**4.4 Vorticity**

**Figure 11** shows the vorticity generated with the curved blade turbines. According to these results, the bulk region of the tank is presented with the medium vorticity value. For the flat and the concave configurations, the propagation of the vorticity is larger than the convex blade. The highest value area is localized in the upper region of the tank which follows the first circulation loop at the same direction of the von Kármán vortex street. The lowest value area is localized in the inferior region of the tank which follows the same direction of the second circulation loop. In fact, it has been noted that the highest recirculation loops are more energetic than the lowest ones. For the convex blade two maximum regions are created presenting the clockwise and the counterclockwise (CW-CCW) vortex pair at the blade tip.

For the staged system (**Figure 12**), the vortical structures are localized at the region between the two blades at the same direction of the discharge flow of each blade, which explains the domination of the trailing vortices at the turbulent flow. **4.5 Turbulent kinetic energy**

**Figure 12.**

**Figure 13.**

*Vorticity for the staged system.*

**4.6 POD analysis**

**173**

of the concave blade than the convex blade.

*Dimensionless turbulent kinetic energy distribution of the one-staged system.*

**Figure 13** shows the distribution of the turbulent kinetic energy of the curved blade turbine. The turbulent kinetic energy is dimensionless by the square of the tip velocity. According to these results, the turbulent kinetic energy is maximum at the blade tip, and it decreases progressively moving away from the blade. As it was found in the previous sections, the convex blade dissipates the highest energy in the flow. The energy produced by the flat blade decreases by 37% and by 27% for the concave configuration. For the staged system (**Figure 14**), the maximum turbulent kinetic energy is localized between the two blades at the same direction as the trailing vortices. In addition, the turbulent kinetic energy is larger at the association

*The Effects of Curved Blade Turbine on the Hydrodynamic Structure of a Stirred Tank*

*DOI: http://dx.doi.org/10.5772/intechopen.92394*

In this section, we used the decomposition of the flow basing on the eigenvalues. This method allows to reveal the smallest vortical structure that cannot be seen by the usual mean flow according to its energetic amount by using the dimensionless eigenfunction. In fact, many vortices are presented with different sizes and shapes. For the one-staged system (**Figures 15–17**), the loop created at the blade tip is the most energetic. The largest one is obtained from the flat turbine. However, the

**Figure 11.** *Vorticity for the one-staged system.*

*The Effects of Curved Blade Turbine on the Hydrodynamic Structure of a Stirred Tank DOI: http://dx.doi.org/10.5772/intechopen.92394*

**Figure 12.** *Vorticity for the staged system.*

**Figure 13.**

convex blade is not able to create a large fluctuation on the turbulent flow and local

**Figure 11** shows the vorticity generated with the curved blade turbines. According to these results, the bulk region of the tank is presented with the medium vorticity value. For the flat and the concave configurations, the propagation of the vorticity is larger than the convex blade. The highest value area is localized in the upper region of the tank which follows the first circulation loop at the same direction of the von Kármán vortex street. The lowest value area is localized in the inferior region of the tank which follows the same direction of the second circulation loop. In fact, it has been noted that the highest recirculation loops are more energetic than the lowest ones. For the convex blade two maximum regions are created presenting the clockwise and the counterclockwise (CW-CCW) vortex pair

For the staged system (**Figure 12**), the vortical structures are localized at the region between the two blades at the same direction of the discharge flow of each blade, which explains the domination of the trailing vortices at the turbulent flow.

vortices are created.

*Rms velocity for the staged system.*

*Vortex Dynamics Theories and Applications*

**4.4 Vorticity**

**Figure 10.**

at the blade tip.

**Figure 11.**

**172**

*Vorticity for the one-staged system.*

*Dimensionless turbulent kinetic energy distribution of the one-staged system.*
