## 1 Introduction  
A high-speed centrifugal pump with a fully sealed structure has the advantages of being small, free of external leakage, and free of any rolling bearings and fans so that it does not need lubricating oil and has no pollution. The inner leakage passage of a pump with a fully sealed structure includes the tip clearance and the hub clearance. The hub clearance, the lubrication passage of the bearing, and the clearance between the stator and the rotor of the built-in motor constitute the internal flow channel. Hub leakage flows through the internal flow channel as the internal flow to lubricate the sliding bearing and cools the motor. This not only solves the problems of cooling the motor and preventing sliding bearing failures caused by friction and the accumulated heat in the lubricant fluid, but also effectively increases the upper speed limit, improving the working performance of the pump [1, 2]. Moreover, due to the changes in the liquid film and displacement of the sliding bearing in the working process, the leakage channel is dynamic [3]. The internal flow increases the tip leakage and complicates the flow field, which generally affect the performance of the pump. Many achievements have been made in the numerical simulation of pump characteristics. [PERSON] et al. [4] conducted an unsteady numerical simulation and a performance test of a centrifugal pump and analyzed the development of the tip leakage vortex and the principles affecting the performance of the pump. Through numerical simulation research, [PERSON] et al. [5] found that the tip leakage channel accounted for a relatively small proportion compared with the mainstream area, but the impact of tip leakage on the pump performance could not be ignored. Additionally, the increase in the impeller tip clearance caused additional losses. Through visual experiments, [PERSON] found that increasing the tip clearance will reduce the pump performance [6]. Through numerical simulation research, [PERSON] et al. [7] found that the leakage vortex formed by tip leakage is an important factor interfering with the internal flow of the impeller. [PERSON] et al. verified though visual experiments the findings of a numerical simulation study (tip leakage affects the pump performance by destroying the flow field and the degree of influence is related to the tip clearance thickness) [8]. Through numerical simulation and experimental research, [PERSON] found that tip leakage will promote the development of a leakage vortex and the separation of the vortex, based on which they proposed a power function law to describe the intensity of the primary tip leakage vortex core along the trajectory [9; 10; 11]. [PERSON] et al. [12; 13] performed a numerical simulation of the entire passage of a centrifugal pump and analyzed the frequency spectrum characteristics, the external characteristics of the tip leakage vortex, and the structural characteristics and their influence on the pump. Through a numerical simulation, [PERSON] et al. found that the existence of tip leakage and hub leakage caused a loss of flow and promoted the growth of a vortex in the pump [14]. [PERSON] et al. [15] numerically simulated the three-dimensional flow field of a centrifugal pump considering tip leakage and hub leakage and put forward structural design suggestions by comparing the influence of structural parameters on the performance of the centrifugal pump. According to the above analysis, the internal leakage in the centrifugal pump affects the pump performance by interfering with the flow field distribution. The numerical simulation of centrifugal pump performance in the above-mentioned studies was used to analyze the influence of internal leakage on the performance of the pump. Most of the studies only considered tip leakage and a few considered hub leakage. However, all of them ignored the influence of the internal flow in the bearing lubrication and motor cooling channel.