*4.1. Torque Produced by PAT on Different Flow Values*

A pump with a flow of 192.1 L/s was designed using the ANSYS (Vista CPD) tool, consisting of a volute and impeller with six blades, as shown in Figure 8. A flow analysis through PAT was conducted in ANSYS CFX [13,28], in which water was used as the material, and the standard atmospheric pressure was considered to be one atm.

**Figure 8.** Side views of the pump designed in Vista CPD.

The pump was meshed using TURBO GRID, while the impeller and volute were separately meshed, achieving a good quality mesh, as shown in Figure 9.

**Figure 9.** Meshing of the impeller and volute.

A detailed mesh report is provided in Table 4, which demonstrates the domains of the analysis, location of the domains, number of nodes, and number of elements.


**Table 4.** Mesh report of the pump.

The mesh independence is checked for the pump and eight different cases with regard to. element numbers, which are obtained by changing the element size and global size factor for the volute and impeller, respectively. Element sizes of 15, 20, 25, 30, 35, 40, 45, and 50 mm were applied for the volute in meshing, yielding 330,438, 281,176, 258,746, 248,172, 240,762, 237,168, 234,902, and 232,452 elements, respectively. In contrast, the global size factor was the main parameter that was manipulated for impeller meshing, achieving a range of eight element numbers. Different global size factors for the impeller were assigned in TURBO GRID; the 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, and 1.5 sizes produced 141,792, 203,553, 280,080, 385,118, 501,128, 781,482, and 1,019,900 elements, respectively. The output parameter was the velocity at the outlet, which is demonstrated by the mesh independence test shown in Figure 10; 886,386 elements were selected for the simulations, which were produced by a 25-mm element size and a 1.3 global size factor.

**Figure 10.** Meshing independency test of the pump.

The steady-state boundary conditions for this simulation were set for the PAT. The stationary (S1) domain is the volute, while the rotating (R1) domain is the impeller of the pump. The inlet was assigned a boundary condition for the mass flow, while the outlet was the pressure, and the standard atmospheric pressure was assigned. The blade and all other boundary walls were assigned a boundary condition (no slip). A frozen-rotor mixing model was adopted for the interface between S1 and R1. The SST turbulence model was applied for the flow analysis, while in the solver control panel, a high resolution was applied as an advection scheme, 1.0 × <sup>10</sup>−<sup>5</sup> for convergence, first order for numeric turbulence, and SIMPLEC [27,29,30]. Transient or unsteady simulations were also performed after steady simulations. The total time was set to 1 s, the time step to 0.0001 s, and the initial time value to 0 s for the transient case. The transient rotor-stator mixing model was assigned to the interface between S1 and R1. Cartesian velocity components were selected as u = 0 m/s, v = 0 m/s, and z = 0 m/s for the global initialization [31].

Here, the pump functions as a turbine; therefore, the outlet of the pump is the inlet of the PAT, and the direction of the flow of water through the PAT is shown in Figure 11.

**Figure 11.** Direction of the flow of water for the PAT.

As indicated in Section 2.1, the torque produced by the variable water flow was calculated using ANSYS CFD-Post, which is a function calculator. A graphical representation of the flow and the produced torque is shown in Figure 12a. When the PWC is integrated, and a new range of flows at the inlet of the PAT is obtained, the model is simulated once again to calculate the new torque produced by the new values of the water flow. A graphical representation of the new flow and torque produced is shown in Figure 12b.

**Figure 12.** Torque produced by PAT (**a**) before PWC integration and (**b**) after PWC integration.

The torque produced by the PAT at variable and smooth flows is compared in Table 5, along with the deviations given before and after the integration of the PWC. These results clearly demonstrate that the values of the produced torque decrease with decreasing flow. Hence, fluctuations in the flow rate significantly affect the torque of the PAT. When the flow rate is kept constant with the integration of the PWC, the torque of the PAT is smoothed and maximized according to the design flow.


**Table 5.** Torque of PAT regarding different flow values.

#### *4.2. Generator Behavior on the Variable and Smooth Torque*

Although a smooth torque is obtained, which ultimately smooths the output of the PAT, in most cases, the PAT and generator are directly coupled. However, a Simulink model was developed to observe the behavior of the generator with variable and smooth torques, as shown in Figure 13.

**Figure 13.** Overall system to observe the behavior of the generator.

A built-in asynchronous machine block rated at 37 kW was selected from the Simulink library to simulate the behavior of the generator. This block can simulate both motors and generators, using (+) and (−) signs with the torque, respectively. The variable and smoothed torques obtained from ANSYS CFX, as shown in Figure 14, were used as the input signals in the Simulink model [32,33]. The model was simulated for 25 s, and each duration of five seconds corresponds to a different torque value.

**Figure 14.** Torque input signal to the generator.

The simulation results of the peak value of the generator current are shown in Figure 15, which demonstrates the variations in the current with respect to the torque obtained from the PAT. In a hydro system, the torque varies with the flow variation. The current depends on the torque value. Therefore, any fluctuation in the flow rate affects the output current of the generator. However, the PWC technique provides a smooth flow, which results in a smooth output.

**Figure 15.** Output current of the generator for both variable and smooth torques.

#### **5. Conclusions**

A simple and economical PWC technique was proposed in this study to maintain the design flow at the inlet of a PAT under variable flow conditions. The proposed technique employs the series integration of parallel water columns with the same dimensions using a double-nozzle design. Paralleling the water columns creates more space for water to provide the design flow at the outlet. When water flow is decreased owing to a decrease in the upstream flow or in a PHS facility, the PWC maintains a flow at the inlet of the PAT by acting as an axillary penstock.

The design of the experiment and its findings indicate that, for a given case, the designed flow of 192.1 L/s can create a maximum torque of 226.559 Nm. The reduction in the flow to 153.7 L/s produced a reduced torque of 145.042 Nm. A total reduction of 38.4 L/s in the water flow was compensated for by integrating five PWCs, each having a flow capacity of 8 L/s. After the integration, the new flow and torque values were 193.7 L/s and 230.342 Nm, respectively, which were nearly identical to the designed values with a deviation of only 1.64%. Furthermore, based on the smooth output of the PAT, the generator output was confirmed. Thus, integration of the PWC using a double-nozzle design is an effective technique for maintaining smooth output of the PAT and generator.

**Author Contributions:** Conceptualization, S.H. and M.H.; methodology, M.H. and T.Y.; software, S.H. and G.A.; formal analysis, M.H., T.Y. and G.A.; writing and draft preparation, S.H., M.H. and T.Y.; review and editing, T.Y. and G.A.; supervision, H.-W.C. and M.H.; funding acquisition, H.-W.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This work was supported by the National Research Foundation of Korea (NRF) grant funded by the South Korean government (No. 2022R1I1A3072104).

**Conflicts of Interest:** The authors declare no conflict of interest.
