# Research of Modal Analysis for Impeller of Reactor Coolant Pump
## 1 Introduction  
The reactor coolant pump (RCP) drives cooling water circulation in the nuclear power plant [1], which brings the heat of the nuclear reactor to the steam generator, thereby producing steam to generate electricity. The RCP impeller rotates at high speed in a high-temperature, high-pressure and strong-radiation environment [2; 3]. To ensure the long-term operation of the nuclear power plant, hydraulic resonance should be avoided [4]. However, it is challenging to accurately calculate natural frequencies of the rotating RCP impeller in high-temperature liquid [5]. Therefore, it is necessary to figure out the impact of different factors and propose a modal analysis method for the underwater rotating impeller.  
The natural frequencies of solids in liquid are different from those in the air [6]. Due to added mass, wet modal natural frequencies of solids are lower than dry modal natural frequencies [7] (The state of a solid in the air is called dry modal, and the state of a solid in water is called wet modal). Besides, rotating centrifugal force and pre-stress also have an influence on natural frequencies. [PERSON]. [8] performed modal tests on rotors at different speeds and discovered that centrifugal force increases natural frequencies of rotors. [PERSON] et al. [9] carried out dynamic tests on five pre-stressedconcrete beams, and found that natural frequencies of those beams increase in step with pre-stress force. In summary, added mass, centrifugal force and pre-stress all can affect natural frequencies of the structure.  
Some researchers have studied the vibration modal of scale RCP impeller. For example, [PERSON]. [10] measured natural frequencies of a wet modal static impeller and found the impact of boundary conditions. [PERSON] et al. [11] analyzed the damping ratio of the underwater static impeller and calculated the dynamic magnification coefficient. However, they only took the influence of added mass into account, while the rotating RCP impeller under operation condition can also be subject to centrifugal force and hydraulic load. Therefore, their studies towards the modal analysis of the RCP impeller are insufficient. The influence of added mass, centrifugal force and hydraulic load on natural frequencies of the rotating impeller should be counted.  
This study analyzed the modal of a scale RCP impeller by theory, and then compared natural vibration modes of the impeller under different conditions by experiment and simulation. An underwater vibration test system was innovatively designed in this research. Through it, the vibrant signals of both static and rotating blades can be brought out, so that natural frequencies under both static and rotating conditions can be measured. Then a simulation was performed synchronously with the test bench to collect more data. According to the comparison among modal data in different environments, it is found that both added mass and hydraulic load have a great influence on natural frequencies of the RCP impeller, but the impact of centrifugal force on them can be ignored. Finally, hydraulic resonance analysis of an RCP impeller was carried out, and a solution of cutting inlet edges of blades was implemented to avoid resonance of the impeller.