*3.2. Pumping Operation Mode*

The use of the Winter–Kennedy method for measuring flow rate in the pump mode of operation of hydraulic machines is not recommended by the standards [4–6]. This made it impossible to compare the pressure-time and volumetric gauging methods in a manner analogous to that used for turbine mode of operation, i.e., based on the results of simultaneous flow measurements. The comparison of results obtained using the analyzed methods was made by referring them to the head of the plant—Figure 11. The analysis also covered the impact of the penstock geometry irregularities on the results obtained using the pressure-time method. The differences between the discharge results obtained from the volumetric gauging method and pressure-time method were from −0.16% to +0.58% for lower (426 m) and higher head (439 m), respectively. Without correction of *F* geometrical factors, the differences were much greater—their values were +0.6% and +1.35%, correspondingly.

The comparison shows that the differences between the results obtained using the analyzed methods are much larger for pump mode of operation than for turbine mode of operation. At this stage of research, the causes of such observations cannot be clearly explained. Measurement of the hydraulic machine discharge using the pressure-time method is much more difficult to perform in pump operation than in turbine operation. This fact may suggest the reasons for this comparison results. This may also be the main reason why current standards do not recommend using this method in pump mode of operation of tested machines. However, it should be emphasized that the differences obtained in the analyzed case are still within the range of the measurement uncertainty characterizing the compared methods.

In addition, it should be emphasized that between the pump and turbine modes, in addition to obvious differences, there are those that can significantly affect the results obtained using the pressure-time method:


Precise identification of how these differences may affect the final accuracy of flow measurement results obtained with the pressure-time method in the pump mode of operation of the hydraulic machines requires thorough professional testing and analysis. Currently, there is insufficient data on this topic, which hinders the extension of the applicability of this method and can also lead to excessive simplifications resulting in increased measurement uncertainty.

**Figure 11.** Pump operation mode of the tested hydrounit: Comparison of the discharges measured by the volumetric gauging method and the pressure-time method.

#### **4. Conclusions**

The paper presents experiences concerning the use of the volumetric gauging method and the pressure-time method for measuring the water discharge through a reversible hydraulic machine at a pumped storage power plant. Research using these methods concerned both turbine and pump mode of operation of the tested machine. As part of the research, new original procedures have been used aimed at significant reduction of the measurement uncertainty.

In the case analyzed in the article by appropriate treatment consisting of the use of high-quality transducers, with the use of appropriate measurement techniques and procedures supporting the measurements of the flow rate with the use of both methods, a satisfactorily low measurement uncertainty was achieved.

The use of a high-class transducer measuring the pressure difference between the upper reservoir and the auxiliary tank in the volumetric gauging method, as well as the original method of analysis of the measured pressure difference, allowed to increase the accuracy of measuring the change in water volume over time significantly, and also allowed us to take into account water waving, which, when ignored, can meaningly distort measurements.

The pressure-time method, which required taking into account the complex geometry of the pipeline connected to the tested hydrounit, was supported by CFD analysis of flow in the area of geometric irregularities (inlet, diameter changes, elbows, changes in cross-sectional shape). The original procedure using the results of this analysis provided the information necessary to introduce appropriate adjustments (correction) to the geometric factor *F*, which in turn, contributed to a significant reduction in the flow rate measurement uncertainty.

In contrast to the very good compliance of the results of discharge measurements obtained with the analyzed methods for the turbine operation of the tested machine (differences in the range of ±0.2%), in the case of pump operation, larger differences between the results were observed; however, they were still in the uncertainty band for measuring each of these methods independently (differences from −0.16% to +0.58%). At this stage, it is difficult to clearly explain these observations. The authors point out the differences in the course of flow phenomena during shut-off in turbine and pumping operation carried out as part of tests executed using the pressure-time method. There is a need for further research to explain the reasons of the obtained differences and their influence on the accuracy of discharge measurement using the pressure-time method in pump operation mode.

It is worth emphasizing the positive effect achieved by using the CFD procedure to support the pressure-time method. A measure of this effect is the reduction of the differences between the measurement results obtained using the volumetric gauging method and the pressure-time method. In the turbine operation mode, the CFD-based correction of the *F* factor resulted in a 1.5-fold increase in the convergence of the compared results. In the case of pumping mode of operation, the convergence has improved several times (more than 2- to almost 5-fold, depending on the point of operation). This result proves the correctness of the assumptions made when using the CFD procedure and using its results for the pressure-time method of measuring the flow.

Particularly noteworthy are the results obtained for the pumping mode of operation, for which the use of the pressure-time method is not recommended by the standards. The comparison and consistency of these results with the results obtained with the volumetric gauging method confirmed the correctness of the assumptions underlying the proposed and applied modifications to the calculation procedure of the pressure-time method. This includes also the correct consideration of the temporary change in the flow direction occurring during its cutting off in the pumping mode of operation. Such experience from using this method in practice can help working out the relevant changes in the standards leading to the recommendation of the pressure-time method also for the pumping mode of reversible hydraulic machine operation.

**Author Contributions:** Conceptualization, A.A.; Data curation, W.J. and M.L.; Formal analysis, A.A.; Investigation, W.J. and M.L.; Methodology, W.J.; Software, W.J.; Supervision, A.A.; Validation, W.J. and M.L.; Visualization, M.L.; Writing—original draft, W.J. and M.L.; Writing—review & editing, A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was financed from the statutory funds of The Szewalski Institute of Fluid Flow Machinery. **Conflicts of Interest:** The authors declare no conflict of interest.
