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FIGURE 10.23 Comparison of experimental ((a) Rutherford et al., 1996) and predicted ((b) Deshpande and Ranade, 2001) results for dual Rushton turbines (merging flow regime).

between two impellers without requiring any adjustable parameter or any empirical input. Similar predictions can also be obtained from other quasi-steady-state approaches such as MRF and inner-outer, or full transient approaches such as sliding mesh. For example, predicted results reported by Micale et al. (1999) for the corresponding dual impeller cases are also shown in Figs 10.25 and 10.26, which more or less agree with the predictions of the snapshot approach. One reason for the observed differences in predictions of the different approaches is the difference in the number of grids used when carrying out the simulations. In general, it can be said that either snapshot or other state of the art approaches (MRF or sliding mesh) may be used to make a priori predictions of the flow field generated by multiple impellers. An absence of rotating framework or moving grids makes the computational snapshot approach easier to implement, especially with higher order discretization schemes and multiphase flows, which are discussed in the following section.

### 10.3.4. Simulation of Multiphase Flows

Many of the situations encountered by reactor engineers involve (refer to Table 10.1) contact with more than one phase in a stirred tank. It is, therefore, essential to examine whether CFD models can simulate complex multiphase flows in stirred tanks. Here the case of gas-liquid flows in a stirred tank is considered. Similar methodology can be applied to simulate other two-phase or multiphase flows in stirred vessels. The computational snapshot approach discussed previously has been extended to simulate gas-liquid flows (see Ranade et al., 2001c for more details). A two-fluid model was used to simulate gas-liquid flow in a stirred vessel: the model equations and boundary conditions are listed below.

T^kli

FIGURE 10.24 Comparison of experimental ((a) Rutherford et al., 1996) and predicted ((b) Deshpande and Ranade, 2001) results for dual Rushton turbines (diverging flow regime).

Mass balance equations:

d t dXj

Momentum balance equations:

d d — (Pk akVki ) + —(Pk akVkiVkj ) d t dXj dp d ( ( d Vki d Vkj

where Fki is interphase momentum exchange term:

4 dB

Balance equations listed here are before time averaging. For more details of time-averaged two-phase balance equations, the reader is referred to Ranade and van den Akker (1994) and the FLUENT manual. Turbulence was modeled using a standard k-e turbulence model. Governing equations for turbulent kinetic energy, k and

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