*3.1. Results of the Fluid Dynamics Model*

The following Figures 7–11 and 12A,B show the characteristic curves obtained from the fluid dynamic model for the range of pumps under examination, both in turbine and pump operation. In this case, the geometric parameters of the pumps are known, as they have been measured, and therefore the model processes these values according to the machine prototype described above. These curves are compared with those measured experimentally to highlight the deviation and an error band of 5%.

**Figure 7.** (**left**) Head and efficiency for the PAT 40-335 (ns = 9.05) in pump operation. (**right**) Head and efficiency for the PAT 40-335 (nst = 5.52) in turbine operation.

**Figure 8.** (**left**) Head and efficiency for the PAT 80-220 (ns = 32.69) in pump operation. (**right**) Head and efficiency for the PAT 80-220 (nst = 26.91) in turbine operation.

**Figure 9.** (**left**) Head and efficiency for the PAT 40-250 (ns = 12.78) in pump operation. (**right**) Head and efficiency for the PAT 40-250 (nst = 8.81) in turbine operation.

**Figure 10.** (**left**) Head and efficiency for the PAT 50-160 (ns = 31.01) in pump operation. (**right**) Head and efficiency for the PAT 50-160 (nst = 26.03) in turbine operation.

**Figure 11.** (**left**) Head and efficiency for the PAT 80-160 (ns = 40.24) in pump operation. (**right**) Head and efficiency for the PAT 80-160 (nst = 32.94) in turbine operation.

**Figure 12.** (**left**) Head and efficiency for the PAT 100-200 (nst = 43.48) in pump operation. (**right**) Head and efficiency for the PAT 100-200 (nst = 35.91) in turbine operation.

As can be seen in the Figures 7–11 and 12A,B, in turbine operation, the PATs are able to provide satisfactory performances under nominal operating conditions. To the right of the BEP point, the efficiency drops slowly, and this represents an advantage of the PATs, because it allows working with good efficiency in a wide range of flow rates. Nevertheless, there are no very high efficiencies, if compared to traditional machines, such as small Francis and Pelton turbines. The main cause is linked to the fact that the PATs are not designed to work as a turbine, and for this reason they are not optimized. In addition, there are instability phenomena that occur inside the machine when it operates outside the design conditions. This instability can occur as follows:


There are therefore strong fluctuations in the torque that is transmitted to the machine shaft which, in the transition from pump to turbine operation, requires long synchronization times of the machine with the generator. The PAT is therefore not able to adapt to the variations of the energy required by the network. These fluctuations can also occur during turbine operation, during synchronization with the generator at the frequency of the electrical network in the starting or braking phase, and for low flow rates or when the load applied to the shaft is zero, as the hydraulic energy is entirely dissipated by the friction in the bearings and the impeller does not accelerate. Regarding pump operation, centrifugal pumps are operating machines and, to obtain high efficiencies, they are designed

to minimize losses. The best pump efficiencies are obtained for machines with high specific speeds. The shape of the impeller is less critical and allows a more regular fluid passage; there are no abrupt changes in shape or strong bends. However, high specific speed pumps process high flow rates but low heads. For low specific speed values, these machines are designed exclusively to provide high heads at the flow rate, at the expense of efficiency. To obtain high heads, the impeller assumes a 'pan' conformation; it is very flattened, and the fluid threads have strong curves, producing high pressure drops and therefore low performances. For example, the 40-335 pump has low efficiency because it only produces head. It must therefore centrifuge, and it is necessary to increase its diameter, flattening its shape.
