## 1 Introduction  
Centrifugal pumps, as the core components of fluid transportation systems in industrial production, are widely used in aerospace, petrochemicals and military ships [1]. Unstable flow in centrifugal pumps has an important impact on their efficiency and stability. In industrial production, centrifugal pumps frequently work under off-design conditions to meet the work requirements. Under part-load and overload conditions, the flow in centrifugal pumps is extremely unstable [2; 3]. Unstable flow structures, such as return vortex at the tongue, shedding vortex at the blade trailing edge and return vortex at the inlet or outlet, will occur in centrifugal pumps when they are operated under part-load conditions [4; 5; 6]. The rotor-stator interaction at the tongue and the shedding vortex at the blade trailing edge are the main causes of unstable pressure pulsation in centrifugal pumps [7; 8]. The internal flow of centrifugal pumps is extremely complicated and is accompanied by a 3D transient unstable strong turbulent motion that is difficult to capture. With the rapid development of high-performance computing equipment and technology, numerical simulation methods based on computational fluid dynamics have been widely used to study the unstable flow characteristics in fluid machinery [9; 10]. A jet wake structure is the common unstable flow structure in a centrifugal pump, which easily causes uneven pressure and velocity distribution between the impeller outlet and the volute,thereby increasing the strength of the rotor-stator interaction and unstable pressure pulsation. [PERSON] et al. [11] studied the pressure pulsation characteristics in guide vanes. They showed that the outlet angle of the impeller blade has a significant effect on the jet wake structure and pressure pulsation in guide vanes. [PERSON] et al. [12] experimentally measured the dynamic pressure pulsation signal at the impeller outlet and found that the pressure pulsation amplitude near the wake vortex is large on the basis of numerical simulation results. [PERSON] et al. [13] modified the impeller and the solute to study the effects of different modification schemes on the energy loss and pressure pulsation intensity of centrifugal pumps. The results show that the splitter blade and the double volute structure can effectively improve the unstable pressure pulsation at the tongue and the wake vortex structure at the impeller outlet. [PERSON] et al. [14] effectively reduced the contact between the wake vortex and the tongue by changing the inclination of the volute outlet, thereby reducing the pressure pulsation at the tongue. [PERSON] et al. [15] experimentally monitored the velocity field distribution of the jet wake structure at the impeller outlet and found that unsteady pressure pulsations are caused by the interaction of the vortex structure between the pressure and blade suction surfaces. Impellers are the main flow and energy conversion components of centrifugal pumps. Changes in different blade parameters, such as blade outlet angle, blade inlet angle, blade wrap angle and blade trailing edge shape, will affect the performance of centrifugal pump and its internal flow. In recent years, domestic and foreign scholars have studied many blade structure modification schemes to improve the performance of centrifugal pumps and reduce unstable flow. [PERSON] et al. [16] studied the influences of the blade outlet angle on internal flow, and the results show that the pressure at the tongue increases with the increase in blade outlet angle at a small flow rate, whereas the velocity gradient at the tongue increases with the outlet angle at a large flow rate. [PERSON] et al. [17] investigated the influences of blade outlet angle on the recirculation characteristics of centrifugal pump. The research results showed that the reflow intensity in impeller wall increases with the increase in blade outlet angle. [PERSON] et al.