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The FLUENT User's Guide tells you what you need to know to use FLUENT. At the end of the User's Guide, you will find a Reference Guide, a nomenclature list, a bibliography, and an index. !! Under U.S. and international copyright law, Fluent is unable to distribute copies of the papers listed in the bibliography, other than those published internally by Fluent. Please use your library or a document delivery service to obtain copies of copyrighted papers. A brief description of what's in each chapter follows: ? Chapter 1, Getting Started, describes the capabilities of FLUENT and the way in which it interacts with other Fluent Inc. and third-party programs. It also advises you on how to choose the appropriate solver formulation for your application, gives an overview of the problem setup steps, and presents a sample session that you can work through at your own pace. Finally, this chapter provides information about accessing the FLUENT manuals on CD-ROM or in the installation area. ? Chapter 2, User Interface, describes the mechanics of using the graphical user interface, the text interface, and the on-line help. It also provides instructions for remote and batch execution. (See the separate Text Command List for information about specific text interface commands.) ? Chapter 3, Reading and Writing Files, contains information about the files that FLUENT can read and write, including hardcopy files. ? Chapter 4, Unit Systems, describes how to use the standard and custom unit systems available in FLUENT. ? Chapter 5, Reading and Manipulating Grids, describes the various sources of computational grids and explains how to obtain diagnostic information about the grid and how to modify it by scaling, translating, and other methods. This chapter also contains information about the use of non-conformal grids. ? Chapter 6, Boundary Conditions, explains the different types of boundary conditions available in FLUENT, when to use them, how to define them, and how to define boundary profiles and volumetric sources and fix the value of a variable in a particular region. It also contains information about porous media and lumped parameter models. ? Chapter 7, Physical Properties, explains how to define the physical properties of materials and the equations that FLUENT uses to compute the properties from the information that you input. ? Chapter 8, Modeling Basic Fluid Flow, describes the governing equations and physical models used by FLUENT to compute fluid flow (including periodic flow, swirling and rotating flows, compressible flows, and inviscid flows), as well as the inputs you need to provide to use these models. ? Chapter 9, Modeling Flows in Moving Zones, describes the use of single rotating reference frames, multiple moving reference frames, mixing planes, and sliding meshes inFLUENT. ? Chapter 10, Modeling Turbulence, describes FLUENT's models for turbulent flow and when and how to use them. ? Chapter 11, Modeling Heat Transfer, describes the physical models used by FLUENT to compute heat transfer (including convective and conductive heat transfer, natural convection, radiative heat transfer, and periodic heat transfer), as well as the inputs you need to provide to use these models. ? Chapter 12, Introduction to Modeling Species Transport and Reacting Flows, provides an overview of the models available in FLUENT for species transport and reactions, as well as guidelines for selecting an appropriate model for your application. ? Chapter 13, Modeling Species Transport and Finite-Rate Chemistry, describes the finite-rate chemistry models in FLUENT and how to use them. This chapter also provides information about modeling species transport in non-reacting flows. ? Chapter 14, Modeling Non-Premixed Combustion, describes the non-premixed combustion model and how to use it. This chapter includes details about using prePDF.

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Chapter 15, Modeling Premixed Combustion, describes the premixed combustion model and how to use it. Chapter 16, Modeling Partially Premixed Combustion, describes the partially premixed combustion model and how to use it. Chapter 17, Modeling Pollutant Formation, describes the models for the formation of NOx and soot and how to use them. Chapter 18, Introduction to Modeling Multiphase Flows, provides an overview of the models for multiphase flow (including the discrete phase, VOF, mixture, and Eulerian models), as well as guidelines for selecting an appropriate model for your application. Chapter 19, Discrete Phase Models, describes the discrete phase models available in FLUENT and how to use them. Chapter 20, General Multiphase Models, describes the general multiphase models available in FLUENT (VOF, mixture, and Eulerian) and how to use them. Chapter 21, Modeling Solidification and Melting, describes FLUENT's model for solidification and melting and how to use it. Chapter 22, Using the Solver, describes the FLUENT solvers and how to use them. Chapter 23, Grid Adaption, explains the solution-adaptive mesh refinement feature in FLUENT and how to use it. Chapter 24, Creating Surfaces for Displaying and Reporting Data, explains how to create surfaces in the domain on which you can examine FLUENT solution data. Chapter 25, Graphics and Visualization, describes the graphics tools that you can use to examine your FLUENT solution. Chapter 26, Alphanumeric Reporting, describes how to obtain reports of fluxes, forces, surface integrals, and other solution data. Chapter 27, Field Function Definitions, defines the flow variables that appear in the variable selection drop-down lists in FLUENT panels, and tells you how to create your own custom field functions. Chapter 28, Parallel Processing, explains the parallel processing features in FLUENT and how to use them. This chapter also provides information about partitioning your grid for parallel processing.

