16.2.2 Model Comparisons

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:

• 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  16.4) or the Eulerian model (described in Section  16.5).

• For slug flows, use the VOF model. See Section  16.3 for more information about the VOF model.

• For stratified/free-surface flows, use the VOF model. See Section  16.3 for more information about the VOF model.

• For pneumatic transport, use the mixture model for homogeneous flow (described in Section  16.4) or the Eulerian model for granular flow (described in Section  16.5).

• For fluidized beds, use the Eulerian model for granular flow. See Section  16.5 for more information about the Eulerian model.

• For slurry flows and hydrotransport , use the mixture or Eulerian model (described, respectively, in Sections  16.4 and 16.5).

• For sedimentation, use the Eulerian model. See Section  16.5 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.

As discussed in this section, the VOF model is appropriate for stratified or free-surface flows, and the mixture and Eulerian models are appropriate for flows in which the phases mix or separate and/or dispersed-phase volume fractions exceed 10%. (Flows in which the dispersed-phase volume fractions are less than or equal to 10% can be modeled using the discrete phase model described in Chapter  15.)

To choose between the mixture model and the Eulerian model, you should consider the following guidelines:

• If there is a wide distribution of the dispersed phases (i.e., if the particles vary in size and the largest particles do not separate from the primary flow field), the mixture model may be preferable (i.e., less computationally expensive). 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 ANSYS FLUENT or through a user-defined function), the Eulerian model can usually provide more accurate results than the mixture model. Even though you can apply the same drag laws to the mixture model, as you can for a nongranular Eulerian simulation, if the interphase drag laws are unknown or their applicability to your system is questionable, the mixture model may be a better choice. For most cases with spherical particles, then the Schiller-Naumann law is more than adequate. For cases with nonspherical particles, then a user-defined function can be used.

• If you want to solve a simpler problem, which requires less computational 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 Eulerian 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.

ANSYS FLUENT's multiphase models are compatible with ANSYS FLUENT's dynamic mesh modeling feature. For more information on the dynamic mesh feature, see Section  3. For more information about how other ANSYS FLUENT models are compatible with ANSYS FLUENT's multiphase models, see this appendix in the separate User's Guide.

Detailed Guidelines

For stratified and slug flows, the choice of the VOF model, as indicated in Section  16.2.2, 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, $\beta$, 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. [ 62]:

where $\kappa = \frac{\beta}{\gamma}$. 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 $\frac{L}{d_d}$ 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 the following 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 (Chapter  15), 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(Chapter  15) , 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 $\tau_d=\frac{\rho_d d_d^2}{18 \mu_c}$ and $t_s$ is based on the characteristic length ( $L_s$) and the characteristic velocity ( $V_s$) of the system under investigation: $t_s = \frac{L_s}{V_s}$.

For ${\rm St} \ll 1.0$, the particle will follow the flow closely and any of the three models (discrete phase(Chapter  15) , 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 ${\rm St} > 1.0$, the particles will move independently of the flow and either the discrete phase model (Chapter  15) or the Eulerian model is applicable. For ${\rm St} \approx 1.0$, again any of the three 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 (Chapter  15), as noted below.)

Other Considerations

Keep in mind that the use of the discrete phase model (Chapter  15) 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.