2.3.3. Flow Rate Measurement, Uncertainty

The values of flow rate (discharge) were calculated based on the difference of pressures measured between the inlet/outlet cross-section of the tested pump-turbine (cross-section (*B-B*)) and the reservoir (cross-section (*A-A*)) and accounting for *Fe* factor obtained using CFD. Calculations were carried out using the computer program *GIB-ADAM* that has been tested and successfully verified on many occasions related to the implementation of laboratory tests as well as e.g., efficiency tests in hydropower plants [11]. Examples of the results measured or calculated for both modes of operation of the pump-turbine under investigation are shown in Figure 9. Measurements begin ca. 30–40 s before shut-off device start closing and end about 30–60 s after its complete closure or after extinction of the free pressure oscillation remaining in the flow system after the flow cut off. The time of closing the wicket gates of the tested machine was about 25 s and 20 s during turbine and pumping mode of operation, respectively. These time intervals were (8–10) times longer than the pipeline pressure wave period of about 2.5 s. Closing of the wicket gates was carried out in two stages in both modes—the faster stage followed by slower one. The reason for this common method of closing the wicket gates is to maintain the safety of the hydraulic system by preventing excessive pressure oscillations caused by too rapid shut-off of the flow, especially in the final phase of wicket gates closing.

The analysis of the influence of the above-mentioned and other parameters on the uncertainty of the results of the flow rate measurement with the applied method is presented in Appendix C.

**Figure 9.** Examples of measured values of wicket gates opening and pressure difference and discharge through the machine calculated using the pressure time method. Left view: turbine operation mode, right view: pump operation mode.

#### **3. Results and Discussion**

The volumetric gauging method of flow measurement, due to the high requirements that must be met, is difficult to apply when testing real objects. For this reason, the examples of its practical application are quite rarely published. More valuable are the results presented in this paper, which were obtained for a pumped-storage power plant equipped with an artificial head water reservoir with known geometric characteristics. This made it possible to use the volumetric gauging method to measure the flow rate through the tested reversible hydrounit. The required narrow uncertainty band was obtained by supplementing the method with a special solution for accurate measurement of the water level change in the reservoir that also allowed including the impact of waves, as well as the amount of rainfall and leaks during measurements. It should be emphasized that measuring the upper water level in a standard way usually cannot ensure sufficient accuracy of the volumetric gauging method used for measuring flow in hydroelectric power plants.

The application of the pressure-time method to measure the flow rate in a real flow system with complex geometry additionally requires the use of an innovative calculation methodology to determine the *F*-factor—one of the critical parameters for maintaining a sufficiently narrow measurement uncertainty band. Owing to this factor, the geometrical characteristics of a pipeline measuring segment and impact of its flow elements on flow irregularities are taken into account. Disregarding changes in flow velocity profiles resulting from the variable shapes of pipeline elements leads to an increase in the inaccuracy of measurement using the pressure-time method, which cannot be corrected only by improving the modeling of friction losses in these elements, as discussed in [27–29] or by improving the computational model [22,28]. In addition, increasing the accuracy of estimation of the leakage rate through closed-flow shut-off devices is not enough [26]. In order to take into account changes in liquid velocity profiles in pipeline bends, the authors proposed a special calculation procedure (described in [24]) using CFD analysis for correction of the *F* factor. Verification of this procedure based on the analyzed examples confirmed that its application significantly increases the measurement accuracy of the pressure-time method. In this paper, the procedure based on CFD has been extended and used for piping systems with complex geometry (including curves, branches, conical elements, and inlets with changes in the shape of the flow section). In contrast to such a solution, the standard application of the pressure-time method does not provide the required uncertainty of flow rate measurement results. This innovative procedure provides the basis for using the pressure-time method in case of geometrically complex pipelines, and not only in turbine mode of operation, but also in the pump flow conditions of the tested reversible machine.

The uncertainties (standard and expanded) of the flow rate measurement results using both methods under consideration were as follows:

