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FIGURE 10.10 Presence of trailing vortices (Rushton turbine). (a) Turbulent kinetic energy (impeller center plane; impeller rotation: counter-clockwise), white: highest level, black: lowest level, (b) Z-vorticity (r/T = 0.165; impeller rotation: from left to right) (from Ranade et al., 2001a). Reproduced in colour plate section between pages 210 and 211.

FIGURE 10.10 Presence of trailing vortices (Rushton turbine). (a) Turbulent kinetic energy (impeller center plane; impeller rotation: counter-clockwise), white: highest level, black: lowest level, (b) Z-vorticity (r/T = 0.165; impeller rotation: from left to right) (from Ranade et al., 2001a). Reproduced in colour plate section between pages 210 and 211.

the Rushton turbine, predicted circumferential profiles at r/T = 0.171 and z/T = 0.329 were compared with the experimental data in Fig. 10.12. Fig. 10.12a shows good agreement between the predicted radial mean velocities and the experimental data. The three curves show the predicted results between the three blades of the Rushton turbine considered in the simulations. It can be seen that these three predicted profiles between the blades are quite similar. Comparison of the predicted tangential mean velocity with the experimental data is shown in Fig. 10.12b. Although overall agreement is reasonable, significant discrepancies were observed in certain areas. For the axial component (Fig. 10.12c), the predicted profiles show significantly less variation than the experimental data. It must, however, be noted that predicted profiles of axial mean velocity in the impeller stream are very sensitive to location. At a slightly different axial location at the same radial location, predicted profiles show similar behavior to that observed in the experimental data. In the case of turbulent kinetic energy (Fig. 10.12d), the agreement between predicted and experimental data is good

0 30 40 50 602 Impeller2tegrees2 (d)2

FIGURE 10.12 Comparison of simulated and experimental results for Rushton turbine (r/T = 0.171; z/T = 0.329). Traces; simulation results; • Schafer et al. (1997) data (from Ranade et al., 2001a).

0 30 40 50 602 Impeller2tegrees2 (d)2

0 30 40 [mpcllcr2icgrccs2

0 30 40 [mpcllcr2icgrccs2

FIGURE 10.12 Comparison of simulated and experimental results for Rushton turbine (r/T = 0.171; z/T = 0.329). Traces; simulation results; • Schafer et al. (1997) data (from Ranade et al., 2001a).

for the region near the trailing blade. In the immediate vicinity of the leading blade, predicted turbulent kinetic energy values are much lower than the experimental data. Reasons for this disagreement are not immediately obvious. A recent study using a different turbulence model (Jenne and Reuss, 1999) indicates that different time scales or anisotropy considerations (Reynolds stress models) are of minor importance and do not lead to significant improvements in the observed agreement. Further studies which combine experimental and computational investigations are needed to evaluate the influence of turbulence models (and grid refinement near the blades) on the predicted characteristics of trailing vortices and on the flow field within the blades. Despite some of the observed discrepancies, predictions using a computational snapshot are very encouraging. The snapshot approach could become a promising tool to design mixing processes in stirred vessels if it can be extended to impellers of any shape, to multiple impellers and to multiphase flows.

10.3.2. Simulation of Flow Generated by an Impeller of Different Shape

In order to examine application of the snapshot approach to simulating flow generated by an impeller of any shape, the case of a pitched blade turbine was considered. The geometry of the stirred vessel agitated by a 45°, four bladed, pitched blade turbine as used by Schafer et al. (1998) was modeled using structured grids. The computational grid was generated using the geometry-modeling tool, GAMBIT (Fluent Inc., USA). In view of the symmetry, only one quarter of the vessel was considered as the solution domain. Solution domains and boundary conditions used in the present work are shown in Fig. 10.13. For these simulations, 269 667 grids were used (57 x 57 x 83 :: r x 0 x z). The blade of the pitched blade turbine was discretized with 22 x 3 x 15 cells (r x 0 x z). Typical grids used are shown in Fig. 10.14. Other boundary conditions and numerical parameters were kept the same as used for the disc turbine. For this case also, turbulence was modeled using the standard k-e model. All the governing equations were discretized using a QUICK discretization scheme with SUPERBEE limiter function (Fluent User Guide, 1997).

Numerical simulations carried out with the computational snapshot approach show the well-known flow patterns generated by a pitched blade turbine. Predicted flow fields for typical r-z planes are shown in Fig. 10.15 (vector plot and contours of turbulent kinetic energy). Simulations of the pitched blade turbine clearly show the presence of a reverse loop directly below the impeller. This is also in agreement with experimental observations (Ranade and Joshi, 1989). The predicted pumping number for the pitched blade turbine (calculated at the K plane just below the impeller) is 1.0, which is in good agreement with published data (Ranade and Joshi, 1989). The predicted results also show good overall agreement with experimental data in the bulk region of the tank. As mentioned in the previous section, it is important to examine the quality of simulations in the region near the impeller since this controls the overall quality. Flow near the impeller blades is, therefore, examined in detail. A single trailing vortex is detected behind the blades of the pitched blade turbine. An iso-surface of predicted Z-vorticity («) for the pitched blade turbine is shown in Fig. 10.16 (the impeller blade is moving inside the plane of the paper). It can be seen that the trailing vortex is attached to the rear side of the blade and flows

FIGURE 10.13 Solution

Pitchedilade2urbine2

r x8 x z

0 0

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