*2.1. Geometry and Mesh*

In this paper, the simulation was performed by using the commercial CFD solver ANSYS Fluent. The geometry of the prototype pump turbine of the Tianhuangping pumpedstorage power station was implemented, and it was the same as that in previous work [23]. A geometric model is shown in Figure 1, and the characteristics of the parameters are listed in Table 1.

**Figure 1.** Pump turbine's (**a**) geometry and (**b**) GV number.



The dynamic meshing technique was used to control the movement of the GVs. Considering the geometry of the GVs and the deformation form of the mesh, a prism mesh was applied in the guide vane domain and stay vane domain (shown in Figure 2). In addition, in order to resolve the near-wall flow, a boundary layer mesh was implemented. In this case, the max Y+ was about 100 in the guide vane domain. A tetrahedral mesh was used in the rest of the domains due to the complex geometries.

**Figure 2.** Mesh of the guide vane domain.

To ensure the accuracy of the results and to keep the computational cost at the minimum level, five sets of different meshes with 7.5 million elements, 8.9 million elements, 9.5 million elements, 11 million elements, and 12 million elements were used in a mesh independence study. The results will be discussed in the "Mesh and Time-Step Independence" section.

## *2.2. Boundary Conditions*

The inlet discharge laws under the 610 m head, which were obtained from a transient process simulation of the Tianhuangping pumped-storage power station (shown in Figure 3), were selected for the boundary condition settings in this study. A velocity inlet and pressure outlet were implemented. A constant runner rotational speed was set at 500 rpm, while the opening rate of the GVs was 1/60 s and the closing rate was 1/25 s. In this case, *Re* = 106.

**Figure 3.** *Cont*.

**Figure 3.** Discharge law of the transient process simulation of the Tianhuangping pumped-storage power station: (**a**) discharge law of the startup process; (**b**) discharge law of the shutdown process.
