The increasing popularity of renewable energy in power systems requires large-scale energy storage technology to compensate for their intermittency [
1]. A pumped storage hydropower (PSH) station is an ideal peaking and emergency appliance because of its flexible operation and quick response. It is not only suitable to use as the peaking load shifting, but also has several performances and dynamic benefits such as frequency and phase modulation, emergency reserves, black startup, and load adjustment, among others [
2,
3]. In the PSH station and diversion power station, a long pipeline is always connected to the front of the unit spiral case and the tail of draft tube [
4]. The flow rate of the unit varies with the working condition, which leads to dramatic rise and fall of the internal pressure in the pipeline, also known as the phenomenon of water hammer, and finally induces instability of the unit [
5,
6,
7]. Therefore, it is necessary to investigate the changing process of the water flow in a pipeline to ensure the safety of the hydropower systems [
8].
Nowadays, there are three methods to research the transient process: the one-dimensional method of characteristics (MOC), the experimental method, and three-dimensional (3D) numerical simulations based on computational fluid dynamics (CFD). Among these approaches, the experimental method [
9] is considered as the most reliable way to investigate the transient process. However, this method is restricted by factors such as funding, security, and test control conditions, so the advantages of this method could not be fully harnessed. The MOC approach can perform an effective prediction of water hammer characteristics, but is inadequate to predict detailed dynamic 3D characteristics such as unit variation regularity, inner flow configuration, and dynamic instability of the PSH unit [
10]. Currently, in order to study the transient behavior on mechanisms and the flow field of turbines, 3D CFD simulation [
11] received extensive attention, as it is very useful to predict flow configuration of hydraulic machinery under normal conditions. Furthermore, the spiral flow can be found through 3D numerical method and the attenuation law of pressure wave obtained by 3D calculation is closer to the actual situation, which is helpful to analyze the transient flow characteristics of pressure wave superposition or wave peak not in the first period.
On the basis of the technical and economic requirements of power stations’ construction, most PSH stations adopt one conduit system shared by multiple units, which will inevitably lead to hydraulic disturbances between units during the transient process. Chen et al. [
12] performed research on the hydraulic turbulence of a high-head PSH station in China. They found that the stable area was different from one of the small load disturbances, and if the parameters of the governor were optimum for load disturbance, the remaining machines were stabilized under hydraulic disturbance. Zhang et al. [
13] conducted some experiments based on a hydropower model, which combines partial diversion tunnels with tailrace tunnels, and interactions between the air and water phases were observed in the combined diversion tunnel, which would significantly alter flow dynamics. With the increasing attention to pipeline safety, the study on flow regime in pipelines has become a relevant research topic. Cheng et al. [
14] applied a 3D-CFD code with the volume of fluid (VOF) model to simulate the complex free surface-pressurized transient flow and the combined transient flow under a load rejection condition. Wang et al. [
15] combined the MOC and the method of implicit (MOI) to simulate an unsteady flow in a pipeline and hydropower transient processes, then the effectiveness of the coupled method was verified by simulating the water hammer in a uniform and variable area duct, and water level fluctuation in a surge tank. Xia et al. [
16] conducted numerical simulations through 1D-MOC and 3D methods, respectively, of a long distance water pipe with an air-cushion surge tank, and achieved relatively consistent results. Zhou et al. [
17] considered 2D and 3D VOF models to compute the valve opening process in pressure pipelines, and the results were consistent with those of the 1D calculation. Simultaneously, the results verified the advantages of the VOF model in the simulation of a gas–liquid two phase flow. Jiang et al. [
18] analyzed a multi-valve protection of the water hammer in a long distance pipeline based on a 1D-MOC method in the transient process for a water supply project. Dutta et al. [
19] studied the influence of Reynolds number on flow separation and reattachment in 90° pipe blends, and the flow separation could be clearly visualized for bend with a low curvature ratio, as well as the secondary motion, which was clearly induced by the movement of fluid from the inner to outer wall of the bend, leading to flow separation. Modesto et al. [
20] studied a pump as turbines (PATs) operating state in water networks from the perspective of the control valve maneuver and over speed effect, and their research characterizes the water hammer phenomenon in the design of PAT systems, emphasizing the transient events that can occur during a normal operation. Jing et al. [
21] studied the pressure variations during transients in pipelines and clarified the effects of an unsteady wall shear stress on the propagation of pressure waves through the analytical and experimental method. For PSH stations, ball valves are widely used, which play an important role in controlling runaway accidents, thus some studies involving ball valve movement were reported. Wen et al. [
22] performed steady calculations in different openings of the ball valve and simulated the water hammer led by linear closing of the ball valve by both 3D-CFD and 1D-MOC; they found that the unstable flow fields within the valve are essential causes of pressure and force fluctuations. Ferreira et al. [
23] investigated the behavior of ball valves under steady and unsteady conditions through the experimental method, and found that the valve geometry, closure percentage, and flow regime have the largest effect on the response of the valve under the steady condition, while the valve effective closure time and pipe length would affect the unsteady characteristics of the ball valve. Martins et al. [
24] analyzed the hydraulic transient flows in pressurized pipes using the CFD method, and the calculated velocity profiles showed two regions when the valve closure was described by a hyperbolic time-domain function.
The above studies have achieved good results in the flow simulation of diversion pipelines during the transient process, but they have not dealt with the spiral flow phenomenon in a pipeline when the load rejection process occurred. Swirl flows have a wide range of applications in various engineering areas such as chemical and mechanical mixing and separating devices, chemical reactors, combustion chambers, turbo machinery, rocketry, fusion reactors, and pollution control devices [
25,
26,
27,
28]. However, public literature rarely reported the study on the spiral flow in the diversion pipeline during the transient process. In addition, the attenuation mechanism of the water hammer pressure wave in a pipeline is also the focus of some of the literature mentioned above. The attenuation rate of the pressure wave measured by the 1D method is always slower than that of the experimental results, and a good agreement cannot be achieved. There are also some scholars who use some improved models to measure the pressure wave to explain the reason that the 1D calculation results do not agree with the experimental results [
29]. Compared with the traditional methods, this study provides further access by considering the influence of the self-excited spiral flow on the pressure wave attenuation. On the basis of the previous research on the pipeline transient process, a 3D numerical simulation method with a VOF two-phase flow model was carried out to study and analyze the 3D internal flow characteristics of the water diversion system with an impedance surge tank during the load rejection transient process of the PSH station, and the numerical data were compared to the results from 1D-MOC.