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Chapter 20. General MultiphaseModelsThis chapter discusses the general multiphase models that are availablein FLUENT. Chapter 18 provides a brief introduction to multiphase mod-eling, Chapter 19 discusses the Lagrangian dispersed phase model, andChapter 21 describes FLUENTs model for solidication and melting. Section 20.1: Choosing a General Multiphase Model Section 20.2: Volume of Fluid (VOF) Model Section 20.3: Mixture Model Section 20.4: Eulerian Model Section 20.5: Cavitation Eects Section 20.6: Setting Up a General Multiphase Problem Section 20.7: Solution Strategies for General Multiphase Problems Section 20.8: Postprocessing for General Multiphase Problems20.1 Choosing a General Multiphase ModelAs discussed in Section 18.4, the VOF model is appropriate for stratiedor free-surface ows, and the mixture and Eulerian models are appropri-ate for ows in which the phases mix or separate and/or dispersed-phasevolume fractions exceed 10%. (Flows in which the dispersed-phase vol-ume fractions are less than or equal to 10% can be modeled using thediscrete phase model described in Chapter 19.)To choose between the mixture model and the Eulerian model, youshould consider the following, in addition to the detailed guidelines inSection 18.4:c Fluent Inc. November 28, 2001 20-1General Multiphase Models If there is a wide distribution of the dispersed phases, the mixturemodel may be preferable. If the dispersed phases are concentratedjust in portions of the domain, you should use the Eulerian modelinstead. If interphase drag laws that are applicable to your system areavailable (either within FLUENT or through a user-dened func-tion), the Eulerian model can usually provide more accurate resultsthan the mixture model. If the interphase drag laws are unknownor their applicability to your system is questionable, the mixturemodel may be a better choice. If you want to solve a simpler problem, which requires less com-putational eort, the mixture model may be a better option, sinceit solves a smaller number of equations than the Eulerian model.If accuracy is more important than computational eort, the Eu-lerian model is a better choice. Keep in mind, however, that thecomplexity of the Eulerian model can make it less computationallystable than the mixture model.Brief overviews of the three models, including their limitations, are pro-vided in Sections 20.1.1, 20.1.2, and 20.1.3. Detailed descriptions of themodels are provided in Sections 20.2, 20.3, and 20.4.20.1.1 Overview and Limitations of the VOF ModelOverviewThe VOF model can model two or more immiscible uids by solving asingle set of momentum equations and tracking the volume fraction ofeach of the uids throughout the domain. Typical applications includethe prediction of jet breakup, the motion of large bubbles in a liquid, themotion of liquid after a dam break, and the steady or transient trackingof any liquid-gas interface.LimitationsThe following restrictions apply to the VOF model in FLUENT:20-2 c Fluent Inc. November 28, 200120.1 Choosing a General Multiphase Model You must use the segregated solver. The VOF model is not avail-able with either of the coupled solvers. All control volumes must be lled with either a single uid phaseor a combination of phases; the VOF model does not allow for voidregions where no uid of any type is present. Only one of the phases can be compressible. Streamwise periodic ow (either specied mass ow rate or spec-ied pressure drop) cannot be modeled when the VOF model isused. Species mixing and reacting ow cannot be modeled when the VOFmodel is used. The LES turbulence model cannot be used with the VOF model. The second-order implicit time-stepping formulation cannot be usedwith the VOF model. The VOF model cannot be used for inviscid ows. The shell conduction model for walls cannot be used with the VOFmodel.Steady -State and Transient VOF CalculationsThe VOF formulation in FLUENT is generally used to compute a time-dependent solution, but for problems in which you are concerned onlywith a steady-state solution, it is possible to perform a steady-state cal-culation. A steady-state VOF calculation is sensible only when yoursolution is independent of the initial conditions and there are distinct in-ow boundaries for the individual phases. For example, since the shapeof the free surface inside a rotating cup depends on the initial level of theuid, such a problem must be solved using the time-dependent formula-tion. On the other hand, the ow of water in a channel with a region ofair on top and a separate air inlet can be solved with the steady-stateformulation.c Fluent Inc. November 28, 2001 20-3General Multiphase Models20.1.2 