Snapshot Approach

Consider a finite volume representation of a basic conservation equation for a general variable 0  

Consider evaluation of Eq. (10.1) in a steady framework by assuming the cyclically repetitive flow between the impeller blades. As mentioned earlier, in a snapshot approach, blades are considered stationary at one position. For an instant, when the blades of the rotating impeller coincide with the position of the blades considered in the snapshot simulation, the following equation is solved in a steady framework  

It is necessary to approximate the time derivative terms appearing in this equation. By separating the variables, one can write the time derivative term as (for constant density fluid) 

Generally in a fixed grid simulation, the volume of any computational cell remains constant. This can be applied to all computational cells used in the snapshot approach except those directly attached to the front and rear sides of blades. As the impeller rotates, the volume of cells attached to the front side of the blade decreases. Correspondingly, the volume of computational cells attached to the rear side of the impeller blade increases (Fig. 10.4). The rate of increase or decrease can be calculated directly from the area of the interface between computational cells and impeller blade and the velocity with which the impeller is rotating. Thus, for the computational cells attached to the front and rear sides of impeller blades, the second term of the right-hand side 

Sourccs/sinks to front/rear sides respectively 

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Concluding, it is essential to represent complex, real-life flow situations by computationally tractable models that retain adequate details. As an example, a computational snapshot approach that simulates the flow in stirred reactors or other vessels for any arbitrary impeller has been developed [5]. This approach lets the engineer simulate the detailed fluid dynamics around the impeller blades with much less computations that would otherwise be required. Improvements in CFD technique are likely to encourage further work along these lines. 

In comparison with Bakker and Van den Akker (1994b) and Venneker et al. (2002), Khopkar et al. (2005) applied a more sophisticated two-fluid approach including a standard k-e turbulence model. Using the incorrect snapshot approach due to Ranade (2002), their simulation results (for gas flow numbers being 4 times higher than those of Bakker and Van den Akker, 1994b) still exhibit major discrepancies with respect to experimental data. One of the... 

A dynamic versus snapshot approach Must recognise that both individuals and societies change over time. Must be able to consider or model the changes that are taking place continuously in tourism... 

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. 

Ranade and Tayalia (2000) validated the snapshot approach by considering a two-dimensional case of rotating flows. Application of this approach to simulating complex, three-dimensional flows in stirred tank reactors is discussed below. The next section will discuss application of this approach to cases relevant to reactor engineering. 

In order to assess the computational snapshot approach in more detail, predicted normalized mean velocity components and normalized turbulent kinetic energy were directly compared with the available data of Schafer et al. (1997). In the case of... 

Results described so far suggest that the snapshot approach can be used to make a priori predictions of the complex flow generated in stirred vessels for impellers of any shape. A number of industrial stirred tank reactors make use of two or more impellers mounted on the same shaft. When more than one impeller is used, the flow complexity is greatly increased, especially when there is interaction between the flow generated by the two impellers. The extent of interaction depends on relative distances between the two impellers (and clearance from the vessel bottom). In order to examine whether the computational snapshot approach can be used to simulate... 

The computational snapshot approach was used to simulate flow generated in these three impeller configurations (for more details, see Deshpande and Ranade, 2001). The predicted velocity vectors in the r-z plane located midway between the two baffles for parallel, merging and diverging flow configurations are shown in... 

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. 

The snapshot approach for gas-liquid flows was implemented using a commercial CFD code, FLUENT (Fluent Inc., USA). User-defined subroutines were used for this purpose. Half of the vessel was considered as a solution domain. The solution domain and details of the finite volume grid used was similar to those used for singlephase flows discussed earlier (however, the number of cells in the 6 direction were half of that used in single-phase simulations). A QUICK discretization scheme with SUPERBEE limiter function was used to integrate all the equations (Fluent User Guide, 1997). Simulations were carried out for three values of dimensionless gas flow rates (Qc/ND ), 0.01, 0.02 and 0.03. 

In general, it may be concluded that the computational snapshot approach or other equivalent, state of the art CFD models can capture the key features of flow in stirred tank reactors and can be used to make either quantitative (for single-phase or pseudo-homogeneous applications) or semi-quantitative (for complex, multiphase applications) predictions. Possible applications to reactor engineering are discussed below. 

Deshpande, V.R. and Ranade, V.V. (2001), Simulation of flow generated by dual Rushton turbines using computational snapshot approach, submitted for publication, Chem. Eng. Commun. 

Ranade, V.V, Perrard, M., Xuereb, C., Le Sauze, N. and Bertrand, J. (2001b), Trailing vortices of Rushton turbine PIV measurements and CFD simulations with snapshot approach, Chem. Eng. Res. Des., 19A, 3-12. 

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