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### Transcript of Chapter 20. General Multiphase Models General Multiphase Models This chapter discusses the general...

• Chapter 20. General Multiphase

Models

This chapter discusses the general multiphase models that are available in FLUENT. Chapter 18 provides a brief introduction to multiphase mod- eling, Chapter 19 discusses the Lagrangian dispersed phase model, and Chapter 21 describes FLUENT’s model for solidification 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 Effects • 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 Problems

20.1 Choosing a General Multiphase Model

As discussed in Section 18.4, the VOF model is appropriate for stratified or free-surface flows, and the mixture and Eulerian models are appropri- ate for flows in which the phases mix or separate and/or dispersed-phase volume fractions exceed 10%. (Flows in which the dispersed-phase vol- ume fractions are less than or equal to 10% can be modeled using the discrete phase model described in Chapter 19.)

To choose between the mixture model and the Eulerian model, you should consider the following, in addition to the detailed guidelines in Section 18.4:

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• General Multiphase Models

• If there is a wide distribution of the dispersed phases, the mixture model may be preferable. If the dispersed phases are concentrated just in portions of the domain, you should use the Eulerian model instead.

• If interphase drag laws that are applicable to your system are available (either within FLUENT or through a user-defined func- tion), the Eulerian model can usually provide more accurate results than the mixture model. If the interphase drag laws are unknown or their applicability to your system is questionable, the mixture model may be a better choice.

• If you want to solve a simpler problem, which requires less com- putational effort, the mixture model may be a better option, since it solves a smaller number of equations than the Eulerian model. If accuracy is more important than computational effort, the Eu- lerian model is a better choice. Keep in mind, however, that the complexity of the Eulerian model can make it less computationally stable 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 the models are provided in Sections 20.2, 20.3, and 20.4.

20.1.1 Overview and Limitations of the VOF Model

Overview

The VOF model can model two or more immiscible fluids by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. Typical applications include the prediction of jet breakup, the motion of large bubbles in a liquid, the motion of liquid after a dam break, and the steady or transient tracking of any liquid-gas interface.

Limitations

The following restrictions apply to the VOF model in FLUENT:

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• 20.1 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 filled with either a single fluid phase or a combination of phases; the VOF model does not allow for void regions where no fluid of any type is present.

• Only one of the phases can be compressible. • Streamwise periodic flow (either specified mass flow rate or spec-

ified pressure drop) cannot be modeled when the VOF model is used.

• Species mixing and reacting flow cannot be modeled when the VOF model is used.

• The LES turbulence model cannot be used with the VOF model. • The second-order implicit time-stepping formulation cannot be used

with the VOF model.

• The VOF model cannot be used for inviscid flows. • The shell conduction model for walls cannot be used with the VOF

model.

The VOF formulation in FLUENT is generally used to compute a time- dependent solution, but for problems in which you are concerned only with a steady-state solution, it is possible to perform a steady-state cal- culation. A steady-state VOF calculation is sensible only when your solution is independent of the initial conditions and there are distinct in- flow boundaries for the individual phases. For example, since the shape of the free surface inside a rotating cup depends on the initial level of the fluid, such a problem must be solved using the time-dependent formula- tion. On the other hand, the flow of water in a channel with a region of air on top and a separate air inlet can be solved with the steady-state formulation.

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• General Multiphase Models

20.1.2 Overview and Limitations of the Mixture Model

Overview

The mixture model is a simplified multiphase model that can be used to model multiphase flows where the phases move at different velocities, but assume local equilibrium over short spatial length scales. The coupling between the phases should be strong. It can also be used to model homogeneous multiphase flows with very strong coupling and the phases moving at the same velocity.

The mixture model can model n phases (fluid or particulate) by solv- ing the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary phases, and algebraic expressions for the relative velocities. Typical applications include sedi- mentation, cyclone separators, particle-laden flows with low loading, and bubbly flows where the gas volume fraction remains low.

The mixture model is a good substitute for the full Eulerian multiphase model in several cases. A full multiphase model may not be feasible when there is a wide distribution of the particulate phase or when the interphase laws are unknown or their reliability can be questioned. A simpler model like the mixture model can perform as well as a full mul- tiphase model while solving a smaller number of variables than the full multiphase model.

Limitations

The following limitations apply to the mixture model in FLUENT:

• You must use the segregated solver. The mixture model is not available with either of the coupled solvers.

• Only one of the phases can be compressible. • Streamwise periodic flow (either specified mass flow rate or speci-

fied pressure drop) cannot be modeled when the mixture model is used.

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• 20.1 Choosing a General Multiphase Model

• Species mixing and reacting flow cannot be modeled when the mix- ture model is used.

• Solidification and melting cannot be modeled in conjunction with the mixture model.

• The LES turbulence model cannot be used with the mixture model. • The second-order implicit time-stepping formulation cannot be used

with the mixture model.

• The mixture model cannot be used for inviscid flows. • The shell conduction model for walls cannot be used with the mix-

ture model.

20.1.3 Overview and Limitations of the Eulerian Model

Overview

The Eulerian multiphase model in FLUENT allows for the modeling of multiple separate, yet interacting phases. The phases can be liquids, gases, or solids in nearly any combination. An Eulerian treatment is used for each phase, in contrast to the Eulerian-Lagrangian treatment that is used for the discrete phase model.

With the Eulerian multiphase model, the number of secondary phases is limited only by memory requirements and convergence behavior. Any number of secondary phases can be modeled, provided that sufficient memory is available. For complex multiphase flows, however, you may find that your solution is limited by convergence behavior. See Sec- tion 20.7.3 for multiphase modeling strategies.

FLUENT’s Eulerian multiphase model differs from the Eulerian model in FLUENT 4 in that there is no global distinction between fluid-fluid and fluid-solid (granular) multiphase flows. A granular flow is simply one that involves at least one phase that has been designated as a granular phase.

The FLUENT solution is based on the following:

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• General 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 fluctuating energy) can be cal- culated for each solid phase. This is based on an algebraic relation.

– Solid-phase shear and bulk viscosities are obtained from appli- cation of kinetic theory to granular flows. Frictional viscosity is also available.

• Several interphase drag coefficient functions are available, which are appropriate for various types of multiphase regimes. (You can also modify the interphase drag coefficient through user-defined functions, as described in the separate UDF Manual.)

• All of the k-� turbulence models are available, and may apply to all phases or to the mixture.

Limitations

All other features available in FLUENT can be used in conjunction with the Eulerian multiphase model, except for the following limitations:

• Only the k-� models can be used for turbulence. • Particle tracking (using the Lagrangian dispersed phase