## 102 Cfdbased Modeling Of Stirred Reactors

Flow in baffled stirred reactors has been modeled by employing several different approaches which can be classified into four types, and are shown schematically in Fig. 10.3. Most flow simulations of stirred vessels published before 1995 were based on steady-state analyses (reviewed by Ranade, 1995) using the black box approach. This approach requires boundary conditions (mean velocity and turbulence characteristics) on the impeller swept surface, which need to be determined experimentally. Although this approach is reasonably successful in predicting the flow characteristics in the bulk of the vessel, its usefulness is inherently limited by the availability of data. Extension of such an approach to multiphase flows and to industrial-scale reactors is not feasible because it is virtually impossible to obtain (from experiments) accurate

Specify boundary conditions on impeller swept surface

(wherever fluid exits impeller swept volume)

Stationary grid

Grid rotating with impeller

Interface over which grids slide

Detailed geometry needs to be modeled, full transient simulations

Stationary grid

Grid rotating with impeller

Interface over which grids slide

Detailed geometry needs to be modeled, full transient simulations

Solution with stationary framework

Solution with rotating framework

Interface over which two solutions communicate

Detailed geometry needs to be modeled (d)

Solution with stationary framework

Solution with rotating framework

Interface over which two solutions communicate

Detailed geometry needs to be modeled (d)

Stationary framework Impeller rotation is modeled using sources/sinks

Transient terms are approximated Transient terms are neglected

Detailed geometry needs to be modeled

Stationary framework Impeller rotation is modeled using sources/sinks

Transient terms are approximated Transient terms are neglected

### Detailed geometry needs to be modeled

FIGURE 10.3 Approaches to modeling flow in stirred reactors. (a) Black box approach, (b) sliding mesh approach, (c) multiple reference frame or inner-outer approach, (d) snapshot approach.

boundary conditions for such systems. More importantly, this approach cannot be used to make a priori simulations. It cannot, therefore, be used as a design tool; hence, studies based on this approach are not discussed in this chapter.

To eliminate some of the limitations described above, recently attempts have been made to simulate flow within and outside the impeller region either with a combination of moving and deforming or with a sliding mesh (Harris et al, 1996; Ranade et al., 1997). In the sliding mesh approach, full transient simulations are carried out using the two grid zones (Fig. 10.3b). One grid zone is attached to the stationary baffles and reactor wall while the other is attached to the rotating impeller. Obviously, the boundary between these two zones should have a radius more than that of the impeller blade tips and less than that of the inner edges of the baffles. The detailed geometry of the impeller needs to be modeled: impeller blades are modeled as solid rotating walls. Flow within the impeller blades is solved using the usual transport equations unlike the black box approach described earlier. The sliding mesh approach has the potential to generate a priori predictions without requiring any experimental input. It can therefore be used as a design tool to screen different configurations, however, the following considerations make the sliding mesh approach less attractive as a reactor-engineering tool:

• As it relies on the solution of full time varying flow in a stirred vessel, its computational requirements are greater by an order of magnitude than those required by steady state simulations.

• Because of the excessive computational requirements, there are restrictions on the number of computational cells that can be used for the simulations. Such a limitation may make a priori predictions of the desired flow characteristics such as energy dissipation rates, shear rates near impeller blades etc. less accurate.

• The results obtained using this approach are not yet sufficiently validated for turbulent regime.

For most engineering applications, knowledge of the full time varying flow field (which becomes cyclically repeating after a number of impeller rotations) may not be necessary. It may, therefore, be desirable to develop an approach which allows a priori simulations of the flow generated by an impeller of any shape with the same computational requirements as required for steady state simulations. Such an approach can be used as a design tool for screening different alternative mixer configurations. There are two main approaches for approximating unsteady flow in stirred vessels. In both approaches, a fictitious cylindrical zone with a radius more than that of the impeller blade tips and less than that of the inner edges of the baffles and height sufficient to include an entire impeller is defined (Fig. 10.3c and 10.3d). The full geometry needs to be modeled and in these approaches also, impeller blades are modeled as walls.

• The first approach is called the 'multiple reference frame' (MRF) or 'inner-outer' approach (inner-outer approach in fact defines inner and outer zones with a finite overlap whereas in the MRF approach there is no overlap between inner and outer regions). In this approach, flow characteristics of the inner region are solved using a rotating framework. These results are used to provide boundary conditions for the outer region (after azimuthal averaging), flow in which is solved using a stationary framework. Solution of the outer region is used to provide boundary conditions for the inner region. A few iterations over inner and outer regions may lead to a converged solution. Brucato et al. (1994) and Harris et al. (1996) applied the inner-outer method to simulate flow in stirred vessels whereas Marshall et al. (1996) used a 'multiple reference frame' approach. The multiple reference frame approach (MRF) is computationally less intensive than the inner-outer method. This approach is available with several commercially available CFD codes.

• The second approach is based on taking a snapshot of flow in stirred vessels with a fixed relative position of blades and baffles. Ranade and Dommeti (1996a) proposed such a computational snapshot approach, in which impeller blades are modeled as solid walls and flow is simulated using a stationary framework for a specific blade position. Appropriate sources are specified to simulate impeller rotation. If necessary, simulations are carried out at different blade positions to obtain ensemble-averaged results over different blade positions. In this approach also, the whole solution domain is divided into two regions, similar to the MRF approach. In the inner region surrounding the impeller, time derivative terms are approximated in terms of spatial derivatives. In the outer region, time derivative terms are usually quite small in magnitude in comparison with the other terms in the governing equations and are neglected.

Recently, attempts have also been made to employ large eddy simulation (LES) models (Derksen and van den Akker, 1999) to simulate flow in stirred vessels. However, computational requirements of these models are much higher than even the sliding mesh approach, and therefore, application of this approach will be restricted to relatively simple impeller shapes. The results obtained by this approach are not yet sufficiently validated. Although sliding mesh and LES approaches look unattractive as design tools, these approaches are important as learning tools to help understand details of fluid dynamics near the impeller blades. MRF or the computational snapshot approach look promising as design tools since these can be extended to impellers of any shape, to any number of impellers and to multiphase flows, without excessive demands on computational resources. Approximations employed with both MRF and computational snapshot methods are of the same level and therefore lead to almost the same results. The computational snapshot approach can be implemented in any stationary frame CFD program without requiring any substantial modifications. Since information about MRF can be found in the manuals of most commercial CFD programs, we restrict our discussion here to the computational snapshot approach.

## Post a comment