**4. Results and Discussion**

The partial results of the Original and the Turbine performance tests indicated the possibility of creating a new construction, which would be a combination of both variants. The aim was to maintain efficiency improvement while minimizing modifications to the pump. In accordance with these requirements, the calculation model was modified, and another variant of PAT was developed, which is referred to as "Hybrid" in the following text. The key outer dimensions of the Hybrid impeller remained the same in order to avoid volute casing modification. The purpose of this variant was to reduce the cost of the modification and, thus, the final price of PAT. The specific geometric parameters of the impeller are subject to the know-how of the author of the modification. It is the intellectual property of the university (CULS Prague) and can be provided on request. To manufacture this variant, the rear shroud of the original pump impeller was again used as a basis. Metal alloy blades were glued to the front shroud, and the entire product was glued to the rear shroud. The final appearance of PAT with this impeller visually corresponds to the variant in Figure 6 on the left.

The following charts indicate the performance characteristics of selected parameters depending on the shaft speed for all three variants of PAT—Original, Turbine, and Hybrid. The curves are created by mean values of three measurements at constant net head of 10 m, 20 m, and 30 m. There are also standard deviations marked on the curves. Values and curves corresponding to the unmodified Original variant are marked in blue. The characteristics of the Turbine and Hybrid variants are marked in red and green, respectively.

Figure 9 presents the first series of characteristics, which are the efficiency courses in dependence on the shaft speed. The increase in efficiency in both innovated variants is obvious. The absolute values of the efficiencies for BEP are summarized in Table 3. The relative increase regarding the Original is indicated in Table 4. The comparison at BEP also indicates a shift in the shaft speed to lower values, especially for the Hybrid variant.

**Figure 9.** Efficiency in terms of dependence on shaft speed.

Figure 10 presents another series of characteristics—the dependence of torque on shaft speed. The comparison again indicates that the Turbine and the Hybrid variants prove higher torque, especially at lower speed.

**Figure 10.** Torque in terms of dependence on shaft speed.

The mechanical power output courses (see Figure 11) basically copy the trends of the efficiency courses. The absolute values of the achieved power outputs obviously increase with increasing net head. The characteristics of the Turbine and the Hybrid also indicate a noticeably greater distance between the curves at higher net heads towards higher values. It is caused by a higher flow rate, as compared to that of the Original.

**Figure 11.** Courses of power output in terms of dependence on shaft speed.

The last series of characteristics represents courses of flow rate in terms of dependence on shaft speed (see Figure 12). The graphs of the flow rate courses indicate that the impeller´s flow rate decreases with increasing shaft speed. This characteristic also applies to Francis turbines with low specific speeds [20]. This is caused by the increasing centrifugal force, which acts against the centripetal direction of water flow.

**Figure 12.** Courses of flow rate in terms of dependence on shaft speed.

**Table 3.** (**a**) Overview of absolute values of performance parameters achieved at BEP at net head of 10 and 20 m. (**b**) Overview of absolute values of performance parameters achieved at BEP at net head of 30 m.




The variability of the flow rate can be used in cases where PAT functions as a replacement for the throttle valve in water distribution networks (WDN). In this case, PAT must be equipped with shaft speed control (e.g., by means of a frequency converter). The disadvantage of these applications is the resulting small range of flow control. Here, in the case of the Original variant, it is possible to regulate the flow rate by changing the shaft speed in the range of 33% of the nominal flow rate (*Q* = 0.77 ÷ 1.1·*QBEP*). The Turbine variant shows higher flow rate, but the regulation range is roughly the same (i.e., 33% again (*Q* = 0.8 ÷ 1.13·*QBEP*)). From this point of view, the most interesting is the Hybrid variant, where the steepest course of the flow rate was indicated—from the highest Turbine values to the lowest Original values. In absolute value, the Hybrid variant allows regulation of up to 44% of the nominal flow rate (*Q* = 0.66 ÷ 1.1·*QBEP*). This modification therefore also opens a greater potential for the use of PAT as a replacement for a throttle valve.

