FIGURE 11.14 Comparison of predictions using three-phase model and experimental data (from Krishna et al., 2000a).

bed reactors. Wu and Gidaspaw (2000) used such a granular flow model to simulate the fluid dynamics of a methanol synthesis reactor. Their results show encouraging agreement with the pilot plant data. Further experimental and computational research on fluid dynamics of dense slurry bubble column reactors is essential to make further progress in predictions of such slurry reactors. Recent experimental techniques such as computer tomography (CT) and computer aided radioactive particle tracking (CARPT), which can 'look' into opaque, dense slurry bubble columns, may provide the necessary experimental data to guide further development.

In general, it may be concluded that it is possible to develop appropriate Eulerian-Eulerian models to simulate complex gas-liquid (solid) flows, with some support from the experimental data. Some of the possible applications of such models are discussed in the next section. Before discussing these applications, recent simulations carried out with Eulerian-Lagrangian and volume of fluid (VOF) approaches are briefly reviewed here.

11.2.2. Eulerian-Lagrangian and VOF Approach

Basic governing equations to apply Eulerian-Lagrangian and VOF approaches to simulate dispersed gas-liquid flows are discussed in Chapter 4. As mentioned therein, the major advantage of the Eulerian-Lagrangian approach is its greater flexibility with respect to incorporation of microscopic, particle-level phenomena. Bubble-bubble interaction and coalescence or break-up can be included in the model. The precise state of individual bubbles can be monitored, which has significant advantage in simulating gas-liquid reactors. However, this flexibility and knowledge of the precise state of individual bubbles comes with associated increase in computational costs. Simulation of large industrial bubble column reactors containing millions of gas bubbles often becomes computationally intractable. However, despite this limitation, Eulerian-Lagrangian simulations can provide very useful insight and can be used to validate the averaging procedure employed in developing Eulerian-Eulerian models.

In order to reduce the computational requirements, Lapin and Lubbert (1994) considered bubble clusters instead of individual bubbles while employing a Eulerian-Lagrangian approach to simulate bubble columns. However, they externally imposed bubble slip velocity rather than calculating it by solving momentum equations. Delnoij (1999) carried out more rigorous Eulerian-Lagrangian simulations of flow in bubble columns. Apart from solving momentum equations for individual bubbles, Delnoij also considered bubble-bubble collisions and their effect on bubble trajectories. Samples of their results are shown in Fig. 11.15. Delnoij (1999) did not consider coalescence and break-up. Ranade and Utikar (1999) used bubble tracking in a Lagrangian framework along with the coalescence models. They have, however, simplified the governing equations using the approximation of potential flow around bubbles. Despite such a simplistic approximation, their model could capture the key features of the dynamics of gas-liquid flows reasonably well. It is necessary to develop a comprehensive computational model based on a Eulerian-Lagrangian framework (with coalescence and break-up models) to simulate dispersed gas-liquid flows in bubble columns. Detailed comparisons of simulated results from Eulerian-Lagrangian approach and Eulerian-Eulerian approach will be very useful to validate averaging procedures employed to derive Eulerian-Eulerian models. Such detailed comparisons and analysis will lead to better formulations of Eulerian-Eulerian models, which may then be reliably used for reactor engineering applications.

It must be noted here that even for Eulerian-Lagrangian simulations, although there is no complexity of averaging over trajectories, the accuracy of simulations of individual bubble trajectories depends on lumped interphase interaction parameters such as drag force, virtual mass force and lift force coefficients. All of these interphase interaction parameters will be functions of bubble size and shape, presence of other bubbles or walls, surrounding pressure field and so on. Unfortunately, adequate information is not available on these aspects. To enhance our understanding of basic t=30.0000 [s] t=30.0000 [s] t=50.0000 [s] t=50.0000 [s] t = 70.0000 [s] t=70.0000 [s]

t=30.0000 [s] t=30.0000 [s] t=50.0000 [s] t=50.0000 [s] t = 70.0000 [s] t=70.0000 [s]

height = 1.3475 m; superficial gas velocity = 0.035 m/s 1; uniform bubbles of diameter 0.002 m.

issues in bubble-bubble interaction and to obtain the required information for model development, it may be necessary to develop and to use volume of fluid (VOF) or interface tracking based simulations. As discussed in Chapter 4, the volume of fluid approach allows resolution of the small-scale flow field around individual bubbles (including possible deformation of bubbles). Such capability will provide valuable information about bubble-bubble interactions. Lin et al. (1996) applied VOF to simulate the motion of gas bubbles in two-dimensional columns. More recently, Li et al. (2000) and Krishna et al. (2000b) also carried out VOF simulations of the rise of single bubbles under different operating conditions. A sample of results from Li et al. (2000) is shown in Fig. 11.16. The agreement between simulated rise velocity and experimental data is quite encouraging. Krishna and van Baten (1999) also tried to simulate interaction between multiple bubbles while they are rising through the two-dimensional columns. However, agreement between predicted and experimentally observed rise velocity is not as good as observed in the case of single bubbles. It may be necessary to carry out detailed three-dimensional VOF simulations to get accurate predictions of bubble-bubble interactions. No such attempt has been published so far. Although the computational requirements of such an exercise will be huge, such VOF simulations will be very useful to develop appropriate sub-models for Eulerian-Eulerian and Eulerian-Lagrangian approaches.

A brief review of recent modeling attempts indicates several limitations of the current state of the art. However, with an appropriate dose of engineering judgment

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