1. Introduction
To date, hydropower has a history of more than 100 years and becomes a major component of the power industry. It promotes the process of social history and makes great contributions to the progress of world civilization. As the production front of the power system, hydropower station plays an important role in the environment of large-scale development and use of electricity. In recent years, China’s achievements and experience in hydropower development have been highly and widely praised by the international community. The construction of large and medium-sized hydropower stations alleviates the employment pressure in the surrounding areas, and increases infrastructure construction such as transportation. Moreover, it greatly improves the financial revenues of local governments and the power generation capacities of hydropower stations along rivers. In addition to generating electricity, some hydropower stations can regulate their own reservoir capacity and control the water flow of upstream and downstream rivers. They also bear part of the flood control pressure while increasing the power generation to ensure flood control safety. Today, in the context of striving to reach the peak of carbon dioxide emissions by 2030 and to achieve carbon neutrality by 2060, China’s energy structure will accelerate its transformation to a low-carbon and clean direction. The proportion of renewable energy power generation represented by hydropower will further increase.
With more generating capacity undertaken by hydropower stations, the number and scale of giant Francis turbine units are increasing gradually. The size and weight of the components of giant units are often large, and the internal structure and processing technology are complex. In particular, the runner blades are vulnerable to the dynamic loads generated by pressure pulsation and various mechanical disturbances, which lead to the vibration and cracking of the blades. Therefore, the assembly accuracy and quality of the unit are crucial for the safe and reliable operation of the unit after it is put into production. The Francis turbine includes a spiral case, stay vane, guide vane, runner, head cover, pressure balance pipe, draft tube, stay ring, and other structures. Given the large size of the giant Francis turbine, the leakage and volume loss of upper crown clearance, lower band clearance, and labyrinth ring caused by the gap between the runner and fixed parts are also large [
1,
2]. The pressure pulsation caused by these fluids is one of the main reasons affecting stable operation. The pressure pulsation of the Francis turbine refers to the alternating random change of water pressure around its average value in the flow passage, which contributes to the vibration of the hydraulic turbine generator unit [
3]. So far, most scholars have mainly studied the vaneless area, runner, draft tube, and leakage water through the combination of numerical simulation [
4,
5] and test [
6]. Through their characteristic frequency and amplitude, they can have a deeper understanding of the flow characteristics and vibration mechanism of the internal flow field [
7,
8,
9]. Trivedi [
10] studied the vaneless area of the turbine and pointed out that the frequency of pressure fluctuation in the rotating and stationary passage is mainly related to the number of guide vanes and runner blades and the frequency of rotation. The two passages are mainly affected by the runner and the guide vanes respectively. Under low load conditions, vortex ropes will appear in the draft tube. Arpe [
11] and others found that the frequency of the vortex rope in the draft tube is mainly 0.2–0.4 times the rotational frequency by studying the pressure pulsation of the straight and elbow section of the draft tube. There will also be the frequency of the vortex rope in the vaneless area, indicating that the vortex rope also has an impact on the flow characteristics in the vaneless area. A large number of studies [
12,
13] show that pressure pulsation will generate noise and vibration, which seriously threatens the stable operation of the unit. Through CFD simulation, Liang Wuke [
14] compared the full-flow passage simulation with and without cavities and found that the cavity has a great influence on the runner stress. So cavities should not be ignored in the study of hydraulic axial force. As a structure to reduce leakage and increase efficiency, Sun Huifang [
15] and others found that the farther the labyrinth ring is away from the central axis, the greater the influence on the axial water force. However, although the accuracy of the labyrinth ring is improved, the calculation cost is increased. The pressure balance pipe connects the clearance with the draft tube to balance the water pressure in the clearance, so as to reduce the impact on the hydraulic axial force and the load on the force bearing. Qu Boxing [
16] analyzed the structure of the pressure balance pipe and the cause of water leakage through examples and proposed improvement measures.
