3

x Wu and Patterson (1989)

x Wu and Patterson (1989)

1 1.5 2 2.5 3 Dimensionless radial co-ordinate, r/R - Standard k- E ■ Experimental ♦ Wu and Patterson (1989)

FIGURE 10.8 Comparison of predicted mean velocity field with angle-averaged PIV data (impeller center plane) (from Ranade et al., 2001b). (a) Radial mean velocity (b) Tangential mean velocity.

1 1.5 2 2.5 3 Dimensionless radial co-ordinate, r/R - Standard k- E ■ Experimental ♦ Wu and Patterson (1989)

FIGURE 10.8 Comparison of predicted mean velocity field with angle-averaged PIV data (impeller center plane) (from Ranade et al., 2001b). (a) Radial mean velocity (b) Tangential mean velocity.

Dimensionless2radial2;;o-ordinate,>/i

- Standard2fc-2 ■ Experimental,2otal2 • Experimental,landom

FIGURE 10.9 Comparison of predicted turbulent kinetic energy with angle-averaged PIV data (impeller center plane) (from Ranade et al., 2001b).

Dimensionless2radial2;;o-ordinate,>/i

- Standard2fc-2 ■ Experimental,2otal2 • Experimental,landom

FIGURE 10.9 Comparison of predicted turbulent kinetic energy with angle-averaged PIV data (impeller center plane) (from Ranade et al., 2001b).

It can be seen that agreement between predicted and experimental profiles of mean velocity is satisfactory. It must be noted that when the experimental data contain contributions due to the periodic motion of the impeller blades, the highest values of turbulent kinetic energy are obtained at the vicinity of the impeller tip, due to the apparent turbulence generated by the periodic motion. When the random turbulent kinetic energy is calculated by considering the mean value of five sets of angle-resolved data, the agreement between experiments and CFD results is improved in the vicinity of the impeller. The difference between the predicted turbulent kinetic energy and experimentally measured turbulent kinetic energy after removing the periodic component is reasonable for the standard k-e model. The contours of predicted turbulent kinetic energy at the impeller center plane of the Rushton turbine are shown in Fig. 10.10a (impeller rotation direction is counter clockwise). It can be seen that snapshot simulations clearly show the presence of higher turbulent kinetic energy at the locations of trailing vortices behind the impeller blades. Z-vorticity contours at the z-6 plane (r/T = 0.165) are shown in Fig. 10.10b. This figure also clearly shows the presence of a pair of trailing vortices behind the rotating impeller blades. The trailing vortices move radially outwards and axially towards the impeller center plane, which is in agreement with experimental observations. To examine the flow structure around impeller blades, the predicted mean velocity field behind the impeller blades of the Rushton turbine at three different angles from the blade (8°, 15°, 30°) are shown in Fig. 10.11. The presence of trailing vortices and their movement within the impeller stream are clearly evident from this figure. Comparison of these predicted results with the experimental data of Schafer et al. (1997) shows good qualitative agreement. The predicted strengths of the trailing vortices are found to be somewhat lower than the experimental values, which leads to relatively early dissipation of trailing vortices in the simulations.

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

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