**4.6 POD analysis**

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

to the development of the trailing vortices of the Rushton turbine [18, 19]. The trailing vortices are more extended by using the concave blade. However, the flow

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

reaches the bottom of the tank faster by using the convex form.

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

**Figure 18.**

**Figure 19.**

**175**

*POD field for the PDh, PI convex.*

**Figure 17.**

*POD field for the convex blade.*

*POD field for the PDh, PI concave.*

#### **Figure 14.**

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

**Figure 15.** *POD field for the flat blade.*

**Figure 16.** *POD field for the concave blade.*

narrowed loop is created by the concave shape, which can be explained by the axial velocity above the impeller. The clockwise and the counter clockwise (CW-CCW) vortex pair at the blade tip can be clearly seen at the highest modes that look similar to the development of the trailing vortices of the Rushton turbine [18, 19]. The trailing vortices are more extended by using the concave blade. However, the flow reaches the bottom of the tank faster by using the convex form.

**Figure 17.** *POD field for the convex blade.*

**Figure 18.** *POD field for the PDh, PI concave.*

**Figure 19.** *POD field for the PDh, PI convex.*

narrowed loop is created by the concave shape, which can be explained by the axial velocity above the impeller. The clockwise and the counter clockwise (CW-CCW) vortex pair at the blade tip can be clearly seen at the highest modes that look similar

**Figure 14.**

**Figure 15.**

**Figure 16.**

**174**

*POD field for the concave blade.*

*POD field for the flat blade.*

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

*Vortex Dynamics Theories and Applications*

several results were evaluated which contain velocity field, axial and radial velocity distribution, root mean square velocity, vorticity, and the turbulent kinetics energy. Two circulation loops were presented. The jet flow is more intensive for the convex blade turbine. However, the concave configuration produces a larger lowest loop than the other configurations. Hence, the downer region of the tank is more turbulent than the flat and the convex configurations. The maximum radial velocity generated by the flat blade turbine spreads to reach farther places. This can be explained by the ability of the blade shape to generate training vortices. The convex shape of the blade gives the turbine the ability to move easily within the water and transmit more velocity and energy while not giving it enough capacity to expand much. In fact, it has been noted that the convex blade is not able to create a large fluctuation on the turbulent flow and local vortices are created. In addition, it has been noted that the fluctuation of the flow is dominated by the trailing vortices more than by the recirculation loops. For the staged system, an oblique flow is created between the two impellers, and turbulent fluctuations are greater at this

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

region due to the interaction between the blades.

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

Bilel Ben Amira\*, Mariem Ammar, Ahmad Kaffel, Zied Driss

\*Address all correspondence to: bba.amira7@gmail.com

Laboratory of Electromechanical Systems (LASEM), National School of Engineers

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**Author details**

**177**

and Mohamed Salah Abid

of Sfax, University of Sfax, Sfax, Tunisia

provided the original work is properly cited.

**Figure 20.** *POD field for the PDb, PI concave.*

**Figure 21.** *POD field for the PDb, PI convex.*

For the staged systems (**Figures 18–21**), it can be seen that many vortices are created at the region localized between the two blades. This region represents the interaction between the highest and the lowest impeller. Hence, the flow becomes more energetic that explain the cause of the development of these vortices. The flow reach the free surface as well as bottom of the tank faster by mounting the flat turbine at the top of the tank. The trailing vortices become more energetic by using the combination between the flat blade at the bottom and the convex blade at the top.

The development of the different modes shows that the shoes of the combination is extremely important and can affect the mixing inside the vessel. Consequently, the combination between impellers can lead to affect the final product in terms of homogeneity and the cost in terms of the time mixing and power consumption. This found contradicts what has been observed in the study of the mean velocity field, as it gives almost the same results. In addition, it proves that the mean flow is not able to show the real behave of the flow.

## **5. Conclusion**

The objective of this paper is to investigate experimentally the hydrodynamic structure of the curved blade turbine using the particle image velocimetry. Thereby,