18. Introduction to Modeling Multiphase Flows A large number of flows encountered in nature and technology are a mixture of phases. Physical phases of matter are gas, liquid, and solid, but the concept of phase in a multiphase flow system is applied in a broader sense. In multiphase flow, a phase can be defined as an identifiable class of material that has a particular inertial response to and interaction with the flow and the potential field in which it is immersed. For example, different-sized solid particles of the same material can be treated as different phases because each collection of particles with the same size will have a similar dynamical response to the flow field. This chapter provides an overview of multiphase modeling in FLUENT, and Chapters 19 and 20 provide details about the multiphase models mentioned here. Chapter 21 provides information about melting and solidification. 18.1 Multiphase Flow Regimes Multiphase flow can be classified by the following regimes, grouped into four categories: gas-liquid or liquid-liquid flows bubbly flow: discrete gaseous or fluid bubbles in a continuous fluid droplet flow: discrete fluid droplets in a continuous gas slug flow: large bubbles in a continuous fluid stratified/free-surface flow: immiscible fluids separated by a clearly-defined interface gas-solid flows particle-laden flow: discrete solid particles in a continuous gas pneumatic transport: flow pattern depends on factors such as solid loading, Reynolds numbers, and particle properties. Typical patterns are dune flow, slug flow, packed beds, and homogeneous flow. fluidized beds: consist of a vertical cylinder containing particles where gas is introduced through a distributor. The gas rising through the bed suspends the particles. Depending on the 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 fundamental behavior of liquid-solid flows varies with the properties of the solid particles relative to those of the liquid. In slurry flows, the Stokes number (see Equation 18.4-4) is normally less than 1. When the Stokes number is larger than 1, the characteristic of the flow is liquid-solid fluidization. hydrotransport: densely-distributed solid particles in a continuous liquid sedimentation: a tall column initially containing a uniform dispersed mixture of particles. At the bottom, the particles will slow down and form a sludge layer. At the top, a clear interface will appear, and in the middle a constant settling zone will exist. three-phase flows (combinations of the others listed above) Each of these flow regimes is illustrated in Figure 18.1.1.

Figure 18.1.1: Multiphase Flow Regimes 18.2 Examples of Multiphase Systems Specific examples of each regime described in Section 18.1 are listed below: Bubbly flow examples: absorbers, aeration, air lift pumps, cavitation, evaporators, flotation, scrubbers Droplet flow examples: absorbers, atomizers, combustors, cryogenic pumping, dryers, evaporation, gas cooling, scrubbers Slug flow examples: large bubble motion in pipes or tanks Stratified/free-surface flow examples: sloshing in offshore separator devices, boiling and condensation in nuclear reactors Particle-laden flow examples: cyclone separators, air classifiers, dust collectors, and dust-laden environmental flows Pneumatic transport examples: transport of cement, grains, and metal powders Fluidized bed examples: fluidized bed reactors, circulating fluidized beds Slurry flow examples: slurry transport, mineral processing Hydrotransport examples: mineral processing, biomedical and physiochemical fluid systems Sedimentation examples: mineral processing 18.3 Approaches to Multiphase Modeling

