, the prediction of jet breakup (surface tension), and thesteady or transient tracking of any liquid-gas Mixture ModelThe mixture model (described in Section ) is designed for two ormore phases (fluid or particulate). As in the Eulerian model, the phasesare treated as interpenetrating continua. The mixture model solves forthe mixture momentum equation and prescribes relative velocities todescribe the dispersed phases. Applications of the mixture model includeparticle-laden flows with low loading, bubbly flows, sedimentation, andcyclone separators.

8 The mixture model can also be used without relativevelocities for the dispersed phases to model homogeneous Eulerian ModelThe Eulerian model (described in Section ) is the most complex ofthe Multiphase models andcontinuity equations for each phase. Coupling is achieved through thepressure and interphase exchange coe cients. The manner in which thiscoupling is handled depends upon the type of phases involved; granular(fluid-solid) flows are handled di erently than non-granular (fluid-fluid)flows. For granular flows, the properties are obtained from application of18-6c Fluent Inc. November 28, Choosing a Multiphase Modelkinetic theory. Momentum exchange between the phases is also depen-dent upon the type of mixture being 's user-de nedfunctions allow you to customize the calculation of the momentum ex-change. Applications of the Eulerian Multiphase model include bubblecolumns, risers, particle suspension, and fluidized Choosing a Multiphase ModelThe rst step in solving any Multiphase problem is to determine whichof the regimes described in Section best represents your flow.

9 Sec-tion provides some broad guidelines for determining appropriatemodels for each regime, and Section provides details about how todetermine the degree of interphase coupling for flows involving bubbles,droplets, or particles, and the appropriate model for di erent amountsof General GuidelinesIn general, once you have determined the flow regime that best representsyour Multiphase system, you can select the appropriate model based onthe following guidelines. Additional details and guidelines for selectingthe appropriate model for flows involving bubbles, droplets, or particlescan be found in Section For bubbly, droplet, and particle-laden flows in which the dispersed-phase volume fractions are less than or equal to 10%, use the dis-crete phase model. See Chapter 19 for more information about thediscrete phase model. For bubbly, droplet, and particle-laden flows in which the phasesmix and/or dispersed-phase volume fractions exceed 10%, use ei-ther the mixture model (described in Section ) or the Eulerianmodel (described in Section ).

10 See Sections and fordetails about how to determine which is more appropriate for yourcase. For slug flows, use the VOF model. See Section for moreinformation about the VOF Fluent Inc. November 28, 200118-7 Introduction to Modeling Multiphase Flows For strati ed/free-surface flows, use the VOF model. See Sec-tion for more information about the VOF model. For pneumatic transport, use the mixture model for homogeneousflow (described in Section ) or the Eulerian model for granularflow (described in Section ). See Sections and fordetails about how to determine which is more appropriate for yourcase. For fluidized beds, use the Eulerian model for granular flow. SeeSection for more information about the Eulerian model. For slurry flows and hydrotransport, use the mixture or Eulerianmodel (described, respectively, in Sections and ). SeeSections and for details about how to determine whichis more appropriate for your case.