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23.2.2 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:

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  22.)

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

FLUENT's multiphase models are compatible with FLUENT's dynamic mesh modeling feature. For more information on the dynamic mesh feature, see Section  11. For more information about how other FLUENT models are compatible with FLUENT's multiphase models, see Appendix  A.



Detailed Guidelines


For stratified and slug flows, the choice of the VOF model, as indicated in Section  23.2.2, 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 ( $c$):


 \beta = \frac{\alpha_d \rho_d}{\alpha_c \rho_c} (23.2-1)

The material density ratio


 \gamma = \frac{\rho_d}{\rho_c} (23.2-2)

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. [ 69]:


 \frac{L}{d_d} = \left(\frac{\pi}{6}\frac{1+\kappa}{\kappa} \right)^{1/3} (23.2-3)

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:

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:


 {\rm St} = \frac{\tau_d}{t_s} (23.2-4)

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  22) , 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  22) 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  22), as noted below.)

Other Considerations

Keep in mind that the use of the discrete phase model (Chapter  22) 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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