Advances in computational fluid mechanics have provided the basis for further insight into the dynamics of multiphase flows. Currently there are two approaches for the numerical calculation of multiphase flows: the Euler-Lagrange approach and the Euler-Euler approach. 18.3.1 The Euler-Lagrange Approach The Lagrangian discrete phase model in FLUENT (described in Chapter 19) follows the Euler-Lagrange approach. The fluid phase is treated as a continuum by solving the time-averaged Navier-Stokes equations, while the dispersed phase is solved by tracking a large number of particles, bubbles, or droplets through the calculated flow field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase. A fundamental assumption made in this model is that the dispersed second phase occupies a low volume fraction, even though high mass loading ( ) is acceptable. The particle or droplet trajectories are computed individually at specified intervals during the fluid phase calculation. This makes the model appropriate for the modeling of spray dryers, coal and liquid fuel combustion, and some particle-laden flows, but inappropriate for the modeling of liquid-liquid mixtures, fluidized beds, or any application where the volume fraction of the second phase is not negligible. 18.3.2 The Euler-Euler Approach In the Euler-Euler approach, the different phases are treated mathematically as interpenetrating continua. Since the volume of a phase cannot be occupied by the other phases, the concept of phasic volume fraction is introduced. These volume fractions are assumed to be continuous functions of space and time and their sum is equal to one. Conservation equations for each phase are derived to obtain a set of equations, which have similar structure for all phases. These equations are closed by providing constitutive relations that are obtained from empirical information, or, in the case of granular flows , by application of kinetic theory. In FLUENT, three different Euler-Euler multiphase models are available: the volume of fluid (VOF) model, the mixture model, and the Eulerian model. The VOF Model The VOF model (described in Section 20.2) is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. Applications of the VOF model include stratified flows , free-surface flows, filling, sloshing , the motion of large bubbles in a liquid, the motion of liquid after a dam break, the prediction of jet breakup (surface tension), and the steady or transient tracking of any liquid-gas interface. The Mixture Model The mixture model (described in Section 20.3) is designed for two or more phases (fluid or particulate). As in the Eulerian model, the phases are treated as interpenetrating continua. The mixture model solves for the mixture momentum equation and prescribes relative velocities to describe the dispersed phases. Applications of the mixture model include particle-laden flows with low loading, bubbly flows, sedimentation , and cyclone separators. The mixture model can also be used without relative velocities for the dispersed phases to model homogeneous multiphase flow. The Eulerian Model The Eulerian model (described in Section 20.4) is the most complex of the multiphase models in FLUENT. It solves a set of n momentum and continuity equations for each phase. Coupling is achieved through the pressure and interphase exchange coefficients. The manner in which this coupling is handled depends upon the type of phases involved; granular (fluid-solid) flows are handled differently than non-granular (fluid-fluid) flows. For granular flows , the properties are obtained from application of kinetic theory. Momentum exchange between the phases is also dependent upon the type of mixture being modeled. FLUENT's user-defined functions allow you to

customize the calculation of the momentum exchange. Applications of the Eulerian multiphase model include bubble columns , risers , particle suspension, and fluidized beds . 18.4 Choosing a Multiphase Model The first step in solving any multiphase problem is to determine which of the regimes described in Section 18.1 best represents your flow. Section 18.4.1 provides some broad guidelines for determining appropriate models for each regime, and Section 18.4.2 provides details about how to determine the degree of interphase coupling for flows involving bubbles, droplets, or particles, and the appropriate model for different amounts of coupling. 18.4.1 General Guidelines In general, once you have determined the flow regime that best represents your multiphase system, you can select the appropriate model based on the following guidelines. Additional details and guidelines for selecting the appropriate model for flows involving bubbles, droplets, or particles can be found in Section 18.4.2. For bubbly, droplet, and particle-laden flows in which the dispersed-phase volume fractions are less than or equal to 10%, use the discrete phase model. See Chapter 19 for more information about the discrete phase model. For bubbly, droplet, and particle-laden flows in which the phases mix and/or dispersed-phase volume fractions exceed 10%, use either the mixture model (described in Section 20.3) or the Eulerian model (described in Section 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case. For slug flows, use the VOF model. See Section 20.2 for more information about the VOF model. For stratified/free-surface flows, use the VOF model. See Section 20.2 for more information about the VOF model. For pneumatic transport, use the mixture model for homogeneous flow (described in Section 20.3) or the Eulerian model for granular flow (described in Section 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case. For fluidized beds, use the Eulerian model for granular flow. See Section 20.4 for more information about the Eulerian model. For slurry flows and hydrotransport , use the mixture or Eulerian model (described, respectively, in Sections 20.3 and 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case. For sedimentation, use the Eulerian model. See Section 20.4 for more information about the Eulerian model. For general, complex multiphase flows that involve multiple flow regimes, select the aspect of the flow that is of most interest, and choose the model that is most appropriate for that aspect of the flow. Note that the accuracy of results will not be as good as for flows that involve just one flow regime, since the model you use will be valid for only part of the flow you are modeling. 18.4.2 Detailed Guidelines For stratified and slug flows, the choice of the VOF model, as indicated in Section 18.4.1, is straightforward. Choosing a model for the other types of flows is less straightforward. As a general guide, there are some parameters that help to identify the appropriate multiphase model for these other flows: the particulate loading, , and the Stokes number, St. (Note that the word ``particle'' is used in this discussion to refer to a particle, droplet, or bubble.) The Effect of Particulate Loading Particulate loading has a major impact on phase interactions. The particulate loading is defined as the mass density ratio of the dispersed phase ( d) to that of the carrier phase ( c):