The following Table 3 summarizes the absolute values of the performance parameters achieved at BEP. The values were corrected using affine relations to a constant net head of 10 m, 20 m, and 30 m.

From the achieved results, the relative increase in the parameters of the Turbine and the Hybrid variant related to the Original was subsequently determined:

$$
\Delta A = 100 \cdot \frac{A\_{\rm m} - A\_0}{A\_0} \quad \text{(\%)}\tag{6}
$$

where *A*<sup>0</sup> is a parameter of the Original and *Am* is a parameter of the modification (Turbine or Hybrid). An overview of the relative increases in the performance parameters in comparison with those of the Original is presented in Table 4.

The technical implementation of such modifications is a challenge. Every PAT modification means an increase in price. From this point of view, the Hybrid variant, considering only a modification of the impeller, appears to be the most advantageous. The volute casing and the draft tube do not have to be modified. At present, the problem of impeller manufacturing could be solved with the help of so-called additive technologies, as they can be used to manufacture virtually any geometry. An alternative way is to manufacture only the impeller blades along with the front shroud. This unit can be then glued or welded to the rear shroud. The resultant experience and test results with such 3D printed impellers are presented by Polák [24].

#### **5. Conclusions**

The focus of this study is two-fold. The first focus is the presentation of a calculation model for the design of a low specific speed Francis turbine impeller. The second focus is an experimental verification of the results of this model for the design of PAT innovation in order to increase its efficiency. The algorithm of the calculation model combines the original graphic–numerical design of the geometry of the Francis impeller so that it is as user-friendly and clear as possible. The example of the numerical solution described in this article presents the results of the design of particular PAT with an impeller with a diameter of *D*<sup>1</sup> = 132 mm and a specific speed of *Ns* = 80 min−1. A comparison of the geometry characteristics designed by the model with the realized Francis turbine impellers gives a corresponding likeness.

Based on the theoretical results, the manufacture of the impeller proposed by the calculation model was instigated. Thus, the Turbine variant, with a new impeller geometry and modification of the closely adjacent parts (i.e., the volute casing and the draft tube), was created.

Testing on a test circuit at 10 m, 20 m, and 30 m head proved that the Turbine variant has a positive effect on improving the efficiency of PAT—in terms of absolute value, the efficiency increased by up to 10% in optimal operation (BEP). The modification further resulted in a flow rate increase of roughly 8%. Added together, the overall PAT power output was increased by 25%. Due to the changed geometry of the impeller blades, the torque was increased by 20 to 30%. These promising results led to the modification of the

calculation model, as well as the construction and testing of another variant—the Hybrid. Its mission was to maintain the positives achieved by the Turbine, but at the same time, to minimize the massive interventions and modifications of the original pump. The results obtained with the Hybrid variant in BEP are as follows: In absolute terms, the efficiency was 10 to 11% higher than that of the unmodified Original variant. The flow rate was about 20% higher. This resulted in an even greater increase in overall power output of 37 to 45%. There was also a significant increase in torque of up to 60%. However, the Hybrid variant had, in BEP, significantly lower shaft speed (approximately by 15%) than the Original. On the other hand, it provided a wider control of the flow range (*Q* = 0.66 ÷ 1.1·*QBEP*), which is advantageous when using PAT as a throttle valve in WDN. In summary, it can be stated that the modifications proposed by the calculation model have a significantly positive effect on increasing the efficiency of PAT operation.

In addition to the modifications described above, another way to increase the efficiency of PAT is to modify the adjacent parts. This mainly concerns a draft tube. Its significance increases as specific speed increases. Further research specifically on high-speed machines will be focused on solving this problem.

**Funding:** This research has been supported by the IGA 2020:31130/1312/3115 Analysis of liquid flow in hydrodynamic pump and in pump as turbine.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are openly available at [10.5293/IJFMS. 202015.8.3.169].

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Nomenclature**


#### **Subscripts and Superscripts**

