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FIGURE 12.17 Some simulation results for gas-solids flows in a riser. (a) Axial particle diameter profiles for different superficial gas velocities (Vsup ) (from Mathiesen et al., 2000). (b) Radial solid volume fraction profiles at 0.7 m from the bottom, Vsup = 1.0ms-1 (from Mathiesen et al., 2000). (c) Radial solids volume fraction profiles at different heights: solid line and circles 1.86 m; short-dashed line and squares 4.18 m; long-dashed line and diamonds: 5.52 m (from Neri and Gidaspaw, 2000).

FIGURE 12.17 Some simulation results for gas-solids flows in a riser. (a) Axial particle diameter profiles for different superficial gas velocities (Vsup ) (from Mathiesen et al., 2000). (b) Radial solid volume fraction profiles at 0.7 m from the bottom, Vsup = 1.0ms-1 (from Mathiesen et al., 2000). (c) Radial solids volume fraction profiles at different heights: solid line and circles 1.86 m; short-dashed line and squares 4.18 m; long-dashed line and diamonds: 5.52 m (from Neri and Gidaspaw, 2000).

then, significant progress has been made and it is now possible to simulate bubbling beds having a large number of bubbles. Ferschneider and Mege (1996) applied a two-fluid model to simulate bubbling fluidization of Geldart group A powders (particle diameter 100 xm) in a two-dimensional column. Comparison of their predicted results with experimental data is shown in Fig. 12.18. It can be seen that although predictions of bubble diameter and bubble rise velocity are reasonable, the model significantly overestimates bubble volume fraction. Such an overestimation may lead to carry-over of the entire dense bed as reported by Ranade (1998).

It should be noted that a two-fluid model along with the kinetic theory of granular flow contains several modeled terms (stress tensors, solid phase bulk and shear viscosity, radial distribution function and so on). Several different modeled versions of each of these have been used (Nieuwland et al., 1996). A general consensus on selection of an appropriate version has not yet emerged. Enwald et al. (1999) used two different stress tensor models to simulate bubbling beds, which led to quite similar results. Fortunately, the existence of bubbles is independent of which stress tensor model is used, since the mechanism of bubble formation originates from general two-fluid model formulation (Glasser et al., 1996). In addition to the selected model equations, numerical issues such as mesh refining and discretization schemes may also play a significant role. Syamlal (1998) reported significant influence of discretization scheme on simulated bubble shapes. His results are shown in Fig. 12.19. Studies by van Wachem et al. (1998, 1999) and Enwald et al. (1999) also indicate the strong influence of numerical parameters on simulated characteristics of bubbling fluidized beds. In both of these studies, bubbling beds of Geldart group B particles were simulated. van Wachem et al. (1998) report that a finer mesh is required to simulate bubbling at lower fluidization velocities. They had to use different mesh sizes for different velocities in order to get similar volume fractions inside bubbles at different fluidization conditions (0.007 m for two times minimum fluidization velocity and 0.01 m for four times minimum fluidization velocity). Their simulated results also indicate reasonably good predictions of bubble size and bubble rise velocity (Fig. 12.20). Enwald et al. (1999) report that as the operating pressure or the ratio of density of fluidizing medium to solid particles decreases, a finer mesh is required. A sample of simulated results reported by Enwald et al. (1999) is shown in Fig. 12.21. It can be seen that simulations with a granular flow model lead to very few bubbles near the distributor, unlike experimental observations. Simulations with constant particle viscosity models carried out with a fine mesh resulted in reasonable agreement with experimental data.

In light of these recent works and progress in the development of robust and efficient parallel solvers, it is now possible to use CFD models for the reactor engineering of bubbling/turbulent fluidized beds. The key issue in developing such models is that the reactor engineer should not focus on developing an all-encompassing model by including every conceivable term. Instead, the reactor engineer should make judicious use of accumulated knowledge about the considered fluidized bed reactor to construct a model which gives predictions consistent with the accumulated experience. For example, Ranade (1998) used an analogy between dense bubbling beds and bubble column reactors to simulate key issues regarding gas distributor and solids entry configuration in a FCC regenerator (as discussed in Chapter 9). Some of the recent applications of CFD models to reactor engineering of fluidized beds are discussed in the following section.

Fluidization velocity (m/s)

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