The material density ratio

is greater than 1000 for gas-solid flows, about 1 for liquid-solid flows, and less than 0.001 for gas-liquid flows. Using these parameters it is possible to estimate the average distance between the individual particles of the particulate phase. An estimate of this distance has been given by Crowe et al. [ 42]:

where

. Information about these parameters is important for determining how the dispersed phase should

be treated. For example, for a gas-particle flow with a particulate loading of 1, the interparticle space is about 8; the particle can therefore be treated as isolated (i.e., very low particulate loading). Depending on the particulate loading, the degree of interaction between the phases can be divided into three categories: For very low loading, the coupling between the phases is one-way; i.e., the fluid carrier influences the particles via drag and turbulence, but the particles have no influence on the fluid carrier. The discrete phase, mixture, and Eulerian models can all handle this type of problem correctly. Since the Eulerian model is the most expensive, the discrete phase or mixture model is recommended. For intermediate loading, the coupling is two-way; i.e., the fluid carrier influences the particulate phase via drag and turbulence, but the particles in turn influence the carrier fluid via reduction in mean momentum and turbulence. The discrete phase, mixture, and Eulerian models are all applicable in this case, but you need to take into account other factors in order to decide which model is more appropriate. See below for information about using the Stokes number as a guide. For high loading, there is two-way coupling plus particle pressure and viscous stresses due to particles (four-way coupling). Only the Eulerian model will handle this type of problem correctly. The Significance of the Stokes Number For systems with intermediate particulate loading, estimating the value of the Stokes number can help you select the most appropriate model. The Stokes number can be defined as the relation between the particle response time and the system response time:

where

and t s is based on the characteristic length ( L s) and the characteristic velocity ( V s) of the .

system under investigation: For

, the particle will follow the flow closely and any of the three models (discrete phase, mixture, or

Eulerian) is applicable; you can therefore choose the least expensive (the mixture model, in most cases), or the

most appropriate considering other factors. For

, the particles will move independently of the flow , again any of the three

and either the discrete phase model or the Eulerian model is applicable. For

models is applicable; you can choose the least expensive or the most appropriate considering other factors. Examples For a coal classifier with a characteristic length of 1 m and a characteristic velocity of 10 m/s, the Stokes number is 0.04 for particles with a diameter of 30 microns, but 4.0 for particles with a diameter of 300 microns. Clearly the mixture model will not be applicable to the latter case. For the case of mineral processing, in a system with a characteristic length of 0.2 m and a characteristic velocity of 2 m/s, the Stokes number is 0.005 for particles with a diameter of 300 microns. In this case, you can choose between the mixture and Eulerian models. (The volume fractions are too high for the discrete phase model, as noted below.) Other Considerations Keep in mind that the use of the discrete phase model is limited to low volume fractions. Also, the discrete phase model is the only multiphase model that allows you to specify the particle distribution or include combustion modeling in your simulation.

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