Overview and Limitations of the Mixture ModelOverviewThe mixture model is a simplied multiphase model that can be used tomodel multiphase ows where the phases move at dierent velocities, butassume local equilibrium over short spatial length scales. The couplingbetween the phases should be strong. It can also be used to modelhomogeneous multiphase ows with very strong coupling and the phasesmoving at the same velocity.The mixture model can model n phases (uid or particulate) by solv-ing the momentum, continuity, and energy equations for the mixture,the volume fraction equations for the secondary phases, and algebraicexpressions for the relative velocities. Typical applications include sedi-mentation, cyclone separators, particle-laden ows with low loading, andbubbly ows where the gas volume fraction remains low.The mixture model is a good substitute for the full Eulerian multiphasemodel in several cases. A full multiphase model may not be feasiblewhen there is a wide distribution of the particulate phase or when theinterphase laws are unknown or their reliability can be questioned. Asimpler model like the mixture model can perform as well as a full mul-tiphase model while solving a smaller number of variables than the fullmultiphase model.LimitationsThe following limitations apply to the mixture model in FLUENT: You must use the segregated solver. The mixture model is notavailable with either of the coupled solvers. Only one of the phases can be compressible. Streamwise periodic ow (either specied mass ow rate or speci-ed pressure drop) cannot be modeled when the mixture model isused.20-4 c Fluent Inc. November 28, 200120.1 Choosing a General Multiphase Model Species mixing and reacting ow cannot be modeled when the mix-ture model is used. Solidication and melting cannot be modeled in conjunction withthe mixture model. The LES turbulence model cannot be used with the mixture model. The second-order implicit time-stepping formulation cannot be usedwith the mixture model. The mixture model cannot be used for inviscid ows. The shell conduction model for walls cannot be used with the mix-ture model.20.1.3 Overview and Limitations of the Eulerian ModelOverviewThe Eulerian multiphase model in FLUENT allows for the modeling ofmultiple separate, yet interacting phases. The phases can be liquids,gases, or solids in nearly any combination. An Eulerian treatment isused for each phase, in contrast to the Eulerian-Lagrangian treatmentthat is used for the discrete phase model.With the Eulerian multiphase model, the number of secondary phasesis limited only by memory requirements and convergence behavior. Anynumber of secondary phases can be modeled, provided that sucientmemory is available. For complex multiphase ows, however, you maynd that your solution is limited by convergence behavior. See Sec-tion 20.7.3 for multiphase modeling strategies.FLUENTs Eulerian multiphase model diers from the Eulerian model inFLUENT 4 in that there is no global distinction between uid-uid anduid-solid (granular) multiphase ows. A granular ow is simply onethat involves at least one phase that has been designated as a granularphase.The FLUENT solution is based on the following:c Fluent Inc. November 28, 2001 20-5General Multiphase Models A single pressure is shared by all phases. Momentum and continuity equations are solved for each phase. The following parameters are available for granular phases: Granular temperature (solids uctuating energy) can be cal-culated for each solid phase. This is based on an algebraicrelation. Solid-phase shear and bulk viscosities are obtained from appli-cation of kinetic theory to granular ows. Frictional viscosityis also available. Several interphase drag coecient functions are available, whichare appropriate for various types of multiphase regimes. (You canalso modify the interphase drag coecient through user-denedfunctions, as described in the separate UDF Manual.) All of the k- turbulence models are available, and may apply toall phases or to the mixture.LimitationsAll other features available in FLUENT can be used in conjunction withthe Eulerian multiphase model, except for the following limitations: Only the k- models can be used for turbulence. Particle tracking (using the Lagrangian dispersed phase model)interacts only with the primary phase. Streamwise periodic ow (either specied mass ow rate or speci-ed pressure drop) cannot be modeled when the Eulerian model isused. Compressible ow is not allowed. Inviscid ow is not allowed. The second-order implicit time-stepping formulation cannot be usedwith the Eulerian model.20-6 c Fluent Inc. November 28, 200120.1 Choosing a General Multiphase Model M

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