The giant Francis turbine is easy to cause large hydraulic axial force, and its safe, efficient, and stable operation affects the entire power supply system significantly. As a result, the design and selection of runners and other structures are very important. The hydraulic axial force of the turbine refers to the axial component force of water flow acting on the runner, mainly including the axial force on the surface of the runner hub, shroud, blade, upper crown clearance, and lower ring clearance [
17]. The calculation methods of hydraulic axial force are mainly theoretical formula [
18], numerical simulation [
19], and experimental measurement [
20]. Nevertheless, the traditional methods generally rely on experience and assumptions [
21,
22], and only consider the constant value, which cannot show the pressure pulsation and the pulsation of axial hydraulic force. Consequently, sometimes there is a large deviation. After the continuous improvement of the calculation method, the accuracy of the hydraulic axial force calculation results has been significantly improved [
23]. Compared with the prototype test measurement, Li Haoliang [
19] and JI Xingying [
24] proposed a more efficient and accurate axial force calculation method based on numerical simulation calculation.
The hydraulic axial force of the hydraulic turbine has a great influence on the structural design and stable operation of the unit. Too much downward will cause overload and damage to the force bearing [
25]. Too much upward will lead to serious turbine lifting and severe vibration [
26], which will seriously affect the operation of the hydropower station. A large number of studies have shown that the hydraulic axial force is related to the pressure distribution [
27,
28,
29,
30]. Xiao Ruofu [
31] and others analyzed the dynamic stress of the Francis turbine based on fluid–structure coupling and found that the dynamic stress resulting from the hydraulic force is one of the main factors causing the fatigue crack of the runner blade. Li Xiangyang [
32] considered that the pressure difference between the upper crown clearance and the runner’s internal passage is the main factor leading to the axial force, which is mainly induced by the flow pattern in the runner. For pumped storage units with frequent startup and shutdown, when the input force of the pump mode gradually decreases, the hydraulic axial force will suddenly change and have an impact on the stable operation of the unit [
33,
34]. When the pump and turbine modes are switched, the hydraulic axial force will have a peak value [
35]. To reduce the harm of the axial force, sealing device, pressure-reducing plate, and drain hole [
36], the pressure balance pipe and other equipment [
37] are generally set in the actual project.
The sealing device is designed to reduce leakage since the hydraulic axial force increases with the raise of flow and head [
38]. The pressure-reducing plate is fixed on the top cover of the turbine by using rib plates and reduces the volume of rotating water flow in the clearance [
39] to reduce the axial force of the turbine. The pressure balance pipe uses the pressure difference between the clearance and the draft tube to discharge the leakage water in the clearance to the draft tube. Compared with other methods, the pressure balance pipe reduces the pressure in the clearance and is used more and more widely in practical projects.
To date, most of the literature studies lack research on the hydraulic axial force of Francis turbines containing clearance and pressure balance pipes [
40], especially for the prototype units of giant hydraulic turbines with the larger size, higher requirements on operation stability and installation accuracy. Hence, the flow pattern in the runner and clearance passage and the trend of the hydraulic axial force of each surface of the runner with the different axial installation deviations of the runner under the rated working conditions are calculated. The influence of uncertain factors such as the shape of the runner passage on the hydraulic force is studied, so as to better understand the characteristics of the internal force of the turbine and provide guidance for the design, manufacturing, and installation.
In this study, the influences of the axial installation deviation of the runner on the hydraulic axial force of the 1000 MW Francis turbine unit are investigated.
5. Conclusions
As the installation position of the runner decreases, the flow pattern distribution and hydraulic axial force in the runner passage change little. The axial force on the outer surface of the upper crown gradually increases, while the total hydraulic axial force and the hydraulic axial force on the outer surface of the lower band gradually decline. As the runner continues to drop, the axial force will gradually stabilize.
In the upper crown clearance and lower band clearance, the flow near the outer surface of the upper crown and the lower band has a large rotation speed and a large centrifugal force. The flow near the fixed wall rotates at a low speed and has a small rotation speed and a small centrifugal force. The difference between these two forces causes vortices in the cavity, which determines the momentum exchange between water particles with different rotating speeds in the flow field and the friction between the water particles and the fixed wall. Thus, the velocity and pressure distribution are affected, and then the hydraulic force is influenced.
The increase of axial installation dropping of the runner has little effect on the streamlined distribution of clearance, but the speed and pressure will change. The pressure and velocity in the upper crown cavity will decrease. The velocity at the lower band inlet will increase, and the pressure will decline. The leakage flow of the clearance is also affected to some extent, but it tends to be stable as the dropping distance increases to a certain value.