# Hydraulic Vibration and Possible Exciting Sources Analysis in a Hydropower System
## 1 Introduction  
Nowadays, the increasing global demands for electricity and environmental protections are gradually bringing about the transformation of energy structure such that clean and renewable energy covers an increasing proportion of energy consumption [1]. In this aspect, hydropower plays an irreplaceable role in the clean and renewable energy system, and attracts much attention [2]. Hydraulic turbines are designed for working at the rated head and rated discharge, which is defined as the best efficiency point (BEP), while the current tendency for hydropower plants is that they are undertaking increasing power frequency regulation tasks in the electric grid, and turbines are required to work at off-design conditions more than before [3]. Vibrations exist in various fields, including hydropower stations, and vibration mitigations have been extensively investigated by researchers [4, 5]. Recently, more hydraulic vibration phenomena in hydropower systems have been reported accompanied by obvious pressure oscillations along with their hydro-mechanical systems, and even severe accidents, such as local structural damages and power swings, have happened [6]. When turbines operate under off-design conditions, pressure fluctuations due to rotor-stator interaction (RSI), rotating stall, vortex rope, and other flow instabilities might beinduced, and accompanying vibration phenomena may be generated [7; 8]. Numerous studies, including model experimental tests and numerical simulations, have been conducted to investigate the pressure fluctuations under various off-design conditions. With an overall literature review, it was pointed out that pressure fluctuations in the turbine caused by transient processes would result in fatigue development in the runner, and then shorten the life span of the runner [9]. Based on CFD simulations and validated by experiments, rotor-stator interactions (RSI) were reported to be the primary cause of pressure fluctuation in the vaneless space, and the geometric and operating parameters of the unit were the main affecting factors [10; 11; 12]. Moreover, vortex rope in the draft tube was an unavoidable problem that formed under off-design conditions, and this would cause low-frequency but high-amplitude pressure fluctuations in the draft tube that propagate upstream and downstream [13; 14]. [PERSON] et al. discovered that the Thoma number influenced not only pressure fluctuation amplitude but also the distribution of the frequency components of pressure fluctuation in the draft tube [15]. [PERSON] et al. discovered that there is a close relation between vortex rope and cavitation in the draft, such tube that the cavitation increases the vortex production as well as the pressure fluctuation frequency induced by vortex rope [16]. Apart from traditional hydraulic turbines, for a pump-turbine operating under off-design conditions, especially in S-shaped regions, pressure fluctuation in the flow passage is also attracting increasing attention [17; 18; 19]. Through numerical simulations of a pump-turbine working in an off-design way, it has been reported that the low-frequency pressure fluctuations originate from the rotation of vortices in the draft tube; further, the number of runner blades had an impact on the dominant frequency of pressure fluctuations in the draft tube [20; 21]. The vibration affected the security of the hydropower station, and various strategies used to suppress vortex rope oscillation in the turbine flow passage have been explored [22; 23]. In view of the pressure fluctuation caused by the vortex rope under off-design conditions, a novel passive control method using an adjustable diaphragm is introduced in decelerating swirling flow; further, the water injection method was proposed to mitigate the pressure fluctuation and change the velocity field in the flow passage, and correlation between the water jet discharge and vortex rope has been investigated [24